620 results sorted by ID
Possible spell-corrected query: Public-key algorithm
A New Cryptographic Algorithm
Ali Mahdoum
Cryptographic protocols
The advent of quantum computing technology will compromise many of the current cryptographic algorithms, especially public-key cryptography, which is widely used to protect digital information. Most algorithms on which we depend are used worldwide in components of many different communications, processing, and storage systems. Once access to practical quantum computers becomes available, all public-key algorithms and associated protocols will be vulnerable to criminals, competitors, and...
An Efficient All-to-All GCD Algorithm for Low Entropy RSA Key Factorization
Elijah Pelofske
Attacks and cryptanalysis
RSA is an incredibly successful and useful asymmetric encryption algorithm. One of the types of implementation flaws in RSA is low entropy of the key generation, specifically the prime number creation stage. This can occur due to flawed usage of random prime number generator libraries, or on computers where there is a lack of a source of external entropy. These implementation flaws result in some RSA keys sharing prime factors, which means that the full factorization of the public modulus...
Quantum-Safe Account Recovery for WebAuthn
Douglas Stebila, Spencer Wilson
Cryptographic protocols
WebAuthn is a passwordless authentication protocol which allows users to authenticate to online services using public-key cryptography. Users prove their identity by signing a challenge with a private key, which is stored on a device such as a cell phone or a USB security token. This approach avoids many of the common security problems with password-based authentication.
WebAuthn's reliance on proof-of-possession leads to a usability issue, however: a user who loses access to their...
2024/652
Last updated: 2024-05-08
Compact and Secure Zero-Knowledge Proofs for Quantum-Resistant Cryptography from Modular Lattice Innovations
Samuel Lavery
Public-key cryptography
This paper presents a comprehensive security analysis of the Adh zero-knowledge proof system, a novel lattice-based, quantum-resistant proof of possession system. The Adh system offers compact key and proof sizes, making it suitable for real-world digital signature and public key agreement protocols. We explore its security by reducing it to the hardness of the Module-ISIS problem and introduce three new variants: Module-ISIS+, Module-ISIS*, and Module-ISIS**. These constructions enhance...
On Proving Pairings
Andrija Novakovic, Liam Eagen
Cryptographic protocols
In this paper we explore efficient ways to prove correctness of elliptic curve pairing relations. Pairing-based cryptographic protocols such as the Groth16 and Plonk SNARKs and the BLS signature scheme are used extensively in public blockchains such as Ethereum due in large part to their small size. However the relatively high cost of pairing computation remains a practical problem for many use cases such as verification ``in circuit" inside a SNARK. This naturally arises in recursive SNARK...
The Case of Small Prime Numbers Versus the Okamoto-Uchiyama Cryptosystem
George Teseleanu
Public-key cryptography
In this paper we study the effect of using small prime numbers within the Okamoto-Uchiyama public key encryption scheme. We introduce two novel versions and prove their security. Then we show how to choose the system's parameters such that the security results hold. Moreover, we provide a practical comparison between the cryptographic algorithms we introduced and the original Okamoto-Uchiyama cryptosystem.
Pairing Optimizations for Isogeny-based Cryptosystems
Shiping Cai, Kaizhan Lin, Chang-An Zhao
Implementation
In isogeny-based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public-key validation and torsion basis generation. However, in most isogeny-based protocols, the performance of pairing computations is unsatisfactory due to the high computational cost of the Miller function. Reducing the computational expense of the Miller function is crucial for enhancing the overall performance of pairing computations in isogeny-based...
Efficient Permutation Correlations and Batched Random Access for Two-Party Computation
Stanislav Peceny, Srinivasan Raghuraman, Peter Rindal, Harshal Shah
Cryptographic protocols
In this work we define the notion of a permutation correlation $(\pi,A,B,C)$ s.t. $\pi(A)=B+C$ for a random permutation $\pi$ of $n$ elements and vectors $A,B,C\in \mathbb{F}^n$. We demonstrate the utility of this correlation for a wide range of applications. The correlation can be derandomized to obliviously shuffle a secret-shared list, permute a secret-shared list by a secret-shared permutation, and more. Similar techniques have emerged as a popular building block for the honest majority...
The Insecurity of SHA2 under the Differential Fault Characteristic of Boolean Functions
Weiqiong Cao, Hua Chen, Hongsong Shi, Haoyuan Li, Jian Wang, Jingyi Feng
Attacks and cryptanalysis
SHA2 has been widely adopted across various traditional public-key cryptosystems, post-quantum cryptography, personal identification, and network communication protocols, etc. Hence, ensuring the robust security of SHA2 is of critical importance. There have been several differential fault attacks based on random word faults targeting SHA1 and SHACAL-2. However, extending such random word-based fault attacks to SHA2 proves significantly more difficult due to the heightened complexity of the...
Re-Randomized FROST
Conrado P. L. Gouvea, Chelsea Komlo
We define a (small) augmentation to the FROST threshold signature scheme that additionally allows for re-randomizable public and secret keys. We build upon the notion of re-randomizable keys in the literature, but tailor this capability when the signing key is secret-shared among a set of mutually trusted parties. We do not make any changes to the plain FROST protocol, but instead define additional algorithms to allow for randomization of the threshold public key and participant’s individual...
Recent Progress in Quantum Computing Relevant to Internet Security
Hilarie Orman
Attacks and cryptanalysis
Quantum computers at some future date might be able
to factor large numbers, and this poses a threat to some public key
and key exchange systems in use today. This overview of recent
progress in devising quantum algorithms and building quantum computing devices is meant to help technologists understand the difficult problems that quantum engineers are working on, where advances have been made, and how those things affect estimates of if and when large scale quantum computation might happen.
Key-Recovery Attack on a Public-Key Encryption Related to Planted Clique
Caicai Chen, Chris Jones
Public-key cryptography
Hudoba proposed a public key encryption (PKE) scheme and conjectured its security to be based on the Planted Clique problem. In this note, we show that this scheme is not secure. We do so by devising an efficient algorithm for the even neighbor independent set problem proposed by Hudoba. This leaves open the possibility of building PKE based on Planted Clique.
An Efficient Adaptive Attack Against FESTA
Guoqing Zhou, Maozhi Xu
Attacks and cryptanalysis
At EUROCRYPT’23, Castryck and Decru, Maino et al., and Robert present efficient attacks against supersingular isogeny Diffie-Hellman key exchange protocol (SIDH). Drawing inspiration from these attacks, Andrea Basso, Luciano Maino, and Giacomo Pope introduce FESTA, an isogeny-based trapdoor function, along with a corresponding IND-CCA secure public key encryption (PKE) protocol at ASIACRYPT’23. FESTA incorporates either a diagonal or circulant matrix into the secret key to mask torsion...
2024/208
Last updated: 2024-05-08
Asymmetric Cryptography from Number Theoretic Transformations
Samuel Lavery
Public-key cryptography
In this work, we introduce a family of asymmetric cryptographic functions based on dynamic number theoretic transformations with multiple rounds of modular arithmetic to enhance diffusion and difficulty of inversion. This function acts as a basic cryptographic building block for a novel communication-efficient zero-knowledge crypto-system. The system as defined exhibits partial homomorphism and behaves as an additive positive accumulator. By using a novel technique to constructively embed...
A Novel Power Analysis Attack against CRYSTALS-Dilithium Implementation
Yong Liu, Yuejun Liu, Yongbin Zhou, Yiwen Gao, Zehua Qiao, Huaxin Wang
Attacks and cryptanalysis
Post-Quantum Cryptography (PQC) was proposed due to the potential threats quantum computer attacks against conventional public key cryptosystems, and four PQC algorithms besides CRYSTALS-Dilithium (Dilithium for short) have so far been selected for NIST standardization. However, the selected algorithms are still vulnerable to side-channel attacks in practice, and their physical security need to be further evaluated.
This study introduces two efficient power analysis attacks, the optimized...
Enabling PERK on Resource-Constrained Devices
Slim Bettaieb, Loïc Bidoux, Alessandro Budroni, Marco Palumbi, Lucas Pandolfo Perin
Implementation
PERK is a digital signature scheme submitted to the recent NIST Post-Quantum Cryptography Standardization Process for Additional Digital Signature Schemes. For NIST security level I, PERK features sizes ranging from 6kB to 8.5kB, encompassing both the signature and public key, depending on the parameter set.
Given its inherent characteristics, PERK's signing and verification algorithms involve the computation of numerous large objects, resulting in substantial stack-memory consumption...
A provably masked implementation of BIKE Key Encapsulation Mechanism
Loïc Demange, Mélissa Rossi
Public-key cryptography
BIKE is a post-quantum key encapsulation mechanism (KEM) selected for the 4th round of the NIST’s standardization campaign. It relies on the hardness of the syndrome decoding problem for quasi-cyclic codes and on the indistinguishability of the public key from a random element, and provides the most competitive performance among round 4 candidates, which makes it relevant for future real-world use cases. Analyzing its side-channel resistance has been highly encouraged by the community and...
FEASE: Fast and Expressive Asymmetric Searchable Encryption
Long Meng, Liqun Chen, Yangguang Tian, Mark Manulis, Suhui Liu
Public-key cryptography
Asymmetric Searchable Encryption (ASE) is a promising cryptographic mechanism that enables a semi-trusted cloud server to perform keyword searches over encrypted data for users. To be useful, an ASE scheme must support expressive search queries, which are expressed as conjunction, disjunction, or any Boolean formulas. In this paper, we propose a fast and expressive ASE scheme that is adaptively secure, called FEASE. It requires only 3 pairing operations for searching any conjunctive set of...
Fiat-Shamir Goes Tropical
Rémi Géraud-Stewart, David Naccache, Ofer Yifrach-Stav
Cryptographic protocols
In a recent ePrint, Brown and Monico propose new attacks on the tropical signature scheme of Chen, Grigoriev and Shpilrain. This note provides a new countermeasures against those attacks. Thereby, we (temporarily?) shift the fire from the signature algorithm to redirect attacks on the key and on tropical polynomial factorization.
Single-Trace Side-Channel Attacks on CRYSTALS-Dilithium: Myth or Reality?
Ruize Wang, Kalle Ngo, Joel Gärtner, Elena Dubrova
Attacks and cryptanalysis
We present a side-channel attack on CRYSTALS-Dilithium, a post-quantum secure digital signature scheme, with two variants of post-processing. The side-channel attack exploits information leakage in the secret key unpacking procedure of the signing algorithm to recover the coefficients of the polynomials in the secret key vectors ${\bf s}_1$ and ${\bf s}_2$ by profiled deep learning-assisted power analysis. In the first variant, one half of the coefficients of ${\bf s}_1$ and ${\bf s}_2$ is...
Hardness of Range Avoidance and Remote Point for Restricted Circuits via Cryptography
Yilei Chen, Jiatu Li
Foundations
A recent line of research has introduced a systematic approach to explore the complexity of explicit construction problems through the use of meta problems, namely, the range avoidance problem (abbrev. $\textsf{Avoid}$) and the remote point problem (abbrev. $\textsf{RPP}$). The upper and lower bounds for these meta problems provide a unified perspective on the complexity of specific explicit construction problems that were previously studied independently. An interesting question largely...
Sender-Anamorphic Encryption Reformulated: Achieving Robust and Generic Constructions
Yi Wang, Rongmao Chen, Xinyi Huang, Moti Yung
Public-key cryptography
Motivated by the violation of two fundamental assumptions in secure communication - receiver-privacy and sender-freedom - by a certain entity referred to as ``the dictator'', Persiano et al. introduced the concept of Anamorphic Encryption (AME) for public key cryptosystems (EUROCRYPT 2022). Specifically, they presented receiver/sender-AME, directly tailored to scenarios where receiver privacy and sender freedom assumptions are compromised, respectively. In receiver-AME, entities share a...
PQC-NN: Post-Quantum Cryptography Neural Network
Abel C. H. Chen
Applications
In recent years, quantum computers and Shor’s quantum algorithm have been able to effectively solve NP (Non-deterministic Polynomial-time) problems such as prime factorization and discrete logarithm problems, posing a threat to current mainstream asymmetric cryptography, including RSA and Elliptic Curve Cryptography (ECC). As a result, the National Institute of Standards and Technology (NIST) in the United States call for Post-Quantum Cryptography (PQC) methods that include lattice-based...
