682 results sorted by ID
Possible spell-corrected query: Public-key algorithm
From Worst-Case Hardness of $\mathsf{NP}$ to Quantum Cryptography via Quantum Indistinguishability Obfuscation
Tomoyuki Morimae, Yuki Shirakawa, Takashi Yamakawa
Foundations
Indistinguishability obfuscation (iO) has emerged as a powerful cryptographic primitive with many implications. While classical iO, combined with the infinitely-often worst-case hardness of $\mathsf{NP}$, is known to imply one-way functions (OWFs) and a range of advanced cryptographic primitives, the cryptographic implications of quantum iO remain poorly understood. In this work, we initiate a study of the power of quantum iO. We define several natural variants of quantum iO, distinguished...
UOV-Based Verifiable Timed Signature Scheme
Erkan Uslu, Oğuz Yayla
Cryptographic protocols
Verifiable Timed Signatures (VTS) are cryptographic primitives that enable the creation of a signature that can only be retrieved after a specific time delay, while also providing verifiable evidence of its existence. This framework is particularly useful in blockchain applications. Current VTS schemes rely on signature algorithms such as BLS, Schnorr, and ECDSA, which are vulnerable to quantum attacks due to the vulnerability of the discrete logarithm problem to Shor's Algorithm. We...
Security Analysis on a Public-Key Inverted-Index Keyword Search Scheme with Designated Tester
Mizuki Hayashi, Keita Emura
Cryptographic protocols
Gao et al. (IEEE Internet of Things Journal 2024) proposed public-key inverted-index keyword search with designated tester as an extension of public key encryption with keyword search (PEKS). In their scheme, a server (a tester) has a secret key and uses the key for running the search algorithm due to the designated tester setting. They proved that no information of keyword is revealed from trapdoors under the decisional Diffie-Hellman (DDH) assumption. However, they also employed a...
Efficient, Scalable Threshold ML-DSA Signatures: An MPC Approach
Alexander Bienstock, Leo de Castro, Daniel Escudero, Antigoni Polychroniadou, Akira Takahashi
Cryptographic protocols
A threshold signature is an advanced protocol that splits a secret signing key among multiple parties, allowing any subset above a threshold to jointly generate a signature. While post-quantum (PQ) threshold signatures are actively being studied --- especially in response to NIST's recent call for threshold schemes --- most existing solutions are tailored to specially designed, threshold-friendly signature schemes. In contrast, many real-world applications, such as distributed certificate...
Security Analysis on UOV Families with Odd Characteristics: Using Symmetric Algebra
Yi Jin, Yuansheng Pan, Xiaoou He, Boru Gong, Jintai Ding
Attacks and cryptanalysis
Multivariate public key cryptosystems represent a promising family of post-quantum cryptographic schemes. Extensive research has demonstrated that multivariate polynomials are particularly well-suited for constructing digital signature schemes. Notably, the Unbalanced Oil and Vinegar (UOV) signature scheme and its variants have emerged as leading candidates in NIST's recent call for additional digital signature proposals.
Security analysis against UOV variants are typically categorized...
Cryptography meets worst-case complexity: Optimal security and more from iO and worst-case assumptions
Rahul Ilango, Alex Lombardi
Foundations
We study several problems in the intersection of cryptography and complexity theory based on the following high-level thesis.
1) Obfuscation can serve as a general-purpose worst-case to average-case reduction, reducing the existence of various forms of cryptography to corresponding worst-case assumptions.
2) We can therefore hope to overcome barriers in cryptography and average-case complexity by (i) making worst-case hardness assumptions beyond $\mathsf{P}\neq \mathsf{NP}$, and...
Insecurity of One Ring Signature Scheme with Batch Verification for Applications in VANETs
Zhengjun Cao, Lihua Liu
Attacks and cryptanalysis
We show that the Negi-Kumar certificateless ring signature scheme [Wirel. Pers. Commun. 134(4): 1987-2011 (2024)] is insecure against forgery attack. The signer's public key $PK_j$ and secret key $PSK_j$ are simply invoked to compute the hash value $H_{2_j}=h_5(m_j\|PSK_j\|PK_j\|t_j)$, which cannot be retrieved by the verifier for checking their dependency. The explicit dependency between the public key and secret key is not properly used to construct some intractable problems, such...
On the security of one certificateless aggregate signature scheme with dynamic revocation in vehicular ad-hoc networks
Zhengjun Cao, Lihua Liu
Attacks and cryptanalysis
We show that the certificateless signature scheme [Veh. Commun. 47: 100763 (2024)] is insecure, because an adversary can launch forgery attack for any message. The signer's certificateless public key is not tightly bound to the system public key. The inherent flaw results in that the adversary can find an efficient signing algorithm functionally equivalent to the valid signing algorithm. The findings in this note could be helpful for newcomers who are not familiar with the designing...
Energy Consumption Framework and Analysis of Post-Quantum Key-Generation on Embedded Devices
J Cameron Patterson, William J Buchanan, Callum Turino
Applications
The emergence of quantum computing and Shor's algorithm necessitates an imminent shift from current public key cryptography techniques to post-quantum robust techniques. NIST has responded by standardising Post-Quantum Cryptography (PQC) algorithms, with ML-KEM (FIPS-203) slated to replace ECDH (Elliptic Curve Diffie-Hellman) for key exchange. A key practical concern for PQC adoption is energy consumption. This paper introduces a new framework for measuring the PQC energy consumption on a...
Public-key Cryptography Attacks Using Adiabatic Quantum Computer
Weishen Zou, Bruno Martin, Thomas Prévost
Attacks and cryptanalysis
We explore the application of the QUBO and Ising models to the integer factorization problem with implications for the security of public-key algorithms such as RSA. A key contribution is a program that applies existing algorithms to parameterize and simulate integer factorization through an Ising model in order to replicate previous works. Due to limited access to quantum hardware, we use classical heuristic methods to approximate solutions.
Classify Directly: A Dynamic Time SPA Classification Method Based on DTW
Yaoling Ding, Haotong Xu, Annyu Liu, An Wang, Jingqi Zhang, Jing Yu, Liehuang Zhu
Attacks and cryptanalysis
Side-channel analysis remains a critical threat to public-key cryptographic implementations. Simple Power Analysis (SPA) techniques can extract secret keys from a single power trace, often using clustering-based classification methods. However, traces captured in real-world environments often suffer from misalignment and variable trace lengths due to unstable clocks and random delays. As a result, clustering methods are required to use alignment methods that may alter the original...
Post-Quantum PKE from Unstructured Noisy Linear Algebraic Assumptions: Beyond LWE and Alekhnovich's LPN
Riddhi Ghosal, Aayush Jain, Paul Lou, Amit Sahai, Neekon Vafa
Public-key cryptography
Noisy linear algebraic assumptions with respect to random matrices, in particular Learning with Errors ($\mathsf{LWE}$) and Alekhnovich Learning Parity with Noise (Alekhnovich $\mathsf{LPN}$), are among the most investigated assumptions that imply post-quantum public-key encryption (PKE). They enjoy elegant mathematical structure. Indeed, efforts to build post-quantum PKE and advanced primitives such as homomorphic encryption and indistinguishability obfuscation have increasingly focused...
A Note on ``CABC: A Cross-Domain Authentication Method Combining Blockchain with Certificateless Signature for IIoT''
Zhengjun Cao, Lihua Liu
Attacks and cryptanalysis
We show that the authentication method [Future Gener. Comput. Syst. 158: 516-529 (2024)] cannot be practically implemented, because the signature scheme is insecure against certificateless public key replacement forgery attack. The explicit dependency between the certificateless public key and secret key is not properly used to construct some intractable problems, such as Elliptic Curve Discrete Logarithm (ECDL). An adversary can find an efficient signing algorithm functionally...
