2489 results sorted by ID
Composing Timed Cryptographic Protocols: Foundations and Applications
Karim Eldefrawy, Benjamin Terner, Moti Yung
Foundations
Time-lock puzzles are unique cryptographic primitives that use computational complexity to keep information secret for some period of time, after which security expires. Unfortunately, current analysis techniques of time-lock primitives provide no sound mechanism to build multi-party cryptographic protocols which use expiring security as a building block. We explain in this paper that all other attempts at this subtle problem lack either composability, a fully consistent analysis, or...
Secure Coded Distributed Computing
Shanuja Sasi, Onur Gunlu
Foundations
In this paper, we consider two critical aspects of security in the distributed computing (DC) model: secure data shuffling and secure coded computing. It is imperative that any external entity overhearing the transmissions does not gain any information about the intermediate values (IVs) exchanged during the shuffling phase of the DC model. Our approach ensures IV confidentiality during data shuffling. Moreover, each node in the system must be able to recover the IVs necessary for computing...
Efficient Quantum Algorithm for SUBSET-SUM Problem
Sanchita Ghosh, Anant Sharma, Sreetama Das, Shibdas Roy
Foundations
Problems in the complexity class $NP$ are not all known to be solvable, but are verifiable given the solution, in polynomial time by a classical computer. The complexity class $BQP$ includes all problems solvable in polynomial time by a quantum computer. Prime factorization is in $NP$ class, and is also in $BQP$ class, owing to Shor's algorithm. The hardest of all problems within the $NP$ class are called $NP$-complete. If a quantum algorithm can solve an $NP$-complete problem in polynomial...
Regev Factoring Beyond Fibonacci: Optimizing Prefactors
Seyoon Ragavan
Foundations
In this note, we improve the space-efficient variant of Regev's quantum factoring algorithm [Reg23] proposed by Ragavan and Vaikuntanathan [RV24] by constant factors in space and/or size. This allows us to bridge the significant gaps in concrete efficiency between the circuits by [Reg23] and [RV24]; [Reg23] uses far fewer gates, while [RV24] uses far fewer qubits.
The main observation is that the space-efficient quantum modular exponentiation technique by [RV24] can be modified to...
Further Investigations on Nonlinear Complexity of Periodic Binary Sequences
Qin Yuan, Chunlei Li, Xiangyong Zeng, Tor Helleseth, Debiao He
Foundations
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit relation between nonlinear complexities of finite-length binary sequences and their corresponding periodic sequences. Based on the relation, we propose two algorithms that can generate all periodic binary sequences with any prescribed nonlinear complexity.
Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms
Cédric Pilatte
Foundations
In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of Shor's algorithm that requires far fewer quantum gates. His algorithm relies on a number-theoretic conjecture on the elements in $(\mathbb{Z}/N\mathbb{Z})^{\times}$ that can be written as short products of very small prime numbers. We prove a version of this conjecture using tools from analytic number theory such...
Exponential Quantum Speedup for the Traveling Salesman Problem
Anant Sharma, Nupur Deshpande, Sanchita Ghosh, Sreetama Das, Shibdas Roy
Foundations
The traveling salesman problem is the problem of finding out the shortest route in a network of cities, that a salesman needs to travel to cover all the cities, without visiting the same city more than once. This problem is known to be $NP$-hard with a brute-force complexity of $O(N^N)$ or $O(N^{2N})$ for $N$ number of cities. This problem is equivalent to finding out the shortest Hamiltonian cycle in a given graph, if at least one Hamiltonian cycle exists in it. Quantum algorithms for this...
Lattice-Based Succinct Mercurial Functional Commitment for Circuits: Definitions and Constructions
Hongxiao Wang, Siu-Ming Yiu, Yanmin Zhao, Zoe L. Jiang, Min Xie
Foundations
Vector commitments gain a lot of attention because of their wide usage in applications such as blockchain and accumulator. Mercurial vector commitments and mercurial functional commitments (MFC), as significant variants of VC, are the central techniques to construct more advanced cryptographic primitives such as zero-knowledge set and zero-knowledge functional elementary database (ZK-FEDB).