Accelerating Polynomial Multiplication for RLWE using Pipelined FFT
Neil Thanawala, Hamid Nejatollahi, Nikil Dutt
Implementation
The evolution of quantum algorithms threatens to break public key cryptography in polynomial time. The development of quantum-resistant algorithms for the post-quantum era has seen a significant growth in the field of
post quantum cryptography (PQC). Polynomial multiplication is the core of
Ring Learning with Error (RLWE) lattice based cryptography (LBC) which
is one of the most promising PQC candidates. In this work, we present the
design of fast and energy-efficient pipelined Number...
Homomorphic Polynomial Public Key Cryptography for Quantum-secure Digital Signature
Randy Kuang, Maria Perepechaenko, Mahmoud Sayed, Dafu Lou
Cryptographic protocols
In their 2022 study, Kuang et al. introduced the Multivariable Polynomial Public Key (MPPK) cryptography, a quantum-safe public key cryptosystem leveraging the mutual inversion relationship between multiplication and division. MPPK employs multiplication for key pair construction and division for decryption, generating public multivariate polynomials. Kuang and Perepechaenko expanded the cryptosystem into the Homomorphic Polynomial Public Key (HPPK), transforming product polynomials over...
A Statistical Verification Method of Random Permutations for Hiding Countermeasure Against Side-Channel Attacks
Jong-Yeon Park, Jang-Won Ju, Wonil Lee, Bo-Gyeong Kang, Yasuyuki Kachi, Kouichi Sakurai
Foundations
As NIST is putting the final touches on the standardization of PQC (Post Quantum Cryptography) public key algorithms, it is a racing certainty that peskier cryptographic attacks undeterred by those new PQC algorithms will surface. Such a trend in turn will prompt more follow-up studies of attacks and countermeasures. As things stand, from the attackers’ perspective, one viable form of attack that can be implemented thereupon is the so-called “side-channel attack”. Two best-known...
Towards the Impossibility of Quantum Public Key Encryption with Classical Keys from One-Way Functions
Samuel Bouaziz--Ermann, Alex B. Grilo, Damien Vergnaud, Quoc-Huy Vu
Foundations
There has been a recent interest in proposing quantum protocols whose security relies on weaker computational assumptions than their classical counterparts. Importantly to our work, it has been recently shown that public-key encryption (PKE) from one-way functions (OWF) is possible if we consider quantum public keys. Notice that we do not expect classical PKE from OWF given the impossibility results of Impagliazzo and Rudich (STOC'89).
However, the distribution of quantum public keys is a...
Lattice-based Public Key Encryption with Authorized Keyword Search: Construction, Implementation, and Applications
Shiyuan Xu, Yibo Cao, Xue Chen, Yu Guo, Yuer Yang, Fangda Guo, Siu-Ming Yiu
Public-key cryptography
Public key encryption with keyword search (PEKS), formalized by Boneh et al. [EUROCRYPT' 04], enables secure searching for specific keywords in the ciphertext. Nevertheless, in certain scenarios, varying user tiers are granted disparate data searching privileges, and administrators need to restrict the searchability of ciphertexts to select users exclusively. To address this concern, Jiang et al. [ACISP' 16] devised a variant of PEKS, namely public key encryption with authorized keyword...
Traitor Tracing Revisited: New Attackers, Stronger Security Model and New Construction
Xu An Wang, Lunhai Pan, Hao Liu, Xiaoyuan Yang
Public-key cryptography
In Crypto 94, Chor, Fiat, and Naor first introduced the traitor tracing (TT) systems, which aim at helping content distributors identify pirates. Since its introduction, many traitor tracing schemes have been proposed. However, we observe until now almost all the traitor tracing systems using probabilistic public key (and secret key) encryption as the the content distribution algorithm, they do not consider this basic fact: the malicious encrypter can plant some trapdoor in the randomness...
SPA-GPT: General Pulse Tailor for Simple Power Analysis Based on Reinforcement Learning
Ziyu Wang, Yaoling Ding, An Wang, Yuwei Zhang, Congming Wei, Shaofei Sun, Liehuang Zhu
Attacks and cryptanalysis
Power analysis of public-key algorithms is a well-known approach in the community of side-channel analysis. We usually classify operations based on the differences in power traces produced by different basic operations (such as modular exponentiation) to recover secret information like private keys. The more accurate the segmentation of power traces, the higher the efficiency of their classification. There exist two commonly used methods: one is equidistant segmentation, which requires a...
Optimized Quantum Implementation of SEED
Yujin Oh, Kyungbae Jang, Yujin Yang, Hwajeong Seo
Implementation
With the advancement of quantum computers, it has been demonstrated that Shor's algorithm enables public key cryptographic attacks to be performed in polynomial time. In response, NIST conducted a Post-Quantum Cryptography Standardization competition. Additionally, due to the potential reduction in the complexity of symmetric key cryptographic attacks to square root with Grover's algorithm, it is increasingly challenging to consider symmetric key cryptography as secure. In order to establish...
Finding Shortest Vector Using Quantum NV Sieve on Grover
Hyunji Kim, Kyoungbae Jang, Yujin Oh, Woojin Seok, Wonhuck Lee, Kwangil Bae, Ilkwon Sohn, Hwajeong Seo
Attacks and cryptanalysis
Quantum computers, especially those with over 10,000 qubits, pose a potential threat to current public key cryptography systems like RSA and ECC due to Shor's algorithms. Grover's search algorithm is another quantum algorithm that could significantly impact current cryptography, offering a quantum advantage in searching unsorted data. Therefore, with the advancement of quantum computers, it is crucial to analyze potential quantum threats.
While many works focus on Grover’s attacks in...
ELCA: Introducing Enterprise-level Cryptographic Agility for a Post-Quantum Era
Dimitrios Sikeridis, David Ott, Sean Huntley, Shivali Sharma, Vasantha Kumar Dhanasekar, Megha Bansal, Akhilesh Kumar, Anwitha U N, Daniel Beveridge, Sairam Veeraswamy
Implementation
Given the importance of cryptography to modern security and privacy solutions, it is surprising how little attention has been given to the problem of \textit{cryptographic agility}, or frameworks enabling the transition from one cryptographic algorithm or implementation to another. In this paper, we argue that traditional notions of cryptographic agility fail to capture the challenges facing modern enterprises that will soon be forced to implement a disruptive migration from today’s public...
Leaky McEliece: Secret Key Recovery From Highly Erroneous Side-Channel Information
Marcus Brinkmann, Chitchanok Chuengsatiansup, Alexander May, Julian Nowakowski, Yuval Yarom
Attacks and cryptanalysis
The McEliece cryptosystem is a strong contender for post-quantum schemes, including key encapsulation for confidentiality of key exchanges in network protocols.
A McEliece secret key is a structured parity check matrix that is transformed via Gaussian elimination into an unstructured public key. We show that this transformation is a highly critical operation with respect to side-channel leakage.
We assume leakage of the elementary row operations during Gaussian elimination, motivated by...
Subversion-Resilient Signatures without Random Oracles
Pascal Bemmann, Sebastian Berndt, Rongmao Chen
Public-key cryptography
In the aftermath of the Snowden revelations in 2013, concerns about the integrity and security of cryptographic systems have grown significantly. As adversaries with substantial resources might attempt to subvert cryptographic algorithms and undermine their intended security guarantees, the need for subversion-resilient cryptography has become paramount. Security properties are preserved in subversion-resilient schemes, even if the adversary implements the scheme used in the security...
QFESTA: Efficient Algorithms and Parameters for FESTA using Quaternion Algebras
Kohei Nakagawa, Hiroshi Onuki
Public-key cryptography
In 2023, Basso, Maino, and Pope proposed FESTA (Fast Encryption from Supersingular Torsion Attacks), an isogeny-based public-key encryption (PKE) protocol that uses the SIDH attack for decryption. In the same paper, they proposed a parameter for that protocol, but the parameter requires high-degree isogeny computations. In this paper, we introduce QFESTA (Quaternion Fast Encapsulation from Supersingular Torsion Attacks), a new variant of FESTA that works with better parameters using...
Blockwise Rank Decoding Problem and LRPC Codes: Cryptosystems with Smaller Sizes
Yongcheng Song, Jiang Zhang, Xinyi Huang, Wei Wu
Public-key cryptography
In this paper, we initiate the study of the Rank Decoding (RD) problem and LRPC codes with blockwise structures in rank-based cryptosystems. First, we introduce the blockwise errors ($\ell$-errors) where each error consists of $\ell$ blocks of coordinates with disjoint supports, and define the blockwise RD ($\ell$-RD) problem as a natural generalization of the RD problem whose solutions are $\ell$-errors (note that the standard RD problem is actually a special $\ell$-RD problem with...
Finding Orientations of Supersingular Elliptic Curves and Quaternion Orders
Sarah Arpin, James Clements, Pierrick Dartois, Jonathan Komada Eriksen, Péter Kutas, Benjamin Wesolowski
Public-key cryptography
Orientations of supersingular elliptic curves encode the information of an endomorphism of the curve. Computing the full endomorphism ring is a known hard problem, so one might consider how hard it is to find one such orientation. We prove that access to an oracle which tells if an elliptic curve is $\mathfrak{O}$-orientable for a fixed imaginary quadratic order $\mathfrak{O}$ provides non-trivial information towards computing an endomorphism corresponding to the $\mathfrak{O}$-orientation....
Quantum security analysis of Wave
Johanna Loyer
Wave is a code-based digital signature scheme. Its hardness relies on the unforgeability of signature and the indistinguishability of its public key, a parity check matrix of a ternary $(U, U+V)$-code.
The best known attacks involve solving the Decoding Problem using the Information Set Decoding algorithm (ISD) to defeat these two problems. Our main contribution is the description of a quantum smoothed Wagner's algorithm within the ISD, which improves the forgery attack on Wave in the...
Public-Key Encryption from Average Hard NP Language
Hongda Li, Peifang Ni, Yao Zan
Public-key cryptography
The question of whether public-key encryption (PKE) can be constructed from the assumption that one-way functions (OWF) exist remains a central open problem. In this paper we give two constructions of bit PKE scheme derived from any NP language L, along with a polynomial-time instance-witness sampling algorithm. Furthermore, we prove that if L is average hard NP language, the the presented schemes is CPA secure. Our results give a positive answer to this longstanding problem, as the...
Securing Lattice-Based KEMs with Code-Based Masking: A Theoretical Approach
Pierre-Augustin Berthet, Cédric Tavernier, Jean-Luc Danger, Laurent Sauvage
The recent technological advances in Post-Quantum Cryptography (PQC) raise the questions of robust implementations of new asymmetric cryptographic primitives in today’s technology. This is the case for the lattice-based Module Lattice-Key Encapsulation Mechanism (ML-KEM) algorithm which is proposed by the NIST as the first standard for Public Key Encryption (PKE) and Key Encapsulation Mechanism (KEM), taking inspiration from CRYSTALS-Kyber. We have notably to make sure the ML-KEM...
HI-Kyber: A novel high-performance implementation scheme of Kyber based on GPU
Xinyi Ji, Jiankuo Dong, Pinchang Zhang, Deng Tonggui, Hua Jiafeng, Fu Xiao
Implementation
CRYSTALS-Kyber, as the only public key encryption (PKE) algorithm selected by the National Institute of Standards and Technology (NIST) in the third round, is considered one of the most promising post-quantum cryptography (PQC) schemes. Lattice-based cryptography uses complex discrete alogarithm problems on lattices to build secure encryption and decryption systems to resist attacks from quantum computing. Performance is an important bottleneck affecting the promotion of post quantum...
Fast batched asynchronous distributed key generation
Jens Groth, Victor Shoup
Cryptographic protocols
We present new protocols for threshold Schnorr signatures that work in an asynchronous communication setting, providing robustness and optimal resilience. These protocols provide unprecedented performance in terms of communication and computational complexity. In terms of communication complexity, for each signature, a single party must transmit a few dozen group elements and scalars across the network (independent of the size of the signing committee). In terms of computational...