Time-Space Tradeoffs of Truncation with Preprocessing
Krzysztof Pietrzak, Pengxiang Wang
Foundations
Truncation of cryptographic outputs is a technique that was recently introduced in Baldimtsi et al. [BCCK22]. The general idea is to try out many inputs to some cryptographic algorithm until the output (e.g. a public-key or some hash value) falls into some sparse set and thus can be compressed: by trying out an expected $2^k$ different inputs one will find an output that starts with $k$ zeros.
Using such truncation one can for example save substantial gas fees on Blockchains where...
Biextensions in pairing-based cryptography
Jianming Lin, Damien Robert, Chang-An Zhao, Yuhao Zheng
Implementation
Bilinear pairings constitute a cornerstone of public-key cryptography, where advancements in Tate pairings and their efficient variants have emerged as a critical research domain within cryptographic science. Currently, the computation of pairings can be effectively implemented through three distinct algorithmic approaches: Miller’s algorithm, the elliptic net algorithm (as developed by Stange), and cubical-based algorithms (as proposed by Damien Robert). Biextensions are the geometric...
Cryptomania v.s. Minicrypt in a Quantum World
Longcheng Li, Qian Li, Xingjian Li, Qipeng Liu
Foundations
We prove that it is impossible to construct perfect-complete quantum public-key encryption (QPKE) with classical keys from quantumly secure one-way functions (OWFs) in a black-box manner, resolving a long-standing open question in quantum cryptography.
Specifically, in the quantum random oracle model (QROM), no perfect-complete QPKE scheme with classical keys, and classical/quantum ciphertext can be secure. This improves the previous works which require either unproven conjectures or...
On breaking McEliece keys using brute force
Lorenz Panny
Attacks and cryptanalysis
In the McEliece public-key encryption scheme, a private key is almost always not determined uniquely by its associated public key. This paper gives a structural characterization of equivalent private keys, generalizing a result known for the more approachable special case $\lvert L\rvert=q$.
These equivalences reduce the cost estimate for a simple private-key search using the support-splitting algorithm (SSA) by a polynomial but practically very substantial factor.
We provide an optimized...
Insecurity of One Decentralized Attribute-based Signature Scheme for Social Co-governance
Zhengjun Cao, Lihua Liu
Attacks and cryptanalysis
We show that the attribute-based signature scheme [Information Sciences, 654(2024), 119839] is insecure, because an adversary can generate valid signatures for any message even though he cannot access the signer's secret key. The four components of signature $\{\delta_1, \delta_2, \delta_3, \delta_4\}$ are not tightly bound to the target message $M$ and the signer's public key. The dependency between the signer's public key and secret key is not properly used to construct any intractable...
Efficient Proofs of Possession for Legacy Signatures
Anna P. Y. Woo, Alex Ozdemir, Chad Sharp, Thomas Pornin, Paul Grubbs
Applications
Digital signatures underpin identity, authenticity, and trust in modern computer systems. Cryptography research has shown that it is possible to prove possession of a valid message and signature for some public key, without revealing the message or signature. These proofs of possession work only for specially-designed signature schemes. Though these proofs of possession have many useful applications to improving security, privacy, and anonymity, they are not currently usable for widely...
An Efficient Sequential Aggregate Signature Scheme with Lazy Verification
Arinjita Paul, Sabyasachi Dutta, Kouichi Sakurai, C. Pandu Rangan
Public-key cryptography
A sequential aggregate signature scheme (SAS) allows multiple potential signers to sequentially aggregate their respective signatures into a single compact signature. Typically, verification of a SAS signatures requires access to all messages and public key pairs utilized in the aggregate generation. However, efficiency is crucial for cryptographic protocols to facilitate their practical implementation. To this end, we propose a sequential aggregate signature scheme with lazy verification...
Side-Channel and Fault Injection Attacks on VOLEitH Signature Schemes: A Case Study of Masked FAEST
Sönke Jendral, Elena Dubrova
Attacks and cryptanalysis
Ongoing efforts to transition to post-quantum public-key cryptosystems have created the need for algorithms with a variety of performance characteristics and security assumptions.
Among the candidates in NIST's post-quantum standardisation process for additional digital signatures is FAEST, a Vector Oblivious Linear Evaluation in-the-Head (VOLEitH)-based scheme, whose security relies on the one-wayness of the Advanced Encryption Standard (AES).
The VOLEitH paradigm enables competitive...
Another Look at the Quantum Security of the Vectorization Problem with Shifted Inputs
Paul Frixons, Valerie Gilchrist, Péter Kutas, Simon-Philipp Merz, Christophe Petit
Attacks and cryptanalysis
Cryptographic group actions provide a basis for simple post-quantum generalizations of many cryptographic protocols based on the discrete logarithm problem (DLP). However, many advanced group action-based protocols do not solely rely on the core group action problem (the so-called vectorization problem), but also on variants of this problem, to either improve efficiency or enable new functionalities. In particular, the security of the CSI-SharK threshold signature protocol relies on the...
(Un)breakable curses - re-encryption in the Fujisaki-Okamoto transform
Kathrin Hövelmanns, Andreas Hülsing, Christian Majenz, Fabrizio Sisinni
Public-key cryptography
The Fujisaki-Okamoto transform (FO) is the go-to method for achieving chosen-ciphertext (CCA) security for post-quantum key encapsulation mechanisms (KEMs). An important step in FO is augmenting the decryption/ decapsulation algorithm with a re-encryption step -- the decrypted message is re-encrypted to check whether the correct encryption randomness was used. While solving a security problem (ciphertext-malleability), re-encryption has turned out to introduce side-channel vulnerabilities...
White-Box Watermarking Signatures against Quantum Adversaries and Its Applications
Fuyuki Kitagawa, Ryo Nishimaki
Public-key cryptography
Software watermarking for cryptographic functionalities enables embedding an arbitrary message (a mark) into a cryptographic function. An extraction algorithm, when provided with a (potentially unauthorized) circuit, retrieves either the embedded mark or a special symbol unmarked indicating the absence of a mark. It is difficult to modify or remove the embedded mark without destroying the functionality of a marked function. Previous works have primarily employed black-box extraction...
Inaccessible Entropy for Watermarking Generative Agents
Daniel Alabi, Lav R. Varshney
Cryptographic protocols
In this work, we construct distortion-free and unforgeable watermarks for language models and generative agents. The watermarked output cannot be forged by a adversary nor removed by the adversary without significantly degrading model output quality. That is, the watermarked output is distortion-free: the watermarking algorithm does not noticeably change the quality of the model output and without the public detection key, no efficient adversary can distinguish output that is watermarked...
Adaptively Secure IBE from Lattices with Asymptotically Better Efficiency
Weidan Ji, Zhedong Wang, Lin Lyu, Dawu Gu
Public-key cryptography
Current adaptively secure identity-based encryption (IBE) constructions from lattices are unable to achieve a good balance among the master public key size, secret key size, modulus and reduction loss. All existing lattice-based IBE schemes share a common restriction: the modulus is quadratic in the trapdoor norm.
In this work, we remove this restriction and present a new adaptively secure IBE scheme from lattices in the standard model, which improves the state-of-the-art construction...
Anamorphic Resistant Encryption: the Good, the Bad and the Ugly
Davide Carnemolla, Dario Catalano, Emanuele Giunta, Francesco Migliaro
Public-key cryptography
Anamorphic encryption (AE), introduced by Persiano, Phan and Yung at Eurocrypt `22, allows to establish secure communication in scenarios where users might be forced to hand over their decryption keys to some hostile authority. Over the last few years, several works have improved our understanding of the primitive by proposing novel realizations, new security notions and studying inherent limitations.
This work makes progress, mainly, on this last line of research.
We show concrete...