However, the current MFC only supports linear functions, limiting its application, i.e. building the...
Low-latency Secure Integrated Sensing and Communication with Transmitter Actions
Truman Welling, Onur Gunlu, Aylin Yener
Foundations
This paper considers an information theoretic model of secure integrated sensing and communication, represented as a wiretap channel with action dependent states. This model allows one to secure a part of the transmitted message against a sensed target that eavesdrops the communication, while allowing transmitter actions to change the channel statistics. An exact secrecy-distortion region is given for a physically-degraded channel. Moreover, a finite-length achievability region is...
Worst-Case to Average-Case Hardness of LWE: A Simple and Practical Perspective
Divesh Aggarwal, Leong Jin Ming, Alexandra Veliche
Foundations
In this work, we study the worst-case to average-case hardness of the Learning with Errors problem (LWE) under an alternative measure of hardness $−$ the maximum success probability achievable by a probabilistic polynomial-time (PPT) algorithm. Previous works by Regev (STOC 2005), Peikert (STOC 2009), and Brakerski, Peikert, Langlois, Regev, Stehle (STOC 2013) give worst-case to average-case reductions from lattice problems, specifically the approximate decision variant of the
Shortest...
Secret-Sharing Schemes for High Slices
Amos Beimel, Oriol Farràs, Oded Nir
Foundations
In a secret-sharing scheme, a secret is shared among $n$ parties such that the secret can be recovered by authorized coalitions, while it should be kept hidden from unauthorized coalitions. In this work we study secret-sharing for $k$-slice access structures, in which coalitions of size $k$ are either authorized or not, larger coalitions are authorized and smaller are unauthorized. Known schemes for these access structures had smaller shares for small $k$'s than for large ones; hence our...
A Complete Beginner Guide to the Number Theoretic Transform (NTT)
Ardianto Satriawan, Rella Mareta, Hanho Lee
Foundations
The Number Theoretic Transform (NTT) is a powerful mathematical tool that has become increasingly important in developing Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE). Its ability to efficiently calculate polynomial multiplication using the convolution theorem with a quasi-linear complexity $O(n \log{n})$ instead of $O(n^2)$ when implemented with Fast Fourier Transform-style algorithms has made it a key component in modern cryptography. FFT-style NTT algorithm or fast-NTT...
On complexity of the problem of solving systems of tropical polynomial equations of degree two
Ivan Buchinskiy, Matvei Kotov, Alexander Treier
Foundations
In this paper, we investigate the computational complexity of the problem of solving a one-sided system of equations of degree two of a special form over the max-plus algebra. Also, we consider the asymptotic density of solvable systems of this form. Such systems have appeared during the analysis of some tropical cryptography protocols that were recently suggested. We show how this problem is related to the integer linear programming problem and prove that this problem is NP-complete. We...
A Note on the Common Haar State Model
Prabhanjan Ananth, Aditya Gulati, Yao-Ting Lin
Foundations
Common random string model is a popular model in classical cryptography with many constructions proposed in this model. We study a quantum analogue of this model called the common Haar state model, which was also studied in an independent work by Chen, Coladangelo and Sattath (arXiv 2024). In this model, every party in the cryptographic system receives many copies of one or more i.i.d Haar states.
Our main result is the construction of a statistically secure PRSG with: (a) the output...
An efficient key generation algorithm for GR-NTRU over dihedral group
Vikas Kumar, Ali Raya, Aditi Kar Gangopadhyay
Foundations
In this article, we focus on deriving an easily implementable and efficient
method of constructing units of the group ring of dihedral group. We provide
a necessary and sufficient condition that relates the units in the group ring
of dihedral group with the units in the group ring of cyclic group. Using this
relation and the methods available for inversion in the group ring of the cyclic
group, we introduce an algorithm to construct units efficiently and check its
performance experimentally.