On the Security of Universal Re-Encryption
Fabio Banfi, Ueli Maurer, Silvia Ritsch
Public-key cryptography
A universal re-encryption (URE) scheme is a public-key encryption scheme enhanced with an algorithm that on input a ciphertext, outputs another ciphertext which is still a valid encryption of the underlying plaintext. Crucially, such a re-encryption algorithm does not need any key as input, but the ciphertext is guaranteed to be valid under the original key-pair. Therefore, URE schemes lend themselves naturally as building blocks of mixnets: A sender transmits the encryption of a message...
Secure Function Extensions to Additively Homomorphic Cryptosystems
Mounika Pratapa, Aleksander Essex
Public-key cryptography
The number-theoretic literature has long studied the question of distributions of sequences of quadratic residue symbols modulo a prime number. In this paper, we present an efficient algorithm for generating primes containing chosen sequences of quadratic residue symbols and use it as the basis of a method extending the functionality of additively homomorphic cryptosystems.
We present an algorithm for encoding a chosen Boolean function into the public key and an efficient two-party...
Outsider-Anonymous Broadcast Encryption with Keyword Search: Generic Construction, CCA Security, and with Sublinear Ciphertexts
Keita Emura, Kaisei Kajita, Go Ohtake
Public-key cryptography
As a multi-receiver variants of public key encryption with keyword search (PEKS), broadcast encryption with keyword search (BEKS) has been proposed (Attrapadung et al. at ASIACRYPT 2006/Chatterjee-Mukherjee at INDOCRYPT 2018). Unlike broadcast encryption, no receiver anonymity is considered because the test algorithm takes a set of receivers as input and thus a set of receivers needs to be contained in a ciphertext. In this paper, we propose a generic construction of BEKS from anonymous and...
A Side-Channel Attack on a Masked Hardware Implementation of CRYSTALS-Kyber
Yanning Ji, Elena Dubrova
Attacks and cryptanalysis
NIST has recently selected CRYSTALS-Kyber as a new public key encryption and key establishment algorithm to be standardized. This makes it important to evaluate the resistance of CRYSTALS-Kyber implementations to side-channel attacks. Software implementations of CRYSTALS-Kyber have already been thoroughly analysed. The discovered vulnerabilities helped improve the subsequently released versions and promoted stronger countermeasures against side-channel attacks. In this paper, we present the...
Public-Key Encryption, Local Pseudorandom Generators, and the Low-Degree Method
Andrej Bogdanov, Pravesh Kothari, Alon Rosen
Public-key cryptography
The low-degree method postulates that no efficient algorithm outperforms low-degree polynomials in certain hypothesis-testing tasks. It has been used to understand computational indistinguishability in high-dimensional statistics.
We explore the use of the low-degree method in the context of cryptography. To this end, we apply it in the design and analysis of a new public-key encryption scheme whose security is based on Goldreich's pseudorandom generator. The scheme is a combination of...
A Side-Channel Attack on a Bitsliced Higher-Order Masked CRYSTALS-Kyber Implementation
Ruize Wang, Martin Brisfors, Elena Dubrova
Attacks and cryptanalysis
In response to side-channel attacks on masked implementations of post-quantum cryptographic algorithms, a new bitsliced higher-order masked implementation of CRYSTALS-Kyber has been presented at CHES'2022. The bitsliced implementations are typically more difficult to break by side-channel analysis because they execute a single instruction across multiple bits in parallel. However, in this paper, we reveal new vulnerabilities in the masked Boolean to arithmetic conversion procedure of this...
PQC Cloudization: Rapid Prototyping of Scalable NTT/INTT Architecture to Accelerate Kyber
Mojtaba Bisheh-Niasar, Daniel Lo, Anjana Parthasarathy, Blake Pelton, Bharat Pillilli, Bryan Kelly
Public-key cryptography
The advent of quantum computers poses a serious challenge to the security of cloud infrastructures and services, as they can potentially break the existing public-key cryptosystems, such as Rivest–Shamir–Adleman (RSA) and Elliptic Curve Cryptography (ECC). Even though the gap between today’s quantum computers and the threats they pose to current public-key cryptography is large, the cloud landscape should act proactively and initiate the transition to the post-quantum era as early as...
Circular Multiplicative Modular Exponentiation: A New Public Key Exchange Algorithm
Michele Fabbrini
Public-key cryptography
The major objective of this paper is to present a theoretical model for an algorithm that has not been previously described in the literature, capable of generating a secret key through the transmission of data over a public channel. We explain how the method creates a shared secret key by attaining commutativity through the multiplication of the modular exponentiation of a minimum of two bases and an equal number of private exponents for each party involved in the exchange. In addition, we...
Tighter QCCA-Secure Key Encapsulation Mechanism with Explicit Rejection in the Quantum Random Oracle Model
Jiangxia Ge, Tianshu Shan, Rui Xue
Public-key cryptography
Hofheinz et al. (TCC 2017) proposed several key encapsulation mechanism (KEM) variants of Fujisaki-Okamoto (\textsf{FO}) transformation, including $\textsf{FO}^{\slashed{\bot}}$, $\textsf{FO}_m^{\slashed{\bot}}$, $\textsf{QFO}_m^{\slashed{\bot}}$, $\textsf{FO}^{\bot}$, $\textsf{FO}_m^\bot$ and $\textsf{QFO}_m^\bot$, and they are widely used in the post-quantum cryptography standardization launched by NIST. These transformations are divided into two types, the implicit and explicit rejection...
Discrete Logarithm Factory
Haetham AL ASWAD, Cécile PIERROT, Emmanuel THOMÉ
Public-key cryptography
The Number Field Sieve and its variants are the best algorithms to solve the discrete logarithm problem in finite fields. The Factory variant accelerates the computation when several prime fields are targeted. This article adapts the Factory variant to non-prime finite fields of medium and large characteristic. We combine this idea with two other variants of NFS, namely the tower and special variant. This combination leads to improvements in the asymptotic complexity. Besides, we lay out...
HPPC: Hidden Product of Polynomial Composition
Borja Gomez Rodriguez
Attacks and cryptanalysis
The article introduces HPPC a new Digital Signature scheme that intends to resist known previous attacks applied to HFE-based schemes like QUARTZ and GeMSS. The idea is to use maximal degree for the central HFE polynomial whereas the trapdoor polynomial has low degree in order to sign messages by finding polynomial roots in an extension field via Berlekamp's algorithm. This work has been submitted to NIST's Post-Quantum Cryptography challenge (PQC) and code is available at...
Migrating Applications to Post-Quantum Cryptography: Beyond Algorithm Replacement
Alexandre Augusto Giron
Applications
Post-Quantum Cryptography (PQC) defines cryptographic algorithms designed to resist the advent of the quantum computer. Most public-key cryptosystems today are vulnerable to quantum attackers, so a global-scale transition to PQC is expected. As a result, several entities foment efforts in PQC standardization, research, development, creation of Work Groups (WGs), and issuing adoption recommendations. However, there is a long road to broad PQC adoption in practice. This position paper...
2023/698
Last updated: 2023-05-19
A public-key based secure quantum-communication protocol using entangled qubits
S Murugesh
Public-key cryptography
We propose a quantum algorithm that crucially involves the receiver's public-key to establish secure communication of an intended message string, using shared entangled-qubits. The public-key in question is a random bit string that proclaims the sequence of measurement basis used by the receiver. As opposed to known quantum key distribution protocols, wherein a random key string is generated at the end of the communication cycle, here the sender's intended bit string itself is...
A 334µW 0.158mm2 ASIC for Post-Quantum Key-Encapsulation Mechanism Saber with Low-latency Striding Toom-Cook Multiplication Extended Version
Archisman Ghosh, Jose Maria Bermudo Mera, Angshuman Karmakar, Debayan Das, Santosh Ghosh, Ingrid Verbauwhede, Shreyas Sen
Public-key cryptography
The hard mathematical problems that assure the security of our current public-key cryptography (RSA, ECC) are broken if and when a quantum computer appears rendering them ineffective for use in the quantum era. Lattice based cryptography is a novel approach to public key cryptography, of which the mathematical investigation (so far) resists attacks from quantum computers. By choosing a module learning with errors (MLWE) algorithm as the next standard, National Institute of Standard \&...
Tracing Quantum State Distinguishers via Backtracking
Mark Zhandry
Foundations
We show the following results:
- The post-quantum equivalence of indistinguishability obfuscation and differing inputs obfuscation in the restricted setting where the outputs differ on at most a polynomial number of points. Our result handles the case where the auxiliary input may contain a quantum state; previous results could only handle classical auxiliary input.
- Bounded collusion traitor tracing from general public key encryption, where the decoder is allowed to contain a...
Fast Enumeration Algorithm for Multivariate Polynomials over General Finite Fields
Hiroki Furue, Tsuyoshi Takagi
Attacks and cryptanalysis
The enumeration of all outputs of a given multivariate polynomial is a fundamental mathematical problem and is incorporated in some algebraic attacks on multivariate public key cryptosystems. For a degree-$d$ polynomial in $n$ variables over the finite field with $q$ elements, solving the enumeration problem classically requires $O\left(\tbinom{n+d}{d} \cdot q^n\right)$ operations. At CHES 2010, Bouillaguet et al. proposed a fast enumeration algorithm over the binary field $\mathbb{F}_2$....
Post-Quantum Public-key Authenticated Searchable Encryption with Forward Security: General Construction, and Applications
Shiyuan Xu, Yibo Cao, Xue Chen, Yanmin Zhao, Siu-Ming Yiu
Public-key cryptography
Public-key encryption with keyword search (PEKS) was first proposed by Boneh et al. (EUROCRYPT 2004), achieving the ability to search for ciphertext files. Nevertheless, it is vulnerable to inside keyword guessing attacks (IKGA). Public-key authenticated encryption with keyword search (PAEKS), introduced by Huang et al. (Inf. Sci. 2017), on the other hand, is secure against IKGA. Nonetheless, it is susceptible to quantum computing attacks. Liu et al. and Cheng et al. addressed this problem...
Wave Parameter Selection
Nicolas Sendrier
Public-key cryptography
Wave is a provably EUF-CMA (existential unforgeability under adaptive chosen message attacks) digital signature scheme based on codes \cite{DST19a}. It is an hash-and-sign primitive and its security is built according to a GPV-like framework \cite{GPV08} under two assumptions related to coding theory: (i) the hardness of finding a word of prescribed Hamming weight and prescribed syndrome, and (ii) the pseudo-randomness of ternary generalized $(U|U+V)$ codes. Forgery attacks (i)---or message...
hinTS: Threshold Signatures with Silent Setup
Sanjam Garg, Abhishek Jain, Pratyay Mukherjee, Rohit Sinha, Mingyuan Wang, Yinuo Zhang
Public-key cryptography
We propose hinTS --- a new threshold signature scheme built on top of the widely used BLS signatures. Our scheme enjoys the following attractive features:
\begin{itemize}
\item A {\em silent setup} process where the joint public key of the parties is computed as a deterministic function of their locally computed public keys.
\item Support for {\em dynamic} choice of thresholds and signers, after the silent setup, without further interaction.
\item Support for {\em general}...
2023/519
Last updated: 2023-05-10
Generalized Inverse Binary Matrix Construction with PKC Application
Farshid Haidary Makoui, Thomas Aaron Guliver
Public-key cryptography
The generalized inverses of systematic non-square binary matrices have applications in mathematics, channel coding and decoding, navigation signals, machine learning, data storage, and cryptography, such as the McEliece and Niederreiter public-key cryptosystems. A systematic non-square (n−k)×n matrix H, n > k, has 2 power k×(n−k) different generalized inverse matrices. This paper presents an algorithm for generating these matrices and compares it with two well-known methods, i.e....
Computing Isogenies of Power-Smooth Degrees Between PPAVs
Jesús-Javier Chi-Domínguez, Amalia Pizarro-Madariaga, Edgardo Riquelme
Public-key cryptography
The wave of attacks by Castryck and Decru (Eurocrypt, 2023), Maino, Martindale, Panny, Pope and Wesolowski (Eurocrypt, 2023) and Robert (Eurocrypt, 2023), highlight the destructive facet of calculating power-smooth degree isogenies between higher-dimensional abelian varieties in isogeny-based cryptography.