Post-Quantum Stealth Address Protocols
Marija Mikić, Mihajlo Srbakoski, Strahinja Praška
Cryptographic protocols
The Stealth Address Protocol (SAP) allows users to receive assets through stealth addresses that are unlinkable to their stealth meta-addresses. The most widely used SAP, Dual-Key SAP (DKSAP), and the most performant SAP, Elliptic Curve Pairing Dual-Key SAP (ECPDKSAP), are based on elliptic curve cryptography, which is vulnerable to quantum attacks. These protocols depend on the elliptic curve discrete logarithm problem, which could be efficiently solved on a sufficiently powerful quantum...
Fully Hybrid TLSv1.3 in WolfSSL on Cortex-M4
Mila Anastasova, Reza Azarderakhsh, Mehran Mozaffari Kermani
Cryptographic protocols
To provide safe communication across an unprotected medium such as the internet, network protocols are being established. These protocols employ public key techniques to perform key exchange and authentication. Transport Layer Security (TLS) is a widely used network protocol that enables secure communication between a server and a client. TLS is employed in billions of transactions per second. Contemporary protocols depend on traditional methods that utilize the computational complexity of...
Generalized Cryptanalysis of Cubic Pell RSA
Hao Kang, Mengce Zheng
Attacks and cryptanalysis
The RSA (Rivest-Shamir-Adleman) cryptosystem is a fundamental algorithm of public key cryptography and is widely used across various information domains. For an RSA modulus represented as $N = pq$, with its factorization remaining unknown, security vulnerabilities arise when attackers exploit the key equation $ed-k(p-1)(q-1)=1$. To enhance the security, Murru and Saettone introduced cubic Pell RSA --- a variant of RSA based on the cubic Pell equation, where the key equation becomes...
Qubit Optimized Quantum Implementation of SLIM
Hasan Ozgur Cildiroglu, Oguz Yayla
Implementation
The advent of quantum computing has profound implications for current technologies, offering advancements in optimization while posing significant threats to cryptographic algorithms. Public-key cryptosystems relying on prime factorization or discrete logarithms are particularly vulnerable, whereas block ciphers (BCs) remain secure through increased key lengths. In this study, we introduce a novel quantum implementation of SLIM, a lightweight block cipher optimized for 32-bit plaintext and...
On the Traceability of Group Signatures: Uncorrupted User Must Exist
Keita Emura
Public-key cryptography
Group signature (GS) is a well-known cryptographic primitive providing anonymity and traceability. Several implication results have been given by mainly focusing on the several security levels of anonymity, e.g., fully anonymous GS implies public key encryption (PKE) and selfless anonymous GS can be constructed from one-way functions and non-interactive zero knowledge poofs, and so on. In this paper, we explore an winning condition of full traceability: an adversary is required to produce a...
Multivariate Encryptions with LL’ perturbations - Is it possible to repair HFE in encryption? -
Jacques Patarin, Pierre Varjabedian
Public-key cryptography
We will present here new multivariate encryption algorithms. This is interesting since few multivariate encryption scheme currently exist, while their exist many more multivariate signature schemes. Our algorithms will combine several ideas, in particular the idea of the LL’ perturbation originally introduced, but only for signature, in [GP06]. In this paper, the LL’ perturbation will be used for encryption and will greatly differ from [GP06]. As we will see, our algorithms resists to all...
Bounded CCA2 Secure Proxy Re-encryption Based on Kyber
Shingo Sato, Junji Shikata
Public-key cryptography
Proxy re-encryption (PRE) allows a semi-honest party (called a proxy) to convert ciphertexts under a public key into ciphertexts under another public key. Due to this functionality, there are various applications such as encrypted email forwarding, key escrow, and secure distributed file systems. On the other hand, post-quantum cryptography (PQC) is one of the most important research areas. However, there is no post-quantum PRE scheme with security against adaptive chosen ciphertext attacks...
MultiReg-FE: Registered FE for Unbounded Inner-Product and Attribute-Weighted Sums
Qiuyan Du, Qiaohan Chu, Jie Chen, Man Ho Au, Debiao He
Public-key cryptography
Francati et al. (Asiacrypt 2023) provided the first registered functional encryption (Reg-FE) beyond predicates. Reg-FE addresses the key escrow problem in functional encryption by allowing users to generate their own key pairs, effectively replacing the traditional private-key generator with a key curator. The key curator holds no secret information and runs deterministic algorithms to generate master public key for encryption and helper keys for decryption. However, existing Reg-FE schemes...
Trustworthy Approaches to RSA: Efficient Exploitation Strategies Based on Common Modulus
Mahdi Mahdavi, Navid Abapour, Zahra Ahmadian
Public-key cryptography
With the increasing integration of crowd computing, new vulnerabilities emerge in widely used cryptographic systems like the RSA cryptosystem, whose security is based on the factoring problem. It is strongly advised to avoid using the same modulus to produce two pairs of public-private keys, as the cryptosystem would be rendered vulnerable to common modulus attacks. Such attacks can take two forms: one that aims to factorize the common modulus based on one key pair and the other that aims to...
Single-trace side-channel attacks on MAYO exploiting leaky modular multiplication
Sönke Jendral, Elena Dubrova
Attacks and cryptanalysis
In response to the quantum threat, new post-quantum cryptographic algorithms will soon be deployed to replace existing public-key schemes. MAYO is a quantum-resistant digital signature scheme whose small keys and signatures make it suitable for widespread adoption, including on embedded platforms with limited security resources. This paper demonstrates two single-trace side-channel attacks on a MAYO implementation in ARM Cortex-M4 that recover a secret key with probabilities of 99.9% and...
Ideal Pseudorandom Codes
Omar Alrabiah, Prabhanjan Ananth, Miranda Christ, Yevgeniy Dodis, Sam Gunn
Foundations
Pseudorandom codes are error-correcting codes with the property that no efficient adversary can distinguish encodings from uniformly random strings. They were recently introduced by Christ and Gunn [CRYPTO 2024] for the purpose of watermarking the outputs of randomized algorithms, such as generative AI models. Several constructions of pseudorandom codes have since been proposed, but none of them are robust to error channels that depend on previously seen codewords. This stronger kind of...
A comprehensive analysis of Regev's quantum algorithm
Razvan Barbulescu, Mugurel Barcau, Vicentiu Pasol
Attacks and cryptanalysis
Public key cryptography can be based on integer factorization and
the discrete logarithm problem (DLP), applicable in multiplicative groups and
elliptic curves. Regev’s recent quantum algorithm was initially designed for the
factorization and was later extended to the DLP in the multiplicative group.
In this article, we further extend the algorithm to address the DLP for elliptic
curves. Notably, based on celebrated conjectures in Number Theory, Regev’s
algorithm is asymptotically...
Computational Analysis of Plausibly Post-Quantum-Secure Recursive Arguments of Knowledge
Dustin Ray, Paulo L. Barreto
Implementation
With the recent standardization of post-quantum cryptographic algorithms, research efforts have largely remained centered on public key exchange and encryption schemes. Argument systems, which allow a party to efficiently argue the correctness of a computation, have received comparatively little attention regarding their quantum-resilient design. These computational integrity frameworks often rely on cryptographic assumptions, such as pairings or group operations, which are vulnerable to...
On the practicality of quantum sieving algorithms for the shortest vector problem
Joao F. Doriguello, George Giapitzakis, Alessandro Luongo, Aditya Morolia
Attacks and cryptanalysis
One of the main candidates of post-quantum cryptography is lattice-based cryptography. Its cryptographic security against quantum attackers is based on the worst-case hardness of lattice problems like the shortest vector problem (SVP), which asks to find the shortest non-zero vector in an integer lattice. Asymptotic quantum speedups for solving SVP are known and rely on Grover's search. However, to assess the security of lattice-based cryptography against these Grover-like quantum speedups,...