Software-Defined Cryptography: A Design Feature of Cryptographic Agility
Jihoon Cho, Changhoon Lee, Eunkyung Kim, Jieun Lee, Beumjin Cho
Foundations
Cryptographic agility, or crypto-agility, is a design feature that enables agile updates to new cryptographic algorithms and standards without the need to modify or replace the surrounding infrastructure. This paper examines the prerequisites for crypto-agility and proposes its desired design feature. More specifically, we investigate the design characteristics of widely deployed cybersecurity paradigms, i.e., zero trust, and apply its design feature to crypto-agility, achieving greater...
Fast pairings via biextensions and cubical arithmetic
Damien Robert
Foundations
Biextensions associated to line bundles on abelian varieties allows to reinterpret the usual Weil, Tate, Ate, optimal Ate, \ldots, pairings as monodromy pairings. We introduce a cubical arithmetic, derived from the canonical cubical torsor structure of these line bundles, to obtain an efficient arithmetic of these biextensions.
This unifies and extends Miller's standard algorithm to compute pairings along with other algorithms like elliptic nets and theta functions, and allows to adapt...
Secure Multi-Party Linear Algebra with Perfect Correctness
Jules Maire, Damien Vergnaud
Foundations
We present new secure multi-party computation protocols for linear algebra over a finite field, which improve the state-of-the-art in terms of security. We look at the case of \emph{unconditional security with perfect correctness}, i.e., information-theoretic security without errors. We notably propose an expected constant-round protocol for solving systems of $m$ linear equations in $n$ variables over $\mathbb{F}_q$ with expected complexity $O(k(n^{2.5} + m^{2.5}+n^2m^{0.5}))$ where $k >...
Real-Valued Somewhat-Pseudorandom Unitaries
Zvika Brakerski, Nir Magrafta
Foundations
We explore a very simple distribution of unitaries: random (binary) phase -- Hadamard -- random (binary) phase -- random computational-basis permutation.
We show that this distribution is statistically indistinguishable from random Haar unitaries for any polynomial set of orthogonal input states (in any basis) with polynomial multiplicity.
This shows that even though real-valued unitaries cannot be completely pseudorandom (Haug, Bharti, Koh, arXiv:2306.11677), we can still obtain some...
Perfect Zero-Knowledge PCPs for #P
Tom Gur, Jack O'Connor, Nicholas Spooner
Foundations
We construct perfect zero-knowledge probabilistically checkable proofs (PZK-PCPs) for every language in #P. This is the first construction of a PZK-PCP for any language outside BPP. Furthermore, unlike previous constructions of (statistical) zero-knowledge PCPs, our construction simultaneously achieves non-adaptivity and zero knowledge against arbitrary (adaptive) polynomial-time malicious verifiers.
Our construction consists of a novel masked sumcheck PCP, which uses the...
The Systemic Errors of Banded Quantum Fourier Transformation
Zhengjun Cao, Zhenfu Cao
Foundations
Quantum Fourier Transformation (QFT) needs to construct the rotation gates with extremely tiny angles. Since it is impossible to physically manipulate such tiny angles (corresponding to extremely weak energies), those gates should be replaced by some scaled and controllable gates. The version of QFT is called banded QFT (BQFT), and can be mathematically specified by Kronecker product and binary fraction. But the systemic errors of BQFT has never been heuristically estimated. In this...
Modeling Mobile Crash in Byzantine Consensus
Hans Schmiedel, Runchao Han, Qiang Tang, Ron Steinfeld, Jiangshan Yu
Foundations
Targeted Denial-of-Service (DoS) attacks have been a practical concern
for permissionless blockchains. Potential solutions, such as random
sampling, are adopted by blockchains.
However, the associated security guarantees have only been informally discussed in prior work. This
is due to the fact that existing adversary models are either not
fully capturing this attack or giving up certain design choices
(as in the sleepy model or asynchronous network model), or too strong to
be...