Despite those recent attacks, there is still interest in using isogenies but for building protocols on top of higher-dimensional abelian varieties. Examples of such protocols are...
Quantum Public-Key Encryption with Tamper-Resilient Public Keys from One-Way Functions
Fuyuki Kitagawa, Tomoyuki Morimae, Ryo Nishimaki, Takashi Yamakawa
Foundations
We construct quantum public-key encryption from one-way functions.
In our construction, public keys are quantum, but ciphertexts are classical.
Quantum public-key encryption from one-way functions (or weaker primitives such as
pseudorandom function-like states) are also proposed in some recent works [Morimae-Yamakawa, eprint:2022/1336; Coladangelo, eprint:2023/282; Barooti-Grilo-Malavolta-Sattath-Vu-Walter, eprint:2023/877]. However, they have a huge drawback: they are secure only when...
$k$-SUM in the Sparse Regime
Shweta Agrawal, Sagnik Saha, Nikolaj Ignatieff Schwartzbach, Akhil Vanukuri, Prashant Nalini Vasudevan
Foundations
In the average-case $k$-SUM problem, given $r$ integers chosen uniformly at random from $\{0,\ldots,M-1\}$, the objective is to find a "solution" set of $k$ numbers that sum to $0$ modulo $M$. In the dense regime of $M \leq r^k$, where solutions exist with high probability, the complexity of these problems is well understood. Much less is known in the sparse regime of $M\gg r^k$, where solutions are unlikely to exist.
In this work, we initiate the study of the sparse regime for...
GeT a CAKE: Generic Transformations from Key Encaspulation Mechanisms to Password Authenticated Key Exchanges
Hugo Beguinet, Céline Chevalier, David Pointcheval, Thomas Ricosset, Mélissa Rossi
Public-key cryptography
Password Authenticated Key Exchange (PAKE) have become a key building block in many security products as they provide interesting efficiency/security trade-offs. Indeed, a PAKE allows to dispense with the heavy public key infrastructures and its efficiency and portability make it well suited for applications such as Internet of Things or e-passports.
With the emerging quantum threat and the effervescent development of post-quantum public key algorithms in the last five years, one would...
2023/448
Last updated: 2023-06-05
Generalized Inverse Matrix Construction for Code Based Cryptography
Farshid Haidary Makoui, T. Aaron Gulliver
Public-key cryptography
The generalized inverses of systematic non-square binary matrices have applications in mathematics, channel coding and decoding, navigation signals, machine learning, data storage and cryptography such as the McEliece and Niederreiter public-key cryptosystems.
A systematic non-square $(n-k) \times n$ matrix $H$, $n > k$, has $2^{k\times(n-k)}$ different generalized inverse matrices.
This paper presents an algorithm for generating these matrices and compares it with two well-known methods,...
Practical Attacks on Small Private Exponent RSA: New Records and New Insights
Qiang Li, Qun-xiong Zheng, Wen-feng Qi
Attacks and cryptanalysis
As a typical representative of the public key cryptosystem, RSA has
attracted a great deal of cryptanalysis since its invention, among which
a famous attack is the small private exponent attack. It is well-known
that the best theoretical upper bound for the private exponent d that
can be attacked is d ≤ N^0.292
, where N is a RSA modulus. However,
this bound may not be achieved in practical attacks since the lattice constructed
by Coppersmith method may have a large enough dimension...
2023/360
Last updated: 2023-06-05
Fast and Efficient Code-Based Digital Signature with Dual Inverse Matrix
Farshid Haidary Makoui, T. Aaron Gulliver, Mohammad Dakhilalian
Digital signatures ensure legitimate access through identity authentication. It is also used to build blocks in blockchains and to authenticate transactions. The Courtois-Finiasz-Sendrier (CFS) digital signature is a well-known code-based digital signature scheme based on the Niederreiter cryptosystem.
The CFS signature, however, is not widely used due to the long processing time required by its signing algorithm. Most code-based digital signature schemes are based on Niederreiter. The...
2023/358
Last updated: 2023-05-10
Efficient Code Based Cryptosystem with Dual Inverse Matrix
Farshid Haidary Makoui, T. Aaron Gulliver, Mohammad Dakhilalian
Public-key cryptography
The security of cryptographic primitives is an important issue.
The Shor algorithm illustrates how quantum attacks threaten the security of these widely used primitives.
Code-based cryptography is one of several approaches resistant to quantum attacks.
To date, no attack has been able to break a code-based cryptosystem in polynomial time.
Despite this level of security, these cryptosystems have not been considered for practical applications such as e-commerce, medical and industrial IoT,...
2023/349
Last updated: 2024-02-11
AAQ-PEKS: An Attribute-based Anti-Quantum Public-Key Encryption Scheme with Keyword Search for E-healthcare Scenarios
Gang Xu, Shiyuan Xu, Yibo Cao, Ke Xiao, Xiu-Bo Chen, Mianxiong Dong, Shui Yu
Public-key cryptography
Electronic Medical Records (EMRs) have been utilized in plentiful medical institutions due to their superior convenience and low storage overhead. Nevertheless, it is difficult for medical departments with disparate management regulations to share EMRs through secure communication channels since sensitive EMRs are prone to be tampered with. Therefore, the EMRs should be encrypted before being outsourced to the network servers. Public key Encryption with Keyword Search (PEKS) has the ability...
Punctured Syndrome Decoding Problem Efficient Side-Channel Attacks Against Classic McEliece
Vincent Grosso, Pierre-Louis Cayrel, Brice Colombier, Vlad-Florin Dragoi
Attacks and cryptanalysis
Among the fourth round finalists of the NIST post-quantum cryptography standardization process for public-key encryption algorithms and key encapsulation mechanisms, three rely on hard problems from coding theory. Key encapsulation mechanisms are frequently used in hybrid cryptographic systems: a public-key algorithm for key exchange and a secret key algorithm for communication. A major point is thus the initial key exchange that is performed thanks to a key encapsulation mechanism. In this...
Do we need to change some things? Open questions posed by the upcoming post-quantum migration to existing standards and deployments
Panos Kampanakis, Tancrède Lepoint
Cryptographic protocols
Cryptographic algorithms are vital components ensuring the privacy and security of computer systems. They have constantly improved and evolved over the years following new developments, attacks, breaks, and lessons learned. A recent example is that of quantum-resistant cryptography, which has gained a lot of attention in the last decade and is leading to new algorithms being standardized today. These algorithms, however, present a real challenge: they come with strikingly different size and...
Public Key Encryption with Secure Key Leasing
Shweta Agrawal, Fuyuki Kitagawa, Ryo Nishimaki, Shota Yamada, Takashi Yamakawa
Public-key cryptography
We introduce the notion of public key encryption with secure key leasing (PKE-SKL). Our notion supports the leasing of decryption keys so that a leased key achieves the decryption functionality but comes with the guarantee that if the quantum decryption key returned by a user passes a validity test, then the user has lost the ability to decrypt. Our notion is similar in spirit to the notion of secure software leasing (SSL) introduced by Ananth and La Placa (Eurocrypt 2021) but captures...
Memory-Efficient Attacks on Small LWE Keys
Andre Esser, Rahul Girme, Arindam Mukherjee, Santanu Sarkar
Public-key cryptography
The LWE problem is one of the prime candidates for building the most efficient post-quantum secure public key cryptosystems. Many of those schemes, like Kyber, Dilithium or those belonging to the NTRU-family, such as NTRU-HPS, -HRSS, BLISS or GLP, make use of small max norm keys to enhance efficiency. The presumably best attack on these schemes is a hybrid attack, which combines combinatorial techniques and lattice reduction. While lattice reduction is not known to be able to exploit the...
A Lightweight Identification Protocol Based on Lattices
Samed Düzlü, Juliane Krämer, Thomas Pöppelmann, Patrick Struck
Cryptographic protocols
In this work we present a lightweight lattice-based identification protocol based on the CPA-secured public key encryption scheme Kyber. It is designed as a replacement for existing classical ECC- or RSA-based identification protocols in IoT, smart card applications, or for device authentication. The proposed protocol is simple, efficient, and implementations are supposed to be easy to harden against side-channel attacks. Compared to standard constructions for identification protocols based...
Time-Efficient Finite Field Microarchitecture Design for Curve448 and Ed448 on Cortex-M4
Mila Anastasova, Reza Azarderakhsh, Mehran Mozaffari Kermani, Lubjana Beshaj
Public-key cryptography
The elliptic curve family of schemes has the lowest computational latency, memory use, energy consumption, and bandwidth requirements, making it the most preferred public key method for adoption into network protocols. Being suitable for embedded devices and applicable for key exchange and authentication, ECC is assuming a prominent position in the field of IoT cryptography. The attractive properties of the relatively new curve Curve448 contribute to its inclusion in the TLS1.3 protocol and...
Compressed M-SIDH: An Instance of Compressed SIDH-like Schemes with Isogenies of Highly Composite Degrees
Kaizhan Lin, Jianming Lin, Shiping Cai, Weize Wang, Chang-An Zhao
Public-key cryptography
Recently, SIDH was broken by a series of attacks. To avoid the attacks, several new countermeasures, such as M-SIDH and binSIDH, have been developed. Different from SIDH, the new SIDH-like schemes have relatively large public key sizes. Besides, the orders of the torsion groups considered in new SIDH-like schemes are the products of many primes. Therefore, the key compression techniques in SIDH can not be directly applied to these schemes. It remains an open problem to compress the public...
Gate-Level Masking of Streamlined NTRU Prime Decapsulation in Hardware
Georg Land, Adrian Marotzke, Jan Richter-Brockmann, Tim Güneysu
Implementation
Streamlined NTRU Prime is a lattice-based Key Encapsulation Mechanism
(KEM) that is, together with X25519, currently the default algorithm in OpenSSH 9. Being based on lattice assumptions, it is assumed to be secure also against attackers with access to large-scale quantum computers. While Post-Quantum Cryptography (PQC) schemes have been subject to extensive research in the recent years, challenges remain with respect to protection mechanisms against attackers that have additional...
Verification of Correctness and Security Properties for CRYSTALS-KYBER
Katharina Kreuzer
Public-key cryptography
Since the post-quantum crypto system CRYSTALS-KYBER has been chosen for standardization by the National Institute for Standards and Technology (US), a formal verification of its correctness and security properties becomes even more relevant.
Using the automated theorem prover Isabelle, we are able to formalize the algorithm specifications and parameter sets of Kyber's public key encryption scheme and verify the $\delta$-correctness and indistinguishability under chosen plaintext attack...
Quantum-Safe Protocols and Application in Data Security of Medical Records
Adrian-Daniel Stefan, Ionut-Petrisor Anghel, Emil Simion
Cryptographic protocols
The use of traditional cryptography based on symmetric keys has been replaced with the revolutionary idea discovered by Diffie and Hellman in 1976 that fundamentally changed communication systems by ensuring a secure transmission of information over an insecure channel. Nowadays public key cryptography is frequently used for authentication in e-commerce, digital signatures and encrypted communication. Most of the public key cryptosystems used in practice are based on integer factorization...
Fermat Factorization in the Wild
Hanno Böck
Attacks and cryptanalysis
We are applying Fermat’s factorization algorithm to sets of public RSA keys. Fermat’s factorization allows efficiently calculating the prime factors of a composite number if the difference between the two primes is small. Knowledge of the prime factors of an RSA public key allows efficiently calculating the private key. A flawed RSA key generation function that produces close primes can therefore be attacked with Fermat’s factorization.
We discovered a small number of vulnerable devices...
M-SIDH and MD-SIDH: countering SIDH attacks by masking information
Tako Boris Fouotsa, Tomoki Moriya, Christophe Petit
Public-key cryptography
The SIDH protocol is an isogeny-based key exchange protocol using supersingular isogenies, designed by Jao and De Feo in 2011.
The protocol underlies the SIKE algorithm which advanced to the fourth round of NIST's post-quantum standardization project in May 2022.
The algorithm was considered very promising: indeed the most significant attacks against SIDH were meet-in-the-middle variants with exponential complexity, and torsion point attacks which only applied to unbalanced parameters...