A Note on the Hint in the Dilithium Digital Signature Scheme
Amit Berman, Ariel Doubchak, Noam Livne
Cryptographic protocols
In the Dilithium digital signature scheme, there is an inherent tradeoff between the length of the public key, and the length of the signature. The coefficients of the main part of the public-key, the vector $\mathbf{t}$, are compressed (in a lossy manner), or "quantized", during the key-generation procedure, in order to save on the public-key size. That is, the coefficients are divided by some fixed denominator, and only the quotients are published. However, this results in some "skew"...
Instance Compression, Revisited
Gal Arnon, Shany Ben-David, Eylon Yogev
Foundations
Collision-resistant hashing (CRH) is a cornerstone of cryptographic protocols. However, despite decades of research, no construction of a CRH based solely on one-way functions has been found. Moreover, there are black-box limitations that separate these two primitives.
Harnik and Naor [HN10] overcame this black-box barrier by introducing the notion of instance compression. Instance compression reduces large NP instances to a size that depends on their witness size while preserving the...
MAYO Key Recovery by Fixing Vinegar Seeds
Sönke Jendral, Elena Dubrova
Attacks and cryptanalysis
As the industry prepares for the transition to post-quantum secure public key cryptographic algorithms, vulnerability analysis of their implementations is gaining importance. A theoretically secure cryptographic algorithm should also be able to withstand the challenges of physical attacks in real-world environments. MAYO is a candidate in the ongoing first round of the NIST post-quantum standardization process for selecting additional digital signature schemes. This paper demonstrates three...
Detecting and Correcting Computationally Bounded Errors: A Simple Construction Under Minimal Assumptions
Jad Silbak, Daniel Wichs
Foundations
We study error detection and error correction in a computationally bounded world, where errors are introduced by an arbitrary polynomial time adversarial channel. We consider codes where the encoding procedure uses random coins and define two distinct variants: (1) in randomized codes, fresh randomness is chosen during each encoding operation and is unknown a priori, while (2) in self-seeded codes, the randomness of the encoding procedure is fixed once upfront and is known to the adversary....
On Multi-user Security of Lattice-based Signature under Adaptive Corruptions and Key Leakages
Masayuki Fukumitsu, Shingo Hasegawa
Public-key cryptography
We consider the multi-user security under the adaptive corruptions and key leakages ($\rm{MU^{c\&l}}$ security) for lattice-based signatures. Although there exists an $\rm{MU^{c\&l}}$ secure signature based on a number-theoretic assumption, or a leakage-resilient lattice-based signature in the single-user setting, $\rm{MU^{c\&l}}$ secure lattice-based signature is not known.
We examine the existing lattice-based signature schemes from the viewpoint of $\rm{MU^{c\&l}}$ security, and find...
Public-key encryption from a trapdoor one-way embedding of $SL_2(\mathbb{N})$
Robert Hines
Public-key cryptography
We obfuscate words of a given length in a free monoid on two generators with a simple factorization algorithm (namely $SL_2(\mathbb{N})$) to create a public-key encryption scheme. We provide a reference implementation in Python and suggested parameters. The security analysis is between weak and non-existent, left to future work.
Uncompressing Dilithium's public key
Paco Azevedo Oliveira, Andersson Calle Viera, Benoît Cogliati, Louis Goubin
Public-key cryptography
The Dilithium signature scheme – recently standardized by NIST under the name ML-DSA – owes part of its success to a specific mechanism that allows an optimizaion of its public key size. Namely, among the data of the MLWE instance $\bf (A,\bf{t})$, which is at the heart of the construction of Dilithium, the least significant part of $\bf{t}$ -- denoted by $\bf{t}_0$ -- is not included in the public key. The verification algorithm had been adapted accordingly, so that it should not require...
Laconic Pre-Constrained Encryption
Shweta Agrawal, Simran Kumari, Ryo Nishimaki
Public-key cryptography
The recent work of Ananth et al. (ITCS 2022) initiated the study of pre-constrained encryption (PCE) which achieves meaningful security even against the system authority, without assuming any trusted setup. They provided constructions for special cases such as pre-constrained Attribute Based Encryption (PC-ABE) for point functions and pre-constrained Identity Based Encryption (PC-IBE) for general functions from the Learning with Errors (LWE) assumption. For the most general notion of PCE for...
EagleSignV3 : A new secure variant of EagleSign signature over lattices
Abiodoun Clement Hounkpevi, Sidoine Djimnaibeye, Michel Seck, Djiby Sow
Public-key cryptography
With the potential arrival of quantum computers, it is essential to build cryptosystems resistant to attackers with the computing power of a quantum computer. With Shor's algorithm, cryptosystems based on discrete logarithms and factorization become obsolete. Reason why NIST has launching two competitions in 2016 and 2023 to standardize post-quantum cryptosystems (such as KEM and signature ) based on problems supposed to resist attacks using quantum computers. EagleSign was prosed to NIT...
A short-list of pairing-friendly curves resistant to the Special TNFS algorithm at the 192-bit security level
Diego F. Aranha, Georgios Fotiadis, Aurore Guillevic
Implementation
For more than two decades, pairings have been a fundamental tool for designing elegant cryptosystems, varying from digital signature schemes to more complex privacy-preserving constructions. However, the advancement of quantum computing threatens to undermine public-key cryptography. Concretely, it is widely accepted that a future large-scale quantum computer would be capable to break any public-key cryptosystem used today, rendering today's public-key cryptography obsolete and mandating the...
Inner Product Ring LWE Problem, Reduction, New Trapdoor Algorithm for Inner Product Ring LWE Problem and Ring SIS Problem
Zhuang Shan, Leyou Zhang, Qing Wu, Qiqi Lai
Foundations
Lattice cryptography is currently a major research focus in public-key encryption, renowned for its ability to resist quantum attacks. The introduction of ideal lattices (ring lattices) has elevated the theoretical framework of lattice cryptography. Ideal lattice cryptography, compared to classical lattice cryptography, achieves more acceptable operational efficiency through fast Fourier transforms. However, to date, issues of impracticality or insecurity persist in ideal lattice problems....
Towards Quantum-Safe Blockchain: Exploration of PQC and Public-key Recovery on Embedded Systems
Dominik Marchsreiter
Applications
Blockchain technology ensures accountability,
transparency, and redundancy in critical applications, includ-
ing IoT with embedded systems. However, the reliance on
public-key cryptography (PKC) makes blockchain vulnerable to
quantum computing threats. This paper addresses the urgent
need for quantum-safe blockchain solutions by integrating Post-
Quantum Cryptography (PQC) into blockchain frameworks.
Utilizing algorithms from the NIST PQC standardization pro-
cess, we aim to fortify...
Rudraksh: A compact and lightweight post-quantum key-encapsulation mechanism
Suparna Kundu, Archisman Ghosh, Angshuman Karmakar, Shreyas Sen, Ingrid Verbauwhede
Public-key cryptography
Resource-constrained devices such as wireless sensors and Internet of Things (IoT) devices have become ubiquitous in our digital ecosystem. These devices generate and handle a major part of our digital data. However, due to the impending threat of quantum computers on our existing public-key cryptographic schemes and the limited resources available on IoT devices, it is important to design lightweight post-quantum cryptographic (PQC) schemes suitable for these devices.
In this work, we...
Leveled Homomorphic Encryption Schemes for Homomorphic Encryption Standard
Shuhong Gao, Kyle Yates
Foundations
Homomorphic encryption allows for computations on encrypted data without exposing the underlying plaintext, enabling secure and private data processing in various applications such as cloud computing and machine learning. This paper presents a comprehensive mathematical foundation for three prominent homomorphic encryption schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski-Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS), all based on the Ring Learning with Errors (RLWE) problem....
Provably Secure Butterfly Key Expansion from the CRYSTALS Post-Quantum Schemes
Edward Eaton, Philippe Lamontagne, Peter Matsakis
Applications
This work presents the first provably secure protocol for Butterfly Key Expansion (BKE) -- a tripartite protocol for provisioning users with pseudonymous certificates -- based on post-quantum cryptographic schemes. Our work builds upon the CRYSTALS family of post-quantum algorithms that have been selected for standardization by NIST. We extend those schemes by imbuing them with the additional functionality of public key expansion: a process by which pseudonymous public keys can be derived by...