Estimating the Unpredictability of Multi-Bit Strong PUF Classes
Ahmed Bendary, Wendson A. S. Barbosa, Andrew Pomerance, C. Emre Koksal
Foundations
With the ongoing advances in machine learning (ML), cybersecurity solutions and security primitives are becoming increasingly vulnerable to successful attacks. Strong physically unclonable functions (PUFs) are a potential solution for providing high resistance to such attacks. In this paper, we propose a generalized attack model that leverages multiple chips jointly to minimize the cloning error. Our analysis shows that the entropy rate over different chips is a relevant measure to the new...
Kolmogorov Comes to Cryptomania: On Interactive Kolmogorov Complexity and Key-Agreement
Marshall Ball, Yanyi Liu, Noam Mazor, Rafael Pass
Foundations
Only a handful candidates for computational assumptions that imply secure key-agreement protocols (KA) are known, and even fewer are believed to be quantum safe. In this paper, we present a new hardness assumption---the worst-case hardness of a promise problem related to an interactive version of Kolmogorov Complexity.
Roughly speaking, the promise problem requires telling apart tuples of strings $(\pi,x,y)$ with relatively (w.r.t. $K(\pi)$) low time-bounded Interactive Kolmogorov...
Gap MCSP is not (Levin) NP-complete in Obfustopia
Noam Mazor, Rafael Pass
Foundations
We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions.
In more detail:
- Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not...
New Upper Bounds for Evolving Secret Sharing via Infinite Branching Programs
Bar Alon, Amos Beimel, Tamar Ben David, Eran Omri, Anat Paskin-Cherniavsky
Foundations
Evolving secret-sharing schemes, defined by Komargodski, Naor, and Yogev [TCC 2016B, IEEE Trans. on Info. Theory 2018], are secret-sharing schemes in which there is no a-priory bound on the number of parties. In such schemes, parties arrive one by one; when a party arrives, the dealer gives it a share and cannot update this share in later stages. The requirement is that some predefined sets (called authorized sets) should be able to reconstruct the secret, while other sets should learn no...
Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations
Joseph Carolan, Alexander Poremba
Foundations
Sponge hashing is a novel class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a short digest which consists of a subset of the final output bits. While much is known about the post-quantum security of the sponge...
Some notes on algorithms for abelian varieties
Damien Robert
Foundations
A compilation of various notes written over the years on some algorithms on abelian varieties.
A Direct PRF Construction from Kolmogorov Complexity
Yanyi Liu, Rafael Pass
Foundations
While classic result in the 1980s establish that one-way functions (OWFs) imply the existence of pseudorandom generators (PRGs) which in turn imply pseudorandom functions (PRFs), the constructions (most notably the one from OWFs to PRGs) is complicated and inefficient.
Consequently, researchers have developed alternative \emph{direct} constructions of PRFs from various different concrete hardness assumptions. In this work, we continue this thread of work and demonstrate the first direct...
Heuristic Ideal Obfuscation Scheme based on LWE Problem, its Variants and Quantum Oracle
Zhuang Shan, Leyou Zhang, Qing Wu
Foundations
This paper presents a heuristic ideal obfuscation scheme based on the learning problem, which di ers from that of Jain, Lin, and Luo [JLLW23]. The paper adopts a method similar to Brakerski, Dottling, Garg, and Malavolta [BDGM22, BDGM20] for constructing iO. It first introduces a variant of the LWR problem and proves its pseudorandomness. Based on the variant of the LWR problem, it constructs LHE, then combines it with sFHE constructed from the LWE problem to further construct the ideal...
On the Feasibility of Sliced Garbling
Tomer Ashur, Carmit Hazay, Rahul Satish
Foundations
Garbling schemes are one of the most fundamental objects in cryptography and have been studied extensively due to their broad applicability. The state-of-the-art is a construction in which XOR gates are free and AND gates require $3\kappa/2+\mathcal{O}(1)$ bits per gate, due to Rosulek and Roy (CRYPTO'21). An important technique in their garbling is slicing, which partitions the labels into two equal-length slices. In this paper, we explore the feasibility of the slicing technique for...