PECO: methods to enhance the privacy of DECO protocol
Manuel B. Santos
Applications
The DECentralized Oracle (DECO) protocol enables the verifiable provenance of data from Transport Layer Security (TLS) connections through secure two-party computation and zero-knowledge proofs. In this paper, we present PECO, an extension of DECO that enhances privacy features through the integration of two new private three-party handshake protocols (P3P-HS). PECO allows any web user to prove to a verifier the properties of data from TLS connections without disclosing the identity of the...
Breaking a Fifth-Order Masked Implementation of CRYSTALS-Kyber by Copy-Paste
Elena Dubrova, Kalle Ngo, Joel Gärtner
Public-key cryptography
CRYSTALS-Kyber has been selected by the NIST as a public-key encryption and key encapsulation mechanism to be standardized. It is also included in the NSA's suite of cryptographic algorithms recommended for national security systems. This makes it important to evaluate the resistance of CRYSTALS-Kyber's implementations to side-channel attacks. The unprotected and first-order masked software implementations have been already analysed. In this paper, we present deep learning-based message...
Digital Signature from Syndrome Decoding Problem
Abdelhaliem Babiker
Public-key cryptography
This paper introduces new digital signature scheme whose security against existential forgery under adaptive chosen message attack is based on hardness of the Syndrome Decoding Problem. The hardness assumption is quite simple and hence easy to analyze and investigate. The scheme as whole is neat with intuitive security definition and proof in addition to elegant and efficient signing and verifying algorithms. We propose parameter sets for three security levels (128-bits, 192-bits, and 256...
Secret Key Recovery Attacks on Masked and Shuffled Implementations of CRYSTALS-Kyber and Saber
Linus Backlund, Kalle Ngo, Joel Gärtner, Elena Dubrova
Attacks and cryptanalysis
Shuffling is a well-known countermeasure against side-channel analysis. It typically uses the Fisher-Yates (FY) algorithm to generate a random permutation which is then utilized as the loop iterator to index the processing of the variables inside the loop. The processing order is scrambled as a result, making side-channel analysis more difficult. Recently, a side-channel attack on a masked and shuffled implementation of Saber requiring 61,680 power traces to extract the secret key was...
GCKSign: Simple and Efficient Signatures from Generalized Compact Knapsacks
Joo Woo, Kwangsu Lee, Jong Hwan Park
Public-key cryptography
In 2009, Lyubashevsky proposed a lattice-based signature scheme by applying the Fiat-Shamir transformation and proved its security under the generalized compact knapsack (GCK) problem. This scheme has a simple structure but has large signature and key sizes due to the security requirement of their security reduction. Dilithium, which was submitted to the NIST Post-Quantum Cryptography standardization and selected as one of the final candidates, is an improvement of the Lyubashevsky's...
NTRU+: Compact Construction of NTRU Using Simple Encoding Method
Jonghyun Kim, Jong Hwan Park
Public-key cryptography
NTRU was the first practical public key encryption scheme constructed on a lattice over a polynomial-based ring and has been considered secure against significant cryptanalytic attacks over the past few decades. However, NTRU and its variants suffer from several drawbacks, including difficulties in achieving worst-case correctness error in a moderate modulus, inconvenient sampling distributions for messages, and relatively slower algorithms compared to other lattice-based schemes.
In...
LowMS: a new rank metric code-based KEM without ideal structure
Nicolas Aragon, Victor Dyseryn, Philippe Gaborit, Pierre Loidreau, Julian Renner, Antonia Wachter-Zeh
Public-key cryptography
We propose and analyze LowMS, a new rank-based key encapsulation mechanism (KEM). The acronym stands for Loidreau with Multiple Syndromes, since our work combines the cryptosystem of Loidreau (presented at PQCrypto 2017) together with the multiple syndrome approach, that allows to reduce parameters by sending several syndromes with the same error support in one ciphertext.
Our scheme is designed without using ideal structures. Considering cryptosystems without such an ideal structure,...
Multi-ciphertext security degradation for lattices
Daniel J. Bernstein
Attacks and cryptanalysis
Typical lattice-based cryptosystems are commonly believed to resist multi-target attacks. For example, the New Hope proposal stated that it avoids "all-for-the-price-of-one attacks". An ACM CCS 2021 paper from Duman–Hövelmanns–Kiltz–Lyubashevsky–Seiler stated that "we can show that Adv_{PKE}^{IND-CPA} ≈ Adv_{PKE}^{(n,q_C)-IND-CPA} for "lattice-based schemes" such as Kyber, i.e. that one-out-of-many-target IND-CPA is as difficult to break as single-target IND-CPA, assuming "the hardness of...
Intermediate Certificate Suppression in Post-Quantum TLS: An Approximate Membership Querying Approach
Dimitrios Sikeridis, Sean Huntley, David Ott, Michael Devetsikiotis
Cryptographic protocols
Quantum computing advances threaten the security of today's public key infrastructure, and have led to the pending standardization of alternative, quantum-resistant key encapsulation and digital signature cryptography schemes. Unfortunately, authentication algorithms based on the new post-quantum (PQ) cryptography create significant performance bottlenecks for TLS due to larger certificate chains which introduce additional packets and round-trips. The TLS handshake slowdown will be...
Peregrine: Toward Fastest FALCON Based on GPV Framework
Eun-Young Seo, Young-Sik Kim, Joon-Woo Lee, Jong-Seon No
Public-key cryptography
FALCON and Crystals-Dilithium are the digital signatures algorithms selected as NIST PQC standards at the end of the third round. FALCON has the advantage of the shortest size of the combined public key and signature but has the disadvantage of the relatively long signing time. Since FALCON algorithm is faithfully designed based on theoretical security analysis, the implementation of the algorithms is quite complex and needs considerable complexity. In order to implement the FALCON...
Let's Meet Ternary Keys on Babai's Plane: A Hybrid of Lattice-reduction and Meet-LWE
Minki Hhan, Jiseung Kim, Changmin Lee, Yongha Son
Attacks and cryptanalysis
A cryptographic primitive based on the Learning With Errors (LWE) problem with variants is a promising candidate for the efficient quantum-resistant public key cryptosystem. As the parameters for such cryptosystems are chosen by the concrete attack cost for the corresponding LWE problem, improving LWE solving algorithm has a significant importance.
In this paper, we present a new hybrid attack on the LWE problem. This new attack combines the primal lattice attack and an improved variant...
A Side-Channel Attack on a Hardware Implementation of CRYSTALS-Kyber
Yanning Ji, Ruize Wang, Kalle Ngo, Elena Dubrova, Linus Backlund
Attacks and cryptanalysis
CRYSTALS-Kyber has been recently selected by the NIST as a new public-key encryption and key-establishment algorithm to be standardized. This makes it important to assess how well CRYSTALS-Kyber implementations withstand side-channel attacks. Software implementations of CRYSTALS-Kyber have been already analyzed and the discovered vulnerabilities were patched in the subsequently released versions. In this paper, we present a profiling side-channel attack on a hardware implementation of...
ParaDiSE: Efficient Threshold Authenticated Encryption in Fully Malicious Model
Shashank Agrawal, Wei Dai, Atul Luykx, Pratyay Mukherjee, Peter Rindal
Cryptographic protocols
Threshold cryptographic algorithms achieve robustness against key and access compromise by distributing secret keys among multiple entities. Most prior work focuses on threshold public-key primitives, despite extensive use of authenticated encryption in practice. Though the latter can be deployed in a threshold manner using multi-party computation (MPC), doing so incurs a high communication cost. In contrast, dedicated constructions of threshold authenticated encryption algorithms can...
Plug-and-play sanitization for TFHE
Florian Bourse, Malika Izabachène
Public-key cryptography
Fully Homomorphic encryption allows the evaluation of any circuits over encrypted data while preserving the privacy of the data. However, without any additional properties, no guarantee is provided for the privacy of the circuits which are evaluated.
A sanitization algorithm allows to destroy all previous information about how a ciphertext was obtained, ensuring that the circuit which was evaluated remains secret. In this paper, we present two techniques to randomize RLWE ciphertexts, and...
Efficient and Generic Transformations for Chosen-Ciphertext Secure Predicate Encryption
Marloes Venema, Leon Botros
Public-key cryptography
Predicate encryption (PE) is a type of public-key encryption that captures many useful primitives such as attribute-based encryption (ABE). Although much progress has been made to generically achieve security against chosen-plaintext attacks (CPA) efficiently, in practice, we also require security against chosen-ciphertext attacks (CCA). Because achieving CCA-security on a case-by-case basis is a complicated task, several generic conversion methods have been proposed. However, these...
Subverting Deniability
Marcel Armour, Elizabeth A. Quaglia
Attacks and cryptanalysis
Deniable public-key encryption (DPKE) is a cryptographic primitive that allows the sender of an encrypted message to later claim that they sent a different message.
DPKE's threat model assumes powerful adversaries who can coerce users to reveal plaintexts; it is thus reasonable to consider other advanced capabilities, such as the ability to subvert algorithms in a so-called Algorithm Substitution Attack (ASA). An ASA replaces a trusted algorithm with a subverted version that undermines...
The advent of quantum computing technology will compromise many of the current cryptographic algorithms, especially public-key cryptography, which is widely used to protect digital information. Most algorithms on which we depend are used worldwide in components of many different communications, processing, and storage systems. Once access to practical quantum computers becomes available, all public-key algorithms and associated protocols will be vulnerable to criminals, competitors, and...
RSA is an incredibly successful and useful asymmetric encryption algorithm. One of the types of implementation flaws in RSA is low entropy of the key generation, specifically the prime number creation stage. This can occur due to flawed usage of random prime number generator libraries, or on computers where there is a lack of a source of external entropy. These implementation flaws result in some RSA keys sharing prime factors, which means that the full factorization of the public modulus...
WebAuthn is a passwordless authentication protocol which allows users to authenticate to online services using public-key cryptography. Users prove their identity by signing a challenge with a private key, which is stored on a device such as a cell phone or a USB security token. This approach avoids many of the common security problems with password-based authentication. WebAuthn's reliance on proof-of-possession leads to a usability issue, however: a user who loses access to their...
This paper presents a comprehensive security analysis of the Adh zero-knowledge proof system, a novel lattice-based, quantum-resistant proof of possession system. The Adh system offers compact key and proof sizes, making it suitable for real-world digital signature and public key agreement protocols. We explore its security by reducing it to the hardness of the Module-ISIS problem and introduce three new variants: Module-ISIS+, Module-ISIS*, and Module-ISIS**. These constructions enhance...
In this paper we explore efficient ways to prove correctness of elliptic curve pairing relations. Pairing-based cryptographic protocols such as the Groth16 and Plonk SNARKs and the BLS signature scheme are used extensively in public blockchains such as Ethereum due in large part to their small size. However the relatively high cost of pairing computation remains a practical problem for many use cases such as verification ``in circuit" inside a SNARK. This naturally arises in recursive SNARK...
In this paper we study the effect of using small prime numbers within the Okamoto-Uchiyama public key encryption scheme. We introduce two novel versions and prove their security. Then we show how to choose the system's parameters such that the security results hold. Moreover, we provide a practical comparison between the cryptographic algorithms we introduced and the original Okamoto-Uchiyama cryptosystem.
In isogeny-based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public-key validation and torsion basis generation. However, in most isogeny-based protocols, the performance of pairing computations is unsatisfactory due to the high computational cost of the Miller function. Reducing the computational expense of the Miller function is crucial for enhancing the overall performance of pairing computations in isogeny-based...
In this work we define the notion of a permutation correlation $(\pi,A,B,C)$ s.t. $\pi(A)=B+C$ for a random permutation $\pi$ of $n$ elements and vectors $A,B,C\in \mathbb{F}^n$. We demonstrate the utility of this correlation for a wide range of applications. The correlation can be derandomized to obliviously shuffle a secret-shared list, permute a secret-shared list by a secret-shared permutation, and more. Similar techniques have emerged as a popular building block for the honest majority...