Reducing the Number of Qubits in Quantum Information Set Decoding
Clémence Chevignard, Pierre-Alain Fouque, André Schrottenloher
Attacks and cryptanalysis
This paper presents an optimization of the memory cost of the quantum Information Set Decoding (ISD) algorithm proposed by Bernstein (PQCrypto 2010), obtained by combining Prange's ISD with Grover's quantum search.
When the code has constant rate and length $n$, this algorithm essentially performs a quantum search which, at each iteration, solves a linear system of dimension $\mathcal{O}(n)$. The typical code lengths used in post-quantum public-key cryptosystems range from $10^3$ to...
Improved Meet-LWE Attack via Ternary Trees
Eunmin Lee, Joohee Lee, Yongha Son, Yuntao Wang
Public-key cryptography
The Learning with Errors (LWE) problem with its variants over structured lattices has been widely exploited in efficient post-quantum cryptosystems. Recently, May suggests the Meet-LWE attack, which poses a significant advancement in the line of work on the Meet-in-the-Middle approach to analyze LWE with ternary secrets.
In this work, we generalize and extend the idea of Meet-LWE by introducing ternary trees, which result in diverse representations of the secrets. More precisely, we...
Batched Distributed Point Function from Sparse LPN and Homomorphic Secret Sharing
Lucas Piske, Jaspal Singh, Ni Trieu
Cryptographic protocols
A function secret sharing (FSS) scheme ($\mathsf{gen},\mathsf{eval}$) for a class of programs $\mathcal{F}$ allows a dealer to secret share any function $f \in \mathcal{F}$, such that each function share hides the function, and the shares can be used to non-interactively compute additive shares of $f(x)$ for any input $x$. All FSS related applications often requires the dealer to generate and share secret sharings for a batch of functions.
We initiate the study of batched function secret...
A new attack against search-LWE using Diophantine approximations
Robin Frot, Daniel Zentai
Attacks and cryptanalysis
In this paper, we present a new attack against search-LWE instances with a small secret key. The method consists of lifting the public key to $\mathbb Z$ and finding a good Diophantine approximation of the public key divided by the modulus $a$. This is done using lattice reduction algorithms. The lattice considered, and the approximation quality needed is similar to known decision-LWE attacks for small keys. However, we do not require an in-depth analysis of the reduction algorithm (any...
Outsourced Cloud Data Privacy-Preserving Framework: An Efficient Broadcast Encrypted Search Realization
Yibo Cao, Shiyuan Xu, Xiu-Bo Chen, Gang Xu, Siu-Ming Yiu, Zongpeng Li
Applications
The development of cloud networks facilitates data outsourcing, sharing, and storage, but it has also raised several security concerns. Public key authenticated encryption with keyword search (PAEKS) enables the encrypted search over cloud data while resisting the insider keyword guessing attacks (IKGAs). However, existing PAEKS schemes are limited to a single receiver, restricting application prospects in cloud networks. In addition, quantum computing attacks and key leakage issues further...
Admissible Parameters for the Crossbred Algorithm and Semi-regular Sequences over Finite Fields
John Baena, Daniel Cabarcas, Sharwan K. Tiwari, Javier Verbel, Luis Villota
Attacks and cryptanalysis
Multivariate public key cryptography (MPKC) is one of the most promising alternatives to build quantum-resistant signature schemes, as evidenced in NIST's call for additional post-quantum signature schemes. The main assumption in MPKC is the hardness of the Multivariate Quadratic (MQ) problem, which seeks for a common root to a system of quadratic polynomials over a finite field. Although the Crossbred algorithm is among the most efficient algorithm to solve MQ over small fields, its...
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 formalize the notion of a two-party permutation correlation $(A, B), (C, \pi)$ s.t. $\pi(A)=B+C$ for a random permutation $\pi$ of $n$ elements and vectors $A,B,C\in \mathbb{F}^n$. This correlation can be viewed as an abstraction and generalization of the Chase et al. (Asiacrypt 2020) share translation protocol. We give a systematization of knowledge for how such a permutation correlation can be derandomized to allow the parties to perform a wide range of oblivious...
The Insecurity of SHA2 under the Differential Fault Characteristic of Boolean Functions
Weiqiong Cao, Hua Chen, Hongsong Shi, Haoyuan Li, Jian Wang
Attacks and cryptanalysis
SHA2 is widely used in various traditional public key ryptosystems, post-quantum cryptography, personal identification, and network communication protocols. Therefore, ensuring its robust security is of critical importance. Several differential fault attacks based on random word fault have targeted SHA1 and SHACAL-2. However, extending such random word-based fault attacks to SHA2 proves to be much more difficult due to the increased complexity of the Boolean functions in SHA2.
In this...
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...
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...
2023/1692
Last updated: 2024-12-28
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...
Publicly-Detectable Watermarking for Language Models
Jaiden Fairoze, Sanjam Garg, Somesh Jha, Saeed Mahloujifar, Mohammad Mahmoody, Mingyuan Wang
Applications
We present a publicly-detectable watermarking scheme for LMs: the detection algorithm contains no secret information, and it is executable by anyone. We embed a publicly-verifiable cryptographic signature into LM output using rejection sampling and prove that this produces unforgeable and distortion-free (i.e., undetectable without access to the public key) text output. We make use of error-correction to overcome periods of low entropy, a barrier for all prior watermarking schemes. We...
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 highly critical with respect to side-channel leakage. We assume leakage of the elementary row operations during Gaussian elimination, motivated by McEliece...
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....
Indistinguishability obfuscation (iO) has emerged as a powerful cryptographic primitive with many implications. While classical iO, combined with the infinitely-often worst-case hardness of $\mathsf{NP}$, is known to imply one-way functions (OWFs) and a range of advanced cryptographic primitives, the cryptographic implications of quantum iO remain poorly understood. In this work, we initiate a study of the power of quantum iO. We define several natural variants of quantum iO, distinguished...
Verifiable Timed Signatures (VTS) are cryptographic primitives that enable the creation of a signature that can only be retrieved after a specific time delay, while also providing verifiable evidence of its existence. This framework is particularly useful in blockchain applications. Current VTS schemes rely on signature algorithms such as BLS, Schnorr, and ECDSA, which are vulnerable to quantum attacks due to the vulnerability of the discrete logarithm problem to Shor's Algorithm. We...
Gao et al. (IEEE Internet of Things Journal 2024) proposed public-key inverted-index keyword search with designated tester as an extension of public key encryption with keyword search (PEKS). In their scheme, a server (a tester) has a secret key and uses the key for running the search algorithm due to the designated tester setting. They proved that no information of keyword is revealed from trapdoors under the decisional Diffie-Hellman (DDH) assumption. However, they also employed a...
A threshold signature is an advanced protocol that splits a secret signing key among multiple parties, allowing any subset above a threshold to jointly generate a signature. While post-quantum (PQ) threshold signatures are actively being studied --- especially in response to NIST's recent call for threshold schemes --- most existing solutions are tailored to specially designed, threshold-friendly signature schemes. In contrast, many real-world applications, such as distributed certificate...
Multivariate public key cryptosystems represent a promising family of post-quantum cryptographic schemes. Extensive research has demonstrated that multivariate polynomials are particularly well-suited for constructing digital signature schemes. Notably, the Unbalanced Oil and Vinegar (UOV) signature scheme and its variants have emerged as leading candidates in NIST's recent call for additional digital signature proposals. Security analysis against UOV variants are typically categorized...