Transmitter Actions for Secure Integrated Sensing and Communication
Truman Welling, Onur Gunlu, Aylin Yener
Foundations
This work models a secure integrated sensing and communication (ISAC) system as a broadcast channel with action-dependent channel states and output feedback. The transmitted message is split into a common and a secure message, both of which must be recovered at the legitimate receiver, while the secure message needs to be kept secret from the eavesdropper. The transmitter actions, such as beamforming vector design, affect the corresponding state distribution at each channel use. The action...
Collision Resistance from Multi-Collision Resistance for all Constant Parameters
Jan Buzek, Stefano Tessaro
Foundations
A $t$-multi-collision-resistant hash function ($t$-MCRH) is a family of shrinking functions for which it is computationally hard to find $t$ distinct inputs mapping to the same output for a function sampled from this family. Several works have shown that $t$-MCRHs are sufficient for many of the applications of collision-resistant hash functions (CRHs), which correspond to the special case of $t = 2$.
An important question is hence whether $t$-MCRHs for $t > 2$ are fundamentally weaker...
Lower Bounds for Differential Privacy Under Continual Observation and Online Threshold Queries
Edith Cohen, Xin Lyu, Jelani Nelson, Tamás Sarlós, Uri Stemmer
Foundations
One of the most basic problems for studying the "price of privacy over time" is the so called private counter problem, introduced by Dwork et al. (2010) and Chan et al. (2010). In this problem, we aim to track the number of events that occur over time, while hiding the existence of every single event. More specifically, in every time step $t\in[T]$ we learn (in an online fashion) that $\Delta_t\geq 0$ new events have occurred, and must respond with an estimate $n_t\approx\sum_{j=1}^t...
The NISQ Complexity of Collision Finding
Yassine Hamoudi, Qipeng Liu, Makrand Sinha
Foundations
Collision-resistant hashing, a fundamental primitive in modern cryptography, ensures that there is no efficient way to find distinct inputs that produce the same hash value. This property underpins the security of various cryptographic applications, making it crucial to understand its complexity. The complexity of this problem is well-understood in the classical setting and $\Theta(N^{1/2})$ queries are needed to find a collision. However, the advent of quantum computing has introduced new...
On Central Primitives for Quantum Cryptography with Classical Communication
Kai-Min Chung, Eli Goldin, Matthew Gray
Foundations
Recent work has introduced the "Quantum-Computation Classical-Communication"
(QCCC) (Chung et. al.) setting for cryptography. There has been some evidence that
One Way Puzzles (OWPuzz) are the natural central cryptographic primitive for this
setting (Khurana and Tomer). For a primitive to be considered central it should
have several characteristics. It should be well behaved (which for this paper we will
think of as having amplification, combiners, and universal constructions); it...
A New Approach for Non-Interactive Zero-Knowledge from Learning with Errors
Brent Waters
Foundations
We put forward a new approach for achieving non-interactive zero-knowledge proofs (NIKZs) from the learning with errors (LWE) assumption (with subexponential modulus to noise ratio). We provide a LWE-based construction of a hidden bits generator that gives rise to a NIZK via the celebrated hidden bits paradigm. A noteable feature of our construction is its simplicity. Our construction employs lattice trapdoors, but beyond that uses only simple operations. Unlike prior solutions we do not...
From Random Probing to Noisy Leakages Without Field-Size Dependence
Gianluca Brian, Stefan Dziembowski, Sebastian Faust
Foundations
Side channel attacks are devastating attacks targeting cryptographic implementations. To protect against these attacks, various countermeasures have been proposed -- in particular, the so-called masking scheme. Masking schemes work by hiding sensitive information via secret sharing all intermediate values that occur during the evaluation of a cryptographic implementation. Over the last decade, there has been broad interest in designing and formally analyzing such schemes. The random probing...
Split-State Non-Malleable Codes and Secret Sharing Schemes for Quantum Messages
Naresh Goud Boddu, Vipul Goyal, Rahul Jain, João Ribeiro
Foundations
Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. One of the strongest and most well-studied adversarial tampering models is $2$-split-state tampering. Here, a codeword is split into two parts which are stored in physically distant servers, and the adversary can then...