SHA2 has been widely adopted across various traditional public-key cryptosystems, post-quantum cryptography, personal identification, and network communication protocols, etc. Hence, ensuring the robust security of SHA2 is of critical importance. There have been several differential fault attacks based on random word faults targeting SHA1 and SHACAL-2. However, extending such random word-based fault attacks to SHA2 proves significantly more difficult due to the heightened complexity of the...
We define a (small) augmentation to the FROST threshold signature scheme that additionally allows for re-randomizable public and secret keys. We build upon the notion of re-randomizable keys in the literature, but tailor this capability when the signing key is secret-shared among a set of mutually trusted parties. We do not make any changes to the plain FROST protocol, but instead define additional algorithms to allow for randomization of the threshold public key and participant’s individual...
Quantum computers at some future date might be able to factor large numbers, and this poses a threat to some public key and key exchange systems in use today. This overview of recent progress in devising quantum algorithms and building quantum computing devices is meant to help technologists understand the difficult problems that quantum engineers are working on, where advances have been made, and how those things affect estimates of if and when large scale quantum computation might happen.
Hudoba proposed a public key encryption (PKE) scheme and conjectured its security to be based on the Planted Clique problem. In this note, we show that this scheme is not secure. We do so by devising an efficient algorithm for the even neighbor independent set problem proposed by Hudoba. This leaves open the possibility of building PKE based on Planted Clique.
At EUROCRYPT’23, Castryck and Decru, Maino et al., and Robert present efficient attacks against supersingular isogeny Diffie-Hellman key exchange protocol (SIDH). Drawing inspiration from these attacks, Andrea Basso, Luciano Maino, and Giacomo Pope introduce FESTA, an isogeny-based trapdoor function, along with a corresponding IND-CCA secure public key encryption (PKE) protocol at ASIACRYPT’23. FESTA incorporates either a diagonal or circulant matrix into the secret key to mask torsion...
In this work, we introduce a family of asymmetric cryptographic functions based on dynamic number theoretic transformations with multiple rounds of modular arithmetic to enhance diffusion and difficulty of inversion. This function acts as a basic cryptographic building block for a novel communication-efficient zero-knowledge crypto-system. The system as defined exhibits partial homomorphism and behaves as an additive positive accumulator. By using a novel technique to constructively embed...
Post-Quantum Cryptography (PQC) was proposed due to the potential threats quantum computer attacks against conventional public key cryptosystems, and four PQC algorithms besides CRYSTALS-Dilithium (Dilithium for short) have so far been selected for NIST standardization. However, the selected algorithms are still vulnerable to side-channel attacks in practice, and their physical security need to be further evaluated. This study introduces two efficient power analysis attacks, the optimized...
PERK is a digital signature scheme submitted to the recent NIST Post-Quantum Cryptography Standardization Process for Additional Digital Signature Schemes. For NIST security level I, PERK features sizes ranging from 6kB to 8.5kB, encompassing both the signature and public key, depending on the parameter set. Given its inherent characteristics, PERK's signing and verification algorithms involve the computation of numerous large objects, resulting in substantial stack-memory consumption...
BIKE is a post-quantum key encapsulation mechanism (KEM) selected for the 4th round of the NIST’s standardization campaign. It relies on the hardness of the syndrome decoding problem for quasi-cyclic codes and on the indistinguishability of the public key from a random element, and provides the most competitive performance among round 4 candidates, which makes it relevant for future real-world use cases. Analyzing its side-channel resistance has been highly encouraged by the community and...
Asymmetric Searchable Encryption (ASE) is a promising cryptographic mechanism that enables a semi-trusted cloud server to perform keyword searches over encrypted data for users. To be useful, an ASE scheme must support expressive search queries, which are expressed as conjunction, disjunction, or any Boolean formulas. In this paper, we propose a fast and expressive ASE scheme that is adaptively secure, called FEASE. It requires only 3 pairing operations for searching any conjunctive set of...
In a recent ePrint, Brown and Monico propose new attacks on the tropical signature scheme of Chen, Grigoriev and Shpilrain. This note provides a new countermeasures against those attacks. Thereby, we (temporarily?) shift the fire from the signature algorithm to redirect attacks on the key and on tropical polynomial factorization.
We present a side-channel attack on CRYSTALS-Dilithium, a post-quantum secure digital signature scheme, with two variants of post-processing. The side-channel attack exploits information leakage in the secret key unpacking procedure of the signing algorithm to recover the coefficients of the polynomials in the secret key vectors ${\bf s}_1$ and ${\bf s}_2$ by profiled deep learning-assisted power analysis. In the first variant, one half of the coefficients of ${\bf s}_1$ and ${\bf s}_2$ is...
A recent line of research has introduced a systematic approach to explore the complexity of explicit construction problems through the use of meta problems, namely, the range avoidance problem (abbrev. $\textsf{Avoid}$) and the remote point problem (abbrev. $\textsf{RPP}$). The upper and lower bounds for these meta problems provide a unified perspective on the complexity of specific explicit construction problems that were previously studied independently. An interesting question largely...
Motivated by the violation of two fundamental assumptions in secure communication - receiver-privacy and sender-freedom - by a certain entity referred to as ``the dictator'', Persiano et al. introduced the concept of Anamorphic Encryption (AME) for public key cryptosystems (EUROCRYPT 2022). Specifically, they presented receiver/sender-AME, directly tailored to scenarios where receiver privacy and sender freedom assumptions are compromised, respectively. In receiver-AME, entities share a...
In recent years, quantum computers and Shor’s quantum algorithm have been able to effectively solve NP (Non-deterministic Polynomial-time) problems such as prime factorization and discrete logarithm problems, posing a threat to current mainstream asymmetric cryptography, including RSA and Elliptic Curve Cryptography (ECC). As a result, the National Institute of Standards and Technology (NIST) in the United States call for Post-Quantum Cryptography (PQC) methods that include lattice-based...
The evolution of quantum algorithms threatens to break public key cryptography in polynomial time. The development of quantum-resistant algorithms for the post-quantum era has seen a significant growth in the field of post quantum cryptography (PQC). Polynomial multiplication is the core of Ring Learning with Error (RLWE) lattice based cryptography (LBC) which is one of the most promising PQC candidates. In this work, we present the design of fast and energy-efficient pipelined Number...
In their 2022 study, Kuang et al. introduced the Multivariable Polynomial Public Key (MPPK) cryptography, a quantum-safe public key cryptosystem leveraging the mutual inversion relationship between multiplication and division. MPPK employs multiplication for key pair construction and division for decryption, generating public multivariate polynomials. Kuang and Perepechaenko expanded the cryptosystem into the Homomorphic Polynomial Public Key (HPPK), transforming product polynomials over...
As NIST is putting the final touches on the standardization of PQC (Post Quantum Cryptography) public key algorithms, it is a racing certainty that peskier cryptographic attacks undeterred by those new PQC algorithms will surface. Such a trend in turn will prompt more follow-up studies of attacks and countermeasures. As things stand, from the attackers’ perspective, one viable form of attack that can be implemented thereupon is the so-called “side-channel attack”. Two best-known...
There has been a recent interest in proposing quantum protocols whose security relies on weaker computational assumptions than their classical counterparts. Importantly to our work, it has been recently shown that public-key encryption (PKE) from one-way functions (OWF) is possible if we consider quantum public keys. Notice that we do not expect classical PKE from OWF given the impossibility results of Impagliazzo and Rudich (STOC'89). However, the distribution of quantum public keys is a...
Public key encryption with keyword search (PEKS), formalized by Boneh et al. [EUROCRYPT' 04], enables secure searching for specific keywords in the ciphertext. Nevertheless, in certain scenarios, varying user tiers are granted disparate data searching privileges, and administrators need to restrict the searchability of ciphertexts to select users exclusively. To address this concern, Jiang et al. [ACISP' 16] devised a variant of PEKS, namely public key encryption with authorized keyword...
In Crypto 94, Chor, Fiat, and Naor first introduced the traitor tracing (TT) systems, which aim at helping content distributors identify pirates. Since its introduction, many traitor tracing schemes have been proposed. However, we observe until now almost all the traitor tracing systems using probabilistic public key (and secret key) encryption as the the content distribution algorithm, they do not consider this basic fact: the malicious encrypter can plant some trapdoor in the randomness...
Power analysis of public-key algorithms is a well-known approach in the community of side-channel analysis. We usually classify operations based on the differences in power traces produced by different basic operations (such as modular exponentiation) to recover secret information like private keys. The more accurate the segmentation of power traces, the higher the efficiency of their classification. There exist two commonly used methods: one is equidistant segmentation, which requires a...
With the advancement of quantum computers, it has been demonstrated that Shor's algorithm enables public key cryptographic attacks to be performed in polynomial time. In response, NIST conducted a Post-Quantum Cryptography Standardization competition. Additionally, due to the potential reduction in the complexity of symmetric key cryptographic attacks to square root with Grover's algorithm, it is increasingly challenging to consider symmetric key cryptography as secure. In order to establish...
Quantum computers, especially those with over 10,000 qubits, pose a potential threat to current public key cryptography systems like RSA and ECC due to Shor's algorithms. Grover's search algorithm is another quantum algorithm that could significantly impact current cryptography, offering a quantum advantage in searching unsorted data. Therefore, with the advancement of quantum computers, it is crucial to analyze potential quantum threats. While many works focus on Grover’s attacks in...
Given the importance of cryptography to modern security and privacy solutions, it is surprising how little attention has been given to the problem of \textit{cryptographic agility}, or frameworks enabling the transition from one cryptographic algorithm or implementation to another. In this paper, we argue that traditional notions of cryptographic agility fail to capture the challenges facing modern enterprises that will soon be forced to implement a disruptive migration from today’s public...
The McEliece cryptosystem is a strong contender for post-quantum schemes, including key encapsulation for confidentiality of key exchanges in network protocols. A McEliece secret key is a structured parity check matrix that is transformed via Gaussian elimination into an unstructured public key. We show that this transformation is a highly critical operation with respect to side-channel leakage. We assume leakage of the elementary row operations during Gaussian elimination, motivated by...
In the aftermath of the Snowden revelations in 2013, concerns about the integrity and security of cryptographic systems have grown significantly. As adversaries with substantial resources might attempt to subvert cryptographic algorithms and undermine their intended security guarantees, the need for subversion-resilient cryptography has become paramount. Security properties are preserved in subversion-resilient schemes, even if the adversary implements the scheme used in the security...
In 2023, Basso, Maino, and Pope proposed FESTA (Fast Encryption from Supersingular Torsion Attacks), an isogeny-based public-key encryption (PKE) protocol that uses the SIDH attack for decryption. In the same paper, they proposed a parameter for that protocol, but the parameter requires high-degree isogeny computations. In this paper, we introduce QFESTA (Quaternion Fast Encapsulation from Supersingular Torsion Attacks), a new variant of FESTA that works with better parameters using...
In this paper, we initiate the study of the Rank Decoding (RD) problem and LRPC codes with blockwise structures in rank-based cryptosystems. First, we introduce the blockwise errors ($\ell$-errors) where each error consists of $\ell$ blocks of coordinates with disjoint supports, and define the blockwise RD ($\ell$-RD) problem as a natural generalization of the RD problem whose solutions are $\ell$-errors (note that the standard RD problem is actually a special $\ell$-RD problem with...
Orientations of supersingular elliptic curves encode the information of an endomorphism of the curve. Computing the full endomorphism ring is a known hard problem, so one might consider how hard it is to find one such orientation. We prove that access to an oracle which tells if an elliptic curve is $\mathfrak{O}$-orientable for a fixed imaginary quadratic order $\mathfrak{O}$ provides non-trivial information towards computing an endomorphism corresponding to the $\mathfrak{O}$-orientation....
Wave is a code-based digital signature scheme. Its hardness relies on the unforgeability of signature and the indistinguishability of its public key, a parity check matrix of a ternary $(U, U+V)$-code. The best known attacks involve solving the Decoding Problem using the Information Set Decoding algorithm (ISD) to defeat these two problems. Our main contribution is the description of a quantum smoothed Wagner's algorithm within the ISD, which improves the forgery attack on Wave in the...