We study several problems in the intersection of cryptography and complexity theory based on the following high-level thesis. 1) Obfuscation can serve as a general-purpose worst-case to average-case reduction, reducing the existence of various forms of cryptography to corresponding worst-case assumptions. 2) We can therefore hope to overcome barriers in cryptography and average-case complexity by (i) making worst-case hardness assumptions beyond $\mathsf{P}\neq \mathsf{NP}$, and...
We show that the Negi-Kumar certificateless ring signature scheme [Wirel. Pers. Commun. 134(4): 1987-2011 (2024)] is insecure against forgery attack. The signer's public key $PK_j$ and secret key $PSK_j$ are simply invoked to compute the hash value $H_{2_j}=h_5(m_j\|PSK_j\|PK_j\|t_j)$, which cannot be retrieved by the verifier for checking their dependency. The explicit dependency between the public key and secret key is not properly used to construct some intractable problems, such...
We show that the certificateless signature scheme [Veh. Commun. 47: 100763 (2024)] is insecure, because an adversary can launch forgery attack for any message. The signer's certificateless public key is not tightly bound to the system public key. The inherent flaw results in that the adversary can find an efficient signing algorithm functionally equivalent to the valid signing algorithm. The findings in this note could be helpful for newcomers who are not familiar with the designing...
The emergence of quantum computing and Shor's algorithm necessitates an imminent shift from current public key cryptography techniques to post-quantum robust techniques. NIST has responded by standardising Post-Quantum Cryptography (PQC) algorithms, with ML-KEM (FIPS-203) slated to replace ECDH (Elliptic Curve Diffie-Hellman) for key exchange. A key practical concern for PQC adoption is energy consumption. This paper introduces a new framework for measuring the PQC energy consumption on a...
We explore the application of the QUBO and Ising models to the integer factorization problem with implications for the security of public-key algorithms such as RSA. A key contribution is a program that applies existing algorithms to parameterize and simulate integer factorization through an Ising model in order to replicate previous works. Due to limited access to quantum hardware, we use classical heuristic methods to approximate solutions.
Side-channel analysis remains a critical threat to public-key cryptographic implementations. Simple Power Analysis (SPA) techniques can extract secret keys from a single power trace, often using clustering-based classification methods. However, traces captured in real-world environments often suffer from misalignment and variable trace lengths due to unstable clocks and random delays. As a result, clustering methods are required to use alignment methods that may alter the original...
Noisy linear algebraic assumptions with respect to random matrices, in particular Learning with Errors ($\mathsf{LWE}$) and Alekhnovich Learning Parity with Noise (Alekhnovich $\mathsf{LPN}$), are among the most investigated assumptions that imply post-quantum public-key encryption (PKE). They enjoy elegant mathematical structure. Indeed, efforts to build post-quantum PKE and advanced primitives such as homomorphic encryption and indistinguishability obfuscation have increasingly focused...
We show that the authentication method [Future Gener. Comput. Syst. 158: 516-529 (2024)] cannot be practically implemented, because the signature scheme is insecure against certificateless public key replacement forgery attack. The explicit dependency between the certificateless public key and secret key is not properly used to construct some intractable problems, such as Elliptic Curve Discrete Logarithm (ECDL). An adversary can find an efficient signing algorithm functionally...
Truncation of cryptographic outputs is a technique that was recently introduced in Baldimtsi et al. [BCCK22]. The general idea is to try out many inputs to some cryptographic algorithm until the output (e.g. a public-key or some hash value) falls into some sparse set and thus can be compressed: by trying out an expected $2^k$ different inputs one will find an output that starts with $k$ zeros. Using such truncation one can for example save substantial gas fees on Blockchains where...
Bilinear pairings constitute a cornerstone of public-key cryptography, where advancements in Tate pairings and their efficient variants have emerged as a critical research domain within cryptographic science. Currently, the computation of pairings can be effectively implemented through three distinct algorithmic approaches: Miller’s algorithm, the elliptic net algorithm (as developed by Stange), and cubical-based algorithms (as proposed by Damien Robert). Biextensions are the geometric...
We prove that it is impossible to construct perfect-complete quantum public-key encryption (QPKE) with classical keys from quantumly secure one-way functions (OWFs) in a black-box manner, resolving a long-standing open question in quantum cryptography. Specifically, in the quantum random oracle model (QROM), no perfect-complete QPKE scheme with classical keys, and classical/quantum ciphertext can be secure. This improves the previous works which require either unproven conjectures or...
In the McEliece public-key encryption scheme, a private key is almost always not determined uniquely by its associated public key. This paper gives a structural characterization of equivalent private keys, generalizing a result known for the more approachable special case $\lvert L\rvert=q$. These equivalences reduce the cost estimate for a simple private-key search using the support-splitting algorithm (SSA) by a polynomial but practically very substantial factor. We provide an optimized...
We show that the attribute-based signature scheme [Information Sciences, 654(2024), 119839] is insecure, because an adversary can generate valid signatures for any message even though he cannot access the signer's secret key. The four components of signature $\{\delta_1, \delta_2, \delta_3, \delta_4\}$ are not tightly bound to the target message $M$ and the signer's public key. The dependency between the signer's public key and secret key is not properly used to construct any intractable...
Digital signatures underpin identity, authenticity, and trust in modern computer systems. Cryptography research has shown that it is possible to prove possession of a valid message and signature for some public key, without revealing the message or signature. These proofs of possession work only for specially-designed signature schemes. Though these proofs of possession have many useful applications to improving security, privacy, and anonymity, they are not currently usable for widely...
A sequential aggregate signature scheme (SAS) allows multiple potential signers to sequentially aggregate their respective signatures into a single compact signature. Typically, verification of a SAS signatures requires access to all messages and public key pairs utilized in the aggregate generation. However, efficiency is crucial for cryptographic protocols to facilitate their practical implementation. To this end, we propose a sequential aggregate signature scheme with lazy verification...
Ongoing efforts to transition to post-quantum public-key cryptosystems have created the need for algorithms with a variety of performance characteristics and security assumptions. Among the candidates in NIST's post-quantum standardisation process for additional digital signatures is FAEST, a Vector Oblivious Linear Evaluation in-the-Head (VOLEitH)-based scheme, whose security relies on the one-wayness of the Advanced Encryption Standard (AES). The VOLEitH paradigm enables competitive...
Cryptographic group actions provide a basis for simple post-quantum generalizations of many cryptographic protocols based on the discrete logarithm problem (DLP). However, many advanced group action-based protocols do not solely rely on the core group action problem (the so-called vectorization problem), but also on variants of this problem, to either improve efficiency or enable new functionalities. In particular, the security of the CSI-SharK threshold signature protocol relies on the...
The Fujisaki-Okamoto transform (FO) is the go-to method for achieving chosen-ciphertext (CCA) security for post-quantum key encapsulation mechanisms (KEMs). An important step in FO is augmenting the decryption/ decapsulation algorithm with a re-encryption step -- the decrypted message is re-encrypted to check whether the correct encryption randomness was used. While solving a security problem (ciphertext-malleability), re-encryption has turned out to introduce side-channel vulnerabilities...
Software watermarking for cryptographic functionalities enables embedding an arbitrary message (a mark) into a cryptographic function. An extraction algorithm, when provided with a (potentially unauthorized) circuit, retrieves either the embedded mark or a special symbol unmarked indicating the absence of a mark. It is difficult to modify or remove the embedded mark without destroying the functionality of a marked function. Previous works have primarily employed black-box extraction...
In this work, we construct distortion-free and unforgeable watermarks for language models and generative agents. The watermarked output cannot be forged by a adversary nor removed by the adversary without significantly degrading model output quality. That is, the watermarked output is distortion-free: the watermarking algorithm does not noticeably change the quality of the model output and without the public detection key, no efficient adversary can distinguish output that is watermarked...
Current adaptively secure identity-based encryption (IBE) constructions from lattices are unable to achieve a good balance among the master public key size, secret key size, modulus and reduction loss. All existing lattice-based IBE schemes share a common restriction: the modulus is quadratic in the trapdoor norm. In this work, we remove this restriction and present a new adaptively secure IBE scheme from lattices in the standard model, which improves the state-of-the-art construction...