Leakage-Tolerant Circuits
Yuval Ishai, Yifan Song
Foundations
A leakage-resilient circuit for $f:\{0,1\}^n\to\{0,1\}^m$ is a randomized Boolean circuit $C$ mapping a randomized encoding of an input $x$ to an encoding of $y=f(x)$, such that applying any leakage function $L\in \cal L$ to the wires of $C$ reveals essentially nothing about $x$. A leakage-tolerant circuit achieves the stronger guarantee that even when $x$ and $y$ are not protected by any encoding, the output of $L$ can be simulated by applying some $L'\in \cal L$ to $x$ and $y$ alone....
Transaction Fee Mechanism Design in a Post-MEV World
Maryam Bahrani, Pranav Garimidi, Tim Roughgarden
Foundations
The incentive-compatibility properties of blockchain transaction fee mechanisms have been investigated with passive block producers that are motivated purely by the net rewards earned at the consensus layer. This paper introduces a model of active block producers that have their own private valuations for blocks (representing, for example, additional value derived from the application layer). The block producer surplus in our model can be interpreted as one of the more common colloquial...
Circuit Bootstrapping: Faster and Smaller
Ruida Wang, Yundi Wen, Zhihao Li, Xianhui Lu, Benqiang Wei, Kun Liu, Kunpeng Wang
Foundations
We present a novel circuit bootstrapping algorithm that outperforms the state-of-the-art TFHE method with 9.9× speedup and 15.6× key size reduction. These improvements can be attributed to two technical contributions. Firstly, we redesigned the circuit bootstrapping workflow to operate exclusively under the ring ciphertext type, which eliminates the need of conversion between LWE and RLWE ciphertexts. Secondly, we improve the LMKC+ blind rotation algorithm by reducing the number of...
Simple constructions of linear-depth t-designs and pseudorandom unitaries
Tony Metger, Alexander Poremba, Makrand Sinha, Henry Yuen
Foundations
Uniformly random unitaries, i.e., unitaries drawn from the Haar measure, have many useful properties, but cannot be implemented efficiently. This has motivated a long line of research into random unitaries that ``look'' sufficiently Haar random while also being efficient to implement.
Two different notions of derandomisation have emerged:
$t$-designs are random unitaries that information-theoretically reproduce the first $t$ moments of the Haar measure, and pseudorandom unitaries (PRUs)...
Quantum Pseudorandomness Cannot Be Shrunk In a Black-Box Way
Samuel Bouaziz--Ermann, Garazi Muguruza
Foundations
Pseudorandom Quantum States (PRS) were introduced by Ji, Liu and Song as quantum analogous to Pseudorandom Generators. They are an ensemble of states efficiently computable but computationally indistinguishable from Haar random states. Subsequent works have shown that some cryptographic primitives can be constructed from PRSs. Moreover, recent classical and quantum oracle separations of PRS from One-Way Functions strengthen the interest in a purely quantum alternative building block for...
Secure Integrated Sensing and Communication Under Correlated Rayleigh Fading
Martin Mittelbach, Rafael F. Schaefer, Matthieu Bloch, Aylin Yener, Onur Gunlu
Foundations
We consider a secure integrated sensing and communication (ISAC) scenario, in which a signal is transmitted through a state-dependent wiretap channel with one legitimate receiver with which the transmitter communicates and one honest-but-curious target that the transmitter wants to sense. The secure ISAC channel is modeled as two state-dependent fast-fading channels with correlated Rayleigh fading coefficients and independent additive Gaussian noise components. Delayed channel outputs are...
A New Approach to Generic Lower Bounds: Classical/Quantum MDL, Quantum Factoring, and More
Minki Hhan
Foundations
This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models.
- In the classical generic group model (GGM), we find simple alternative proofs for the lower bounds of variants of the discrete logarithm (DL) problem: the multiple-instance DL and one-more DL problems (and their mixture). We also re-prove the unknown-order GGM lower bounds, such as the order finding, root extraction, and repeated squaring.