The question of whether public-key encryption (PKE) can be constructed from the assumption that one-way functions (OWF) exist remains a central open problem. In this paper we give two constructions of bit PKE scheme derived from any NP language L, along with a polynomial-time instance-witness sampling algorithm. Furthermore, we prove that if L is average hard NP language, the the presented schemes is CPA secure. Our results give a positive answer to this longstanding problem, as the...
The recent technological advances in Post-Quantum Cryptography (PQC) raise the questions of robust implementations of new asymmetric cryptographic primitives in today’s technology. This is the case for the lattice-based Module Lattice-Key Encapsulation Mechanism (ML-KEM) algorithm which is proposed by the NIST as the first standard for Public Key Encryption (PKE) and Key Encapsulation Mechanism (KEM), taking inspiration from CRYSTALS-Kyber. We have notably to make sure the ML-KEM...
CRYSTALS-Kyber, as the only public key encryption (PKE) algorithm selected by the National Institute of Standards and Technology (NIST) in the third round, is considered one of the most promising post-quantum cryptography (PQC) schemes. Lattice-based cryptography uses complex discrete alogarithm problems on lattices to build secure encryption and decryption systems to resist attacks from quantum computing. Performance is an important bottleneck affecting the promotion of post quantum...
We present new protocols for threshold Schnorr signatures that work in an asynchronous communication setting, providing robustness and optimal resilience. These protocols provide unprecedented performance in terms of communication and computational complexity. In terms of communication complexity, for each signature, a single party must transmit a few dozen group elements and scalars across the network (independent of the size of the signing committee). In terms of computational...
A universal re-encryption (URE) scheme is a public-key encryption scheme enhanced with an algorithm that on input a ciphertext, outputs another ciphertext which is still a valid encryption of the underlying plaintext. Crucially, such a re-encryption algorithm does not need any key as input, but the ciphertext is guaranteed to be valid under the original key-pair. Therefore, URE schemes lend themselves naturally as building blocks of mixnets: A sender transmits the encryption of a message...
The number-theoretic literature has long studied the question of distributions of sequences of quadratic residue symbols modulo a prime number. In this paper, we present an efficient algorithm for generating primes containing chosen sequences of quadratic residue symbols and use it as the basis of a method extending the functionality of additively homomorphic cryptosystems. We present an algorithm for encoding a chosen Boolean function into the public key and an efficient two-party...
As a multi-receiver variants of public key encryption with keyword search (PEKS), broadcast encryption with keyword search (BEKS) has been proposed (Attrapadung et al. at ASIACRYPT 2006/Chatterjee-Mukherjee at INDOCRYPT 2018). Unlike broadcast encryption, no receiver anonymity is considered because the test algorithm takes a set of receivers as input and thus a set of receivers needs to be contained in a ciphertext. In this paper, we propose a generic construction of BEKS from anonymous and...
NIST has recently selected CRYSTALS-Kyber as a new public key encryption and key establishment algorithm to be standardized. This makes it important to evaluate the resistance of CRYSTALS-Kyber implementations to side-channel attacks. Software implementations of CRYSTALS-Kyber have already been thoroughly analysed. The discovered vulnerabilities helped improve the subsequently released versions and promoted stronger countermeasures against side-channel attacks. In this paper, we present the...
The low-degree method postulates that no efficient algorithm outperforms low-degree polynomials in certain hypothesis-testing tasks. It has been used to understand computational indistinguishability in high-dimensional statistics. We explore the use of the low-degree method in the context of cryptography. To this end, we apply it in the design and analysis of a new public-key encryption scheme whose security is based on Goldreich's pseudorandom generator. The scheme is a combination of...
In response to side-channel attacks on masked implementations of post-quantum cryptographic algorithms, a new bitsliced higher-order masked implementation of CRYSTALS-Kyber has been presented at CHES'2022. The bitsliced implementations are typically more difficult to break by side-channel analysis because they execute a single instruction across multiple bits in parallel. However, in this paper, we reveal new vulnerabilities in the masked Boolean to arithmetic conversion procedure of this...
The advent of quantum computers poses a serious challenge to the security of cloud infrastructures and services, as they can potentially break the existing public-key cryptosystems, such as Rivest–Shamir–Adleman (RSA) and Elliptic Curve Cryptography (ECC). Even though the gap between today’s quantum computers and the threats they pose to current public-key cryptography is large, the cloud landscape should act proactively and initiate the transition to the post-quantum era as early as...
The major objective of this paper is to present a theoretical model for an algorithm that has not been previously described in the literature, capable of generating a secret key through the transmission of data over a public channel. We explain how the method creates a shared secret key by attaining commutativity through the multiplication of the modular exponentiation of a minimum of two bases and an equal number of private exponents for each party involved in the exchange. In addition, we...
Hofheinz et al. (TCC 2017) proposed several key encapsulation mechanism (KEM) variants of Fujisaki-Okamoto (\textsf{FO}) transformation, including $\textsf{FO}^{\slashed{\bot}}$, $\textsf{FO}_m^{\slashed{\bot}}$, $\textsf{QFO}_m^{\slashed{\bot}}$, $\textsf{FO}^{\bot}$, $\textsf{FO}_m^\bot$ and $\textsf{QFO}_m^\bot$, and they are widely used in the post-quantum cryptography standardization launched by NIST. These transformations are divided into two types, the implicit and explicit rejection...
The Number Field Sieve and its variants are the best algorithms to solve the discrete logarithm problem in finite fields. The Factory variant accelerates the computation when several prime fields are targeted. This article adapts the Factory variant to non-prime finite fields of medium and large characteristic. We combine this idea with two other variants of NFS, namely the tower and special variant. This combination leads to improvements in the asymptotic complexity. Besides, we lay out...
The article introduces HPPC a new Digital Signature scheme that intends to resist known previous attacks applied to HFE-based schemes like QUARTZ and GeMSS. The idea is to use maximal degree for the central HFE polynomial whereas the trapdoor polynomial has low degree in order to sign messages by finding polynomial roots in an extension field via Berlekamp's algorithm. This work has been submitted to NIST's Post-Quantum Cryptography challenge (PQC) and code is available at...
Post-Quantum Cryptography (PQC) defines cryptographic algorithms designed to resist the advent of the quantum computer. Most public-key cryptosystems today are vulnerable to quantum attackers, so a global-scale transition to PQC is expected. As a result, several entities foment efforts in PQC standardization, research, development, creation of Work Groups (WGs), and issuing adoption recommendations. However, there is a long road to broad PQC adoption in practice. This position paper...
We propose a quantum algorithm that crucially involves the receiver's public-key to establish secure communication of an intended message string, using shared entangled-qubits. The public-key in question is a random bit string that proclaims the sequence of measurement basis used by the receiver. As opposed to known quantum key distribution protocols, wherein a random key string is generated at the end of the communication cycle, here the sender's intended bit string itself is...
The hard mathematical problems that assure the security of our current public-key cryptography (RSA, ECC) are broken if and when a quantum computer appears rendering them ineffective for use in the quantum era. Lattice based cryptography is a novel approach to public key cryptography, of which the mathematical investigation (so far) resists attacks from quantum computers. By choosing a module learning with errors (MLWE) algorithm as the next standard, National Institute of Standard \&...
We show the following results: - The post-quantum equivalence of indistinguishability obfuscation and differing inputs obfuscation in the restricted setting where the outputs differ on at most a polynomial number of points. Our result handles the case where the auxiliary input may contain a quantum state; previous results could only handle classical auxiliary input. - Bounded collusion traitor tracing from general public key encryption, where the decoder is allowed to contain a...
The enumeration of all outputs of a given multivariate polynomial is a fundamental mathematical problem and is incorporated in some algebraic attacks on multivariate public key cryptosystems. For a degree-$d$ polynomial in $n$ variables over the finite field with $q$ elements, solving the enumeration problem classically requires $O\left(\tbinom{n+d}{d} \cdot q^n\right)$ operations. At CHES 2010, Bouillaguet et al. proposed a fast enumeration algorithm over the binary field $\mathbb{F}_2$....
Public-key encryption with keyword search (PEKS) was first proposed by Boneh et al. (EUROCRYPT 2004), achieving the ability to search for ciphertext files. Nevertheless, it is vulnerable to inside keyword guessing attacks (IKGA). Public-key authenticated encryption with keyword search (PAEKS), introduced by Huang et al. (Inf. Sci. 2017), on the other hand, is secure against IKGA. Nonetheless, it is susceptible to quantum computing attacks. Liu et al. and Cheng et al. addressed this problem...
Wave is a provably EUF-CMA (existential unforgeability under adaptive chosen message attacks) digital signature scheme based on codes \cite{DST19a}. It is an hash-and-sign primitive and its security is built according to a GPV-like framework \cite{GPV08} under two assumptions related to coding theory: (i) the hardness of finding a word of prescribed Hamming weight and prescribed syndrome, and (ii) the pseudo-randomness of ternary generalized $(U|U+V)$ codes. Forgery attacks (i)---or message...
We propose hinTS --- a new threshold signature scheme built on top of the widely used BLS signatures. Our scheme enjoys the following attractive features: \begin{itemize} \item A {\em silent setup} process where the joint public key of the parties is computed as a deterministic function of their locally computed public keys. \item Support for {\em dynamic} choice of thresholds and signers, after the silent setup, without further interaction. \item Support for {\em general}...
The generalized inverses of systematic non-square binary matrices have applications in mathematics, channel coding and decoding, navigation signals, machine learning, data storage, and cryptography, such as the McEliece and Niederreiter public-key cryptosystems. A systematic non-square (n−k)×n matrix H, n > k, has 2 power k×(n−k) different generalized inverse matrices. This paper presents an algorithm for generating these matrices and compares it with two well-known methods, i.e....
The wave of attacks by Castryck and Decru (Eurocrypt, 2023), Maino, Martindale, Panny, Pope and Wesolowski (Eurocrypt, 2023) and Robert (Eurocrypt, 2023), highlight the destructive facet of calculating power-smooth degree isogenies between higher-dimensional abelian varieties in isogeny-based cryptography. Despite those recent attacks, there is still interest in using isogenies but for building protocols on top of higher-dimensional abelian varieties. Examples of such protocols are...
We construct quantum public-key encryption from one-way functions. In our construction, public keys are quantum, but ciphertexts are classical. Quantum public-key encryption from one-way functions (or weaker primitives such as pseudorandom function-like states) are also proposed in some recent works [Morimae-Yamakawa, eprint:2022/1336; Coladangelo, eprint:2023/282; Barooti-Grilo-Malavolta-Sattath-Vu-Walter, eprint:2023/877]. However, they have a huge drawback: they are secure only when...
In the average-case $k$-SUM problem, given $r$ integers chosen uniformly at random from $\{0,\ldots,M-1\}$, the objective is to find a "solution" set of $k$ numbers that sum to $0$ modulo $M$. In the dense regime of $M \leq r^k$, where solutions exist with high probability, the complexity of these problems is well understood. Much less is known in the sparse regime of $M\gg r^k$, where solutions are unlikely to exist. In this work, we initiate the study of the sparse regime for...
Password Authenticated Key Exchange (PAKE) have become a key building block in many security products as they provide interesting efficiency/security trade-offs. Indeed, a PAKE allows to dispense with the heavy public key infrastructures and its efficiency and portability make it well suited for applications such as Internet of Things or e-passports. With the emerging quantum threat and the effervescent development of post-quantum public key algorithms in the last five years, one would...
The generalized inverses of systematic non-square binary matrices have applications in mathematics, channel coding and decoding, navigation signals, machine learning, data storage and cryptography such as the McEliece and Niederreiter public-key cryptosystems. A systematic non-square $(n-k) \times n$ matrix $H$, $n > k$, has $2^{k\times(n-k)}$ different generalized inverse matrices. This paper presents an algorithm for generating these matrices and compares it with two well-known methods,...
As a typical representative of the public key cryptosystem, RSA has attracted a great deal of cryptanalysis since its invention, among which a famous attack is the small private exponent attack. It is well-known that the best theoretical upper bound for the private exponent d that can be attacked is d ≤ N^0.292 , where N is a RSA modulus. However, this bound may not be achieved in practical attacks since the lattice constructed by Coppersmith method may have a large enough dimension...