Anamorphic encryption (AE), introduced by Persiano, Phan and Yung at Eurocrypt `22, allows to establish secure communication in scenarios where users might be forced to hand over their decryption keys to some hostile authority. Over the last few years, several works have improved our understanding of the primitive by proposing novel realizations, new security notions and studying inherent limitations. This work makes progress, mainly, on this last line of research. We show concrete...
The Stealth Address Protocol (SAP) allows users to receive assets through stealth addresses that are unlinkable to their stealth meta-addresses. The most widely used SAP, Dual-Key SAP (DKSAP), and the most performant SAP, Elliptic Curve Pairing Dual-Key SAP (ECPDKSAP), are based on elliptic curve cryptography, which is vulnerable to quantum attacks. These protocols depend on the elliptic curve discrete logarithm problem, which could be efficiently solved on a sufficiently powerful quantum...
To provide safe communication across an unprotected medium such as the internet, network protocols are being established. These protocols employ public key techniques to perform key exchange and authentication. Transport Layer Security (TLS) is a widely used network protocol that enables secure communication between a server and a client. TLS is employed in billions of transactions per second. Contemporary protocols depend on traditional methods that utilize the computational complexity of...
The RSA (Rivest-Shamir-Adleman) cryptosystem is a fundamental algorithm of public key cryptography and is widely used across various information domains. For an RSA modulus represented as $N = pq$, with its factorization remaining unknown, security vulnerabilities arise when attackers exploit the key equation $ed-k(p-1)(q-1)=1$. To enhance the security, Murru and Saettone introduced cubic Pell RSA --- a variant of RSA based on the cubic Pell equation, where the key equation becomes...
The advent of quantum computing has profound implications for current technologies, offering advancements in optimization while posing significant threats to cryptographic algorithms. Public-key cryptosystems relying on prime factorization or discrete logarithms are particularly vulnerable, whereas block ciphers (BCs) remain secure through increased key lengths. In this study, we introduce a novel quantum implementation of SLIM, a lightweight block cipher optimized for 32-bit plaintext and...
Group signature (GS) is a well-known cryptographic primitive providing anonymity and traceability. Several implication results have been given by mainly focusing on the several security levels of anonymity, e.g., fully anonymous GS implies public key encryption (PKE) and selfless anonymous GS can be constructed from one-way functions and non-interactive zero knowledge poofs, and so on. In this paper, we explore an winning condition of full traceability: an adversary is required to produce a...
We will present here new multivariate encryption algorithms. This is interesting since few multivariate encryption scheme currently exist, while their exist many more multivariate signature schemes. Our algorithms will combine several ideas, in particular the idea of the LL’ perturbation originally introduced, but only for signature, in [GP06]. In this paper, the LL’ perturbation will be used for encryption and will greatly differ from [GP06]. As we will see, our algorithms resists to all...
Proxy re-encryption (PRE) allows a semi-honest party (called a proxy) to convert ciphertexts under a public key into ciphertexts under another public key. Due to this functionality, there are various applications such as encrypted email forwarding, key escrow, and secure distributed file systems. On the other hand, post-quantum cryptography (PQC) is one of the most important research areas. However, there is no post-quantum PRE scheme with security against adaptive chosen ciphertext attacks...
Francati et al. (Asiacrypt 2023) provided the first registered functional encryption (Reg-FE) beyond predicates. Reg-FE addresses the key escrow problem in functional encryption by allowing users to generate their own key pairs, effectively replacing the traditional private-key generator with a key curator. The key curator holds no secret information and runs deterministic algorithms to generate master public key for encryption and helper keys for decryption. However, existing Reg-FE schemes...
With the increasing integration of crowd computing, new vulnerabilities emerge in widely used cryptographic systems like the RSA cryptosystem, whose security is based on the factoring problem. It is strongly advised to avoid using the same modulus to produce two pairs of public-private keys, as the cryptosystem would be rendered vulnerable to common modulus attacks. Such attacks can take two forms: one that aims to factorize the common modulus based on one key pair and the other that aims to...
In response to the quantum threat, new post-quantum cryptographic algorithms will soon be deployed to replace existing public-key schemes. MAYO is a quantum-resistant digital signature scheme whose small keys and signatures make it suitable for widespread adoption, including on embedded platforms with limited security resources. This paper demonstrates two single-trace side-channel attacks on a MAYO implementation in ARM Cortex-M4 that recover a secret key with probabilities of 99.9% and...
Pseudorandom codes are error-correcting codes with the property that no efficient adversary can distinguish encodings from uniformly random strings. They were recently introduced by Christ and Gunn [CRYPTO 2024] for the purpose of watermarking the outputs of randomized algorithms, such as generative AI models. Several constructions of pseudorandom codes have since been proposed, but none of them are robust to error channels that depend on previously seen codewords. This stronger kind of...
Public key cryptography can be based on integer factorization and the discrete logarithm problem (DLP), applicable in multiplicative groups and elliptic curves. Regev’s recent quantum algorithm was initially designed for the factorization and was later extended to the DLP in the multiplicative group. In this article, we further extend the algorithm to address the DLP for elliptic curves. Notably, based on celebrated conjectures in Number Theory, Regev’s algorithm is asymptotically...
With the recent standardization of post-quantum cryptographic algorithms, research efforts have largely remained centered on public key exchange and encryption schemes. Argument systems, which allow a party to efficiently argue the correctness of a computation, have received comparatively little attention regarding their quantum-resilient design. These computational integrity frameworks often rely on cryptographic assumptions, such as pairings or group operations, which are vulnerable to...
One of the main candidates of post-quantum cryptography is lattice-based cryptography. Its cryptographic security against quantum attackers is based on the worst-case hardness of lattice problems like the shortest vector problem (SVP), which asks to find the shortest non-zero vector in an integer lattice. Asymptotic quantum speedups for solving SVP are known and rely on Grover's search. However, to assess the security of lattice-based cryptography against these Grover-like quantum speedups,...
In the Dilithium digital signature scheme, there is an inherent tradeoff between the length of the public key, and the length of the signature. The coefficients of the main part of the public-key, the vector $\mathbf{t}$, are compressed (in a lossy manner), or "quantized", during the key-generation procedure, in order to save on the public-key size. That is, the coefficients are divided by some fixed denominator, and only the quotients are published. However, this results in some "skew"...
Collision-resistant hashing (CRH) is a cornerstone of cryptographic protocols. However, despite decades of research, no construction of a CRH based solely on one-way functions has been found. Moreover, there are black-box limitations that separate these two primitives. Harnik and Naor [HN10] overcame this black-box barrier by introducing the notion of instance compression. Instance compression reduces large NP instances to a size that depends on their witness size while preserving the...
As the industry prepares for the transition to post-quantum secure public key cryptographic algorithms, vulnerability analysis of their implementations is gaining importance. A theoretically secure cryptographic algorithm should also be able to withstand the challenges of physical attacks in real-world environments. MAYO is a candidate in the ongoing first round of the NIST post-quantum standardization process for selecting additional digital signature schemes. This paper demonstrates three...
We study error detection and error correction in a computationally bounded world, where errors are introduced by an arbitrary polynomial time adversarial channel. We consider codes where the encoding procedure uses random coins and define two distinct variants: (1) in randomized codes, fresh randomness is chosen during each encoding operation and is unknown a priori, while (2) in self-seeded codes, the randomness of the encoding procedure is fixed once upfront and is known to the adversary....
We consider the multi-user security under the adaptive corruptions and key leakages ($\rm{MU^{c\&l}}$ security) for lattice-based signatures. Although there exists an $\rm{MU^{c\&l}}$ secure signature based on a number-theoretic assumption, or a leakage-resilient lattice-based signature in the single-user setting, $\rm{MU^{c\&l}}$ secure lattice-based signature is not known. We examine the existing lattice-based signature schemes from the viewpoint of $\rm{MU^{c\&l}}$ security, and find...