-...
SoK: Decentralized Storage Network
Chuanlei Li, Minghui Xu, Jiahao Zhang, Hechuan Guo, Xiuzhen Cheng
Foundations
Decentralized Storage Networks (DSNs) represent a paradigm shift in data storage methodology, distributing and housing data across multiple network nodes rather than relying on a centralized server or data center architecture. The fundamental objective of DSNs is to enhance security, reinforce reliability, and mitigate censorship risks by eliminating a single point of failure. Leveraging blockchain technology for functions such as access control, ownership validation, and transaction...
Fiat-Shamir for Bounded-Depth Adversaries
Liyan Chen, Yilei Chen, Zikuan Huang, Nuozhou Sun, Tianqi Yang, Yiding Zhang
Foundations
We study how to construct hash functions that can securely instantiate the Fiat-Shamir transformation against bounded-depth adversaries. The motivation is twofold. First, given the recent fruitful line of research of constructing cryptographic primitives against bounded-depth adversaries under worst-case complexity assumptions, and the rich applications of Fiat-Shamir, instantiating Fiat-Shamir hash functions against bounded-depth adversaries under worst-case complexity assumptions might...
Adaptive Security in SNARGs via iO and Lossy Functions
Brent Waters, Mark Zhandry
Foundations
We construct an adaptively sound SNARGs in the plain model with CRS
relying on the assumptions of (subexponential) indistinguishability obfuscation (iO), subexponential one-way functions and a notion of lossy functions we call length parameterized lossy functions. Length parameterized lossy functions take in separate security and input length parameters and have the property that the function image size in lossy mode depends only on the security parameter. We then show a novel way of...
FRIDA: Data Availability Sampling from FRI
Mathias Hall-Andersen, Mark Simkin, Benedikt Wagner
Foundations
As blockchains like Ethereum continue to grow, clients with limited resources can no longer store the entire chain.
Light nodes that want to use the blockchain, without verifying that it is in a good state overall, can just download the block headers without the corresponding block contents.
As those light nodes may eventually need some of the block contents, they would like to ensure that they are in principle available.
Data availability sampling, introduced by Bassam et al., is a...
Collusion-Resilience in Transaction Fee Mechanism Design
Hao Chung, Tim Roughgarden, Elaine Shi
Foundations
Users bid in a transaction fee mechanism (TFM) to get their transactions included and confirmed by a blockchain protocol. Roughgarden (EC'21) initiated the formal treatment of TFMs and proposed three requirements: user incentive compatibility (UIC), miner incentive compatibility (MIC), and a form of collusion-resilience called OCA-proofness. Ethereum's EIP-1559 mechanism satisfies all three properties simultaneously when there is no contention between transactions, but loses the UIC property...
Public-Key Cryptography through the Lens of Monoid Actions
Hart Montgomery, Sikhar Patranabis
Foundations
We show that key exchange and two-party computation are exactly equivalent to monoid actions with certain structural and hardness properties. To the best of our knowledge, this is the first "natural" characterization of the mathematical structure inherent to any key exchange or two-party computation protocol, and the first explicit proof of the necessity of mathematical structure for public-key cryptography. We then utilize these characterizations to show a new black-box separation result,...
Pseudorandom Error-Correcting Codes
Miranda Christ, Sam Gunn
Foundations
We construct pseudorandom error-correcting codes (or simply pseudorandom codes), which are error-correcting codes with the property that any polynomial number of codewords are pseudorandom to any computationally-bounded adversary. Efficient decoding of corrupted codewords is possible with the help of a decoding key.
We build pseudorandom codes that are robust to substitution and deletion errors, where pseudorandomness rests on standard cryptographic assumptions. Specifically,...
On the Security of Nova Recursive Proof System
Hyeonbum Lee, Jae Hong Seo
Foundations
Nova is a new type of recursive proof system that uses folding scheme as its core building block. This brilliant idea of folding relations can significantly reduce recursion overhead. In this paper, we study some issues related to Nova's soundness proof that relies on the soundness of the folding scheme in a recursive manner.