Digital signatures ensure legitimate access through identity authentication. It is also used to build blocks in blockchains and to authenticate transactions. The Courtois-Finiasz-Sendrier (CFS) digital signature is a well-known code-based digital signature scheme based on the Niederreiter cryptosystem. The CFS signature, however, is not widely used due to the long processing time required by its signing algorithm. Most code-based digital signature schemes are based on Niederreiter. The...
The security of cryptographic primitives is an important issue. The Shor algorithm illustrates how quantum attacks threaten the security of these widely used primitives. Code-based cryptography is one of several approaches resistant to quantum attacks. To date, no attack has been able to break a code-based cryptosystem in polynomial time. Despite this level of security, these cryptosystems have not been considered for practical applications such as e-commerce, medical and industrial IoT,...
Electronic Medical Records (EMRs) have been utilized in plentiful medical institutions due to their superior convenience and low storage overhead. Nevertheless, it is difficult for medical departments with disparate management regulations to share EMRs through secure communication channels since sensitive EMRs are prone to be tampered with. Therefore, the EMRs should be encrypted before being outsourced to the network servers. Public key Encryption with Keyword Search (PEKS) has the ability...
Among the fourth round finalists of the NIST post-quantum cryptography standardization process for public-key encryption algorithms and key encapsulation mechanisms, three rely on hard problems from coding theory. Key encapsulation mechanisms are frequently used in hybrid cryptographic systems: a public-key algorithm for key exchange and a secret key algorithm for communication. A major point is thus the initial key exchange that is performed thanks to a key encapsulation mechanism. In this...
Cryptographic algorithms are vital components ensuring the privacy and security of computer systems. They have constantly improved and evolved over the years following new developments, attacks, breaks, and lessons learned. A recent example is that of quantum-resistant cryptography, which has gained a lot of attention in the last decade and is leading to new algorithms being standardized today. These algorithms, however, present a real challenge: they come with strikingly different size and...
We introduce the notion of public key encryption with secure key leasing (PKE-SKL). Our notion supports the leasing of decryption keys so that a leased key achieves the decryption functionality but comes with the guarantee that if the quantum decryption key returned by a user passes a validity test, then the user has lost the ability to decrypt. Our notion is similar in spirit to the notion of secure software leasing (SSL) introduced by Ananth and La Placa (Eurocrypt 2021) but captures...
The LWE problem is one of the prime candidates for building the most efficient post-quantum secure public key cryptosystems. Many of those schemes, like Kyber, Dilithium or those belonging to the NTRU-family, such as NTRU-HPS, -HRSS, BLISS or GLP, make use of small max norm keys to enhance efficiency. The presumably best attack on these schemes is a hybrid attack, which combines combinatorial techniques and lattice reduction. While lattice reduction is not known to be able to exploit the...
In this work we present a lightweight lattice-based identification protocol based on the CPA-secured public key encryption scheme Kyber. It is designed as a replacement for existing classical ECC- or RSA-based identification protocols in IoT, smart card applications, or for device authentication. The proposed protocol is simple, efficient, and implementations are supposed to be easy to harden against side-channel attacks. Compared to standard constructions for identification protocols based...
The elliptic curve family of schemes has the lowest computational latency, memory use, energy consumption, and bandwidth requirements, making it the most preferred public key method for adoption into network protocols. Being suitable for embedded devices and applicable for key exchange and authentication, ECC is assuming a prominent position in the field of IoT cryptography. The attractive properties of the relatively new curve Curve448 contribute to its inclusion in the TLS1.3 protocol and...
Recently, SIDH was broken by a series of attacks. To avoid the attacks, several new countermeasures, such as M-SIDH and binSIDH, have been developed. Different from SIDH, the new SIDH-like schemes have relatively large public key sizes. Besides, the orders of the torsion groups considered in new SIDH-like schemes are the products of many primes. Therefore, the key compression techniques in SIDH can not be directly applied to these schemes. It remains an open problem to compress the public...
Streamlined NTRU Prime is a lattice-based Key Encapsulation Mechanism (KEM) that is, together with X25519, currently the default algorithm in OpenSSH 9. Being based on lattice assumptions, it is assumed to be secure also against attackers with access to large-scale quantum computers. While Post-Quantum Cryptography (PQC) schemes have been subject to extensive research in the recent years, challenges remain with respect to protection mechanisms against attackers that have additional...
Since the post-quantum crypto system CRYSTALS-KYBER has been chosen for standardization by the National Institute for Standards and Technology (US), a formal verification of its correctness and security properties becomes even more relevant. Using the automated theorem prover Isabelle, we are able to formalize the algorithm specifications and parameter sets of Kyber's public key encryption scheme and verify the $\delta$-correctness and indistinguishability under chosen plaintext attack...
The use of traditional cryptography based on symmetric keys has been replaced with the revolutionary idea discovered by Diffie and Hellman in 1976 that fundamentally changed communication systems by ensuring a secure transmission of information over an insecure channel. Nowadays public key cryptography is frequently used for authentication in e-commerce, digital signatures and encrypted communication. Most of the public key cryptosystems used in practice are based on integer factorization...
We are applying Fermat’s factorization algorithm to sets of public RSA keys. Fermat’s factorization allows efficiently calculating the prime factors of a composite number if the difference between the two primes is small. Knowledge of the prime factors of an RSA public key allows efficiently calculating the private key. A flawed RSA key generation function that produces close primes can therefore be attacked with Fermat’s factorization. We discovered a small number of vulnerable devices...
The SIDH protocol is an isogeny-based key exchange protocol using supersingular isogenies, designed by Jao and De Feo in 2011. The protocol underlies the SIKE algorithm which advanced to the fourth round of NIST's post-quantum standardization project in May 2022. The algorithm was considered very promising: indeed the most significant attacks against SIDH were meet-in-the-middle variants with exponential complexity, and torsion point attacks which only applied to unbalanced parameters...
The DECentralized Oracle (DECO) protocol enables the verifiable provenance of data from Transport Layer Security (TLS) connections through secure two-party computation and zero-knowledge proofs. In this paper, we present PECO, an extension of DECO that enhances privacy features through the integration of two new private three-party handshake protocols (P3P-HS). PECO allows any web user to prove to a verifier the properties of data from TLS connections without disclosing the identity of the...
CRYSTALS-Kyber has been selected by the NIST as a public-key encryption and key encapsulation mechanism to be standardized. It is also included in the NSA's suite of cryptographic algorithms recommended for national security systems. This makes it important to evaluate the resistance of CRYSTALS-Kyber's implementations to side-channel attacks. The unprotected and first-order masked software implementations have been already analysed. In this paper, we present deep learning-based message...
This paper introduces new digital signature scheme whose security against existential forgery under adaptive chosen message attack is based on hardness of the Syndrome Decoding Problem. The hardness assumption is quite simple and hence easy to analyze and investigate. The scheme as whole is neat with intuitive security definition and proof in addition to elegant and efficient signing and verifying algorithms. We propose parameter sets for three security levels (128-bits, 192-bits, and 256...
Shuffling is a well-known countermeasure against side-channel analysis. It typically uses the Fisher-Yates (FY) algorithm to generate a random permutation which is then utilized as the loop iterator to index the processing of the variables inside the loop. The processing order is scrambled as a result, making side-channel analysis more difficult. Recently, a side-channel attack on a masked and shuffled implementation of Saber requiring 61,680 power traces to extract the secret key was...
In 2009, Lyubashevsky proposed a lattice-based signature scheme by applying the Fiat-Shamir transformation and proved its security under the generalized compact knapsack (GCK) problem. This scheme has a simple structure but has large signature and key sizes due to the security requirement of their security reduction. Dilithium, which was submitted to the NIST Post-Quantum Cryptography standardization and selected as one of the final candidates, is an improvement of the Lyubashevsky's...
NTRU was the first practical public key encryption scheme constructed on a lattice over a polynomial-based ring and has been considered secure against significant cryptanalytic attacks over the past few decades. However, NTRU and its variants suffer from several drawbacks, including difficulties in achieving worst-case correctness error in a moderate modulus, inconvenient sampling distributions for messages, and relatively slower algorithms compared to other lattice-based schemes. In...
We propose and analyze LowMS, a new rank-based key encapsulation mechanism (KEM). The acronym stands for Loidreau with Multiple Syndromes, since our work combines the cryptosystem of Loidreau (presented at PQCrypto 2017) together with the multiple syndrome approach, that allows to reduce parameters by sending several syndromes with the same error support in one ciphertext. Our scheme is designed without using ideal structures. Considering cryptosystems without such an ideal structure,...
Typical lattice-based cryptosystems are commonly believed to resist multi-target attacks. For example, the New Hope proposal stated that it avoids "all-for-the-price-of-one attacks". An ACM CCS 2021 paper from Duman–Hövelmanns–Kiltz–Lyubashevsky–Seiler stated that "we can show that Adv_{PKE}^{IND-CPA} ≈ Adv_{PKE}^{(n,q_C)-IND-CPA} for "lattice-based schemes" such as Kyber, i.e. that one-out-of-many-target IND-CPA is as difficult to break as single-target IND-CPA, assuming "the hardness of...
Quantum computing advances threaten the security of today's public key infrastructure, and have led to the pending standardization of alternative, quantum-resistant key encapsulation and digital signature cryptography schemes. Unfortunately, authentication algorithms based on the new post-quantum (PQ) cryptography create significant performance bottlenecks for TLS due to larger certificate chains which introduce additional packets and round-trips. The TLS handshake slowdown will be...
FALCON and Crystals-Dilithium are the digital signatures algorithms selected as NIST PQC standards at the end of the third round. FALCON has the advantage of the shortest size of the combined public key and signature but has the disadvantage of the relatively long signing time. Since FALCON algorithm is faithfully designed based on theoretical security analysis, the implementation of the algorithms is quite complex and needs considerable complexity. In order to implement the FALCON...
A cryptographic primitive based on the Learning With Errors (LWE) problem with variants is a promising candidate for the efficient quantum-resistant public key cryptosystem. As the parameters for such cryptosystems are chosen by the concrete attack cost for the corresponding LWE problem, improving LWE solving algorithm has a significant importance. In this paper, we present a new hybrid attack on the LWE problem. This new attack combines the primal lattice attack and an improved variant...
CRYSTALS-Kyber has been recently selected by the NIST as a new public-key encryption and key-establishment algorithm to be standardized. This makes it important to assess how well CRYSTALS-Kyber implementations withstand side-channel attacks. Software implementations of CRYSTALS-Kyber have been already analyzed and the discovered vulnerabilities were patched in the subsequently released versions. In this paper, we present a profiling side-channel attack on a hardware implementation of...
Threshold cryptographic algorithms achieve robustness against key and access compromise by distributing secret keys among multiple entities. Most prior work focuses on threshold public-key primitives, despite extensive use of authenticated encryption in practice. Though the latter can be deployed in a threshold manner using multi-party computation (MPC), doing so incurs a high communication cost. In contrast, dedicated constructions of threshold authenticated encryption algorithms can...
Fully Homomorphic encryption allows the evaluation of any circuits over encrypted data while preserving the privacy of the data. However, without any additional properties, no guarantee is provided for the privacy of the circuits which are evaluated. A sanitization algorithm allows to destroy all previous information about how a ciphertext was obtained, ensuring that the circuit which was evaluated remains secret. In this paper, we present two techniques to randomize RLWE ciphertexts, and...
Predicate encryption (PE) is a type of public-key encryption that captures many useful primitives such as attribute-based encryption (ABE). Although much progress has been made to generically achieve security against chosen-plaintext attacks (CPA) efficiently, in practice, we also require security against chosen-ciphertext attacks (CCA). Because achieving CCA-security on a case-by-case basis is a complicated task, several generic conversion methods have been proposed. However, these...
Deniable public-key encryption (DPKE) is a cryptographic primitive that allows the sender of an encrypted message to later claim that they sent a different message. DPKE's threat model assumes powerful adversaries who can coerce users to reveal plaintexts; it is thus reasonable to consider other advanced capabilities, such as the ability to subvert algorithms in a so-called Algorithm Substitution Attack (ASA). An ASA replaces a trusted algorithm with a subverted version that undermines...