We obfuscate words of a given length in a free monoid on two generators with a simple factorization algorithm (namely $SL_2(\mathbb{N})$) to create a public-key encryption scheme. We provide a reference implementation in Python and suggested parameters. The security analysis is between weak and non-existent, left to future work.
The Dilithium signature scheme – recently standardized by NIST under the name ML-DSA – owes part of its success to a specific mechanism that allows an optimizaion of its public key size. Namely, among the data of the MLWE instance $\bf (A,\bf{t})$, which is at the heart of the construction of Dilithium, the least significant part of $\bf{t}$ -- denoted by $\bf{t}_0$ -- is not included in the public key. The verification algorithm had been adapted accordingly, so that it should not require...
The recent work of Ananth et al. (ITCS 2022) initiated the study of pre-constrained encryption (PCE) which achieves meaningful security even against the system authority, without assuming any trusted setup. They provided constructions for special cases such as pre-constrained Attribute Based Encryption (PC-ABE) for point functions and pre-constrained Identity Based Encryption (PC-IBE) for general functions from the Learning with Errors (LWE) assumption. For the most general notion of PCE for...
With the potential arrival of quantum computers, it is essential to build cryptosystems resistant to attackers with the computing power of a quantum computer. With Shor's algorithm, cryptosystems based on discrete logarithms and factorization become obsolete. Reason why NIST has launching two competitions in 2016 and 2023 to standardize post-quantum cryptosystems (such as KEM and signature ) based on problems supposed to resist attacks using quantum computers. EagleSign was prosed to NIT...
For more than two decades, pairings have been a fundamental tool for designing elegant cryptosystems, varying from digital signature schemes to more complex privacy-preserving constructions. However, the advancement of quantum computing threatens to undermine public-key cryptography. Concretely, it is widely accepted that a future large-scale quantum computer would be capable to break any public-key cryptosystem used today, rendering today's public-key cryptography obsolete and mandating the...
Lattice cryptography is currently a major research focus in public-key encryption, renowned for its ability to resist quantum attacks. The introduction of ideal lattices (ring lattices) has elevated the theoretical framework of lattice cryptography. Ideal lattice cryptography, compared to classical lattice cryptography, achieves more acceptable operational efficiency through fast Fourier transforms. However, to date, issues of impracticality or insecurity persist in ideal lattice problems....
Blockchain technology ensures accountability, transparency, and redundancy in critical applications, includ- ing IoT with embedded systems. However, the reliance on public-key cryptography (PKC) makes blockchain vulnerable to quantum computing threats. This paper addresses the urgent need for quantum-safe blockchain solutions by integrating Post- Quantum Cryptography (PQC) into blockchain frameworks. Utilizing algorithms from the NIST PQC standardization pro- cess, we aim to fortify...
Resource-constrained devices such as wireless sensors and Internet of Things (IoT) devices have become ubiquitous in our digital ecosystem. These devices generate and handle a major part of our digital data. However, due to the impending threat of quantum computers on our existing public-key cryptographic schemes and the limited resources available on IoT devices, it is important to design lightweight post-quantum cryptographic (PQC) schemes suitable for these devices. In this work, we...
Homomorphic encryption allows for computations on encrypted data without exposing the underlying plaintext, enabling secure and private data processing in various applications such as cloud computing and machine learning. This paper presents a comprehensive mathematical foundation for three prominent homomorphic encryption schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski-Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS), all based on the Ring Learning with Errors (RLWE) problem....
This work presents the first provably secure protocol for Butterfly Key Expansion (BKE) -- a tripartite protocol for provisioning users with pseudonymous certificates -- based on post-quantum cryptographic schemes. Our work builds upon the CRYSTALS family of post-quantum algorithms that have been selected for standardization by NIST. We extend those schemes by imbuing them with the additional functionality of public key expansion: a process by which pseudonymous public keys can be derived by...
This paper presents an optimization of the memory cost of the quantum Information Set Decoding (ISD) algorithm proposed by Bernstein (PQCrypto 2010), obtained by combining Prange's ISD with Grover's quantum search. When the code has constant rate and length $n$, this algorithm essentially performs a quantum search which, at each iteration, solves a linear system of dimension $\mathcal{O}(n)$. The typical code lengths used in post-quantum public-key cryptosystems range from $10^3$ to...
The Learning with Errors (LWE) problem with its variants over structured lattices has been widely exploited in efficient post-quantum cryptosystems. Recently, May suggests the Meet-LWE attack, which poses a significant advancement in the line of work on the Meet-in-the-Middle approach to analyze LWE with ternary secrets. In this work, we generalize and extend the idea of Meet-LWE by introducing ternary trees, which result in diverse representations of the secrets. More precisely, we...
A function secret sharing (FSS) scheme ($\mathsf{gen},\mathsf{eval}$) for a class of programs $\mathcal{F}$ allows a dealer to secret share any function $f \in \mathcal{F}$, such that each function share hides the function, and the shares can be used to non-interactively compute additive shares of $f(x)$ for any input $x$. All FSS related applications often requires the dealer to generate and share secret sharings for a batch of functions. We initiate the study of batched function secret...
In this paper, we present a new attack against search-LWE instances with a small secret key. The method consists of lifting the public key to $\mathbb Z$ and finding a good Diophantine approximation of the public key divided by the modulus $a$. This is done using lattice reduction algorithms. The lattice considered, and the approximation quality needed is similar to known decision-LWE attacks for small keys. However, we do not require an in-depth analysis of the reduction algorithm (any...
The development of cloud networks facilitates data outsourcing, sharing, and storage, but it has also raised several security concerns. Public key authenticated encryption with keyword search (PAEKS) enables the encrypted search over cloud data while resisting the insider keyword guessing attacks (IKGAs). However, existing PAEKS schemes are limited to a single receiver, restricting application prospects in cloud networks. In addition, quantum computing attacks and key leakage issues further...
Multivariate public key cryptography (MPKC) is one of the most promising alternatives to build quantum-resistant signature schemes, as evidenced in NIST's call for additional post-quantum signature schemes. The main assumption in MPKC is the hardness of the Multivariate Quadratic (MQ) problem, which seeks for a common root to a system of quadratic polynomials over a finite field. Although the Crossbred algorithm is among the most efficient algorithm to solve MQ over small fields, its...
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 formalize the notion of a two-party permutation correlation $(A, B), (C, \pi)$ s.t. $\pi(A)=B+C$ for a random permutation $\pi$ of $n$ elements and vectors $A,B,C\in \mathbb{F}^n$. This correlation can be viewed as an abstraction and generalization of the Chase et al. (Asiacrypt 2020) share translation protocol. We give a systematization of knowledge for how such a permutation correlation can be derandomized to allow the parties to perform a wide range of oblivious...
SHA2 is widely used in various traditional public key ryptosystems, post-quantum cryptography, personal identification, and network communication protocols. Therefore, ensuring its robust security is of critical importance. Several differential fault attacks based on random word fault have targeted SHA1 and SHACAL-2. However, extending such random word-based fault attacks to SHA2 proves to be much more difficult due to the increased complexity of the Boolean functions in SHA2. In this...
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...
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...
We present a publicly-detectable watermarking scheme for LMs: the detection algorithm contains no secret information, and it is executable by anyone. We embed a publicly-verifiable cryptographic signature into LM output using rejection sampling and prove that this produces unforgeable and distortion-free (i.e., undetectable without access to the public key) text output. We make use of error-correction to overcome periods of low entropy, a barrier for all prior watermarking schemes. We...
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 highly critical with respect to side-channel leakage. We assume leakage of the elementary row operations during Gaussian elimination, motivated by McEliece...
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....