First, its proof strategy, due to its recursive nature, inevitably expands the running time of the recursive extractor polynomially for each additional recursive...
Strong Batching for Non-Interactive Statistical Zero-Knowledge
Changrui Mu, Shafik Nassar, Ron D. Rothblum, Prashant Nalini Vasudevan
Foundations
A zero-knowledge proof enables a prover to convince a verifier that $x \in S$, without revealing anything beyond this fact. By running a zero-knowledge proof $k$ times, it is possible to prove (still in zero-knowledge) that $k$ separate instances $x_1,\dots,x_k$ are all in $S$. However, this increases the communication by a factor of $k$. Can one do better? In other words, is (non-trivial) zero-knowledge batch verification for $S$ possible?
Recent works by Kaslasi et al. (TCC 2020,...
Universal Computational Extractors from Lattice Assumptions
Yilei Chen, Xinyu Mao
Foundations
Universal computational extractors (UCEs), introduced by Bellare, Hoang, and Keelveedhi [BHK13], can securely replace random oracles in various applications, including KDM-secure encryption, deterministic encryption, RSA-OAEP, etc. Despite its usefulness, constructing UCE in the standard model is challenging. The only known positive result is given by Brzuska and Mittelbach [BM14], who construct UCE with strongly computationally unpredictable one-query source assuming indistinguishability...
Game-Theoretically Fair Distributed Sampling
Sri Aravinda Krishnan Thyagarajan, Ke Wu, Pratik Soni
Foundations
Cleve's celebrated result (STOC'86) showed that a strongly fair multi-party coin-toss is impossible in the presence of majority-sized coalitions. Recently, however, a fascinating line of work studied a relaxed fairness notion called \emph{game-theoretic fairness}, which guarantees that no coalition should be incentivized to deviate from the prescribed protocol.
A sequence of works has explored the feasibility of game-theoretic fairness for \emph{two-sided} coin-toss, and indeed...
Analysis of a Programmable Quantum Annealer as a Random Number Generator
Elijah Pelofske
Foundations
Quantum devices offer a highly useful function - that is generating random numbers in a non-deterministic way since the measurement of a quantum state is not deterministic. This means that quantum devices can be constructed that generate qubits in a uniform superposition and then measure the state of those qubits. If the preparation of the qubits in a uniform superposition is unbiased, then quantum computers can be used to create high entropy, secure random numbers. Typically, preparing and...
General Adversary Structures in Byzantine Agreement and Multi-Party Computation with Active and Omission Corruption
Konstantinos Brazitikos, Vassilis Zikas
Foundations
Typical results in multi-party computation (in short, MPC) capture faulty parties by assuming a threshold adversary corrupting parties actively and/or fail-corrupting. These corruption types are, however, inadequate for capturing correct parties that might suffer temporary network failures and/or localized faults - these are particularly relevant for MPC over large, global scale networks. Omission faults and general adversary structures have been proposed as more suitable alternatives....
NIZKs with Maliciously Chosen CRS: Subversion Advice-ZK and Accountable Soundness
Prabhanjan Ananth, Gilad Asharov, Vipul Goyal, Hadar Kaner, Pratik Soni, Brent Waters
Foundations
Trusted setup is commonly used for non-interactive proof and argument systems. However, there is no guarantee that the setup parameters in these systems are generated in a trustworthy manner. Building upon previous works, we conduct a systematic study of non-interactive zero-knowledge arguments in the common reference string model where the authority running the trusted setup might be corrupted. We explore both zero-knowledge and soundness properties in this setting.
- We consider a new...
A Simpler and More Efficient Reduction of DLog to CDH for Abelian Group Actions
Steven Galbraith, Yi-Fu Lai, Hart Montgomery
Foundations
Abelian group actions appear in several areas of cryptography, especially isogeny-based post-quantum cryptography. A natural problem is to relate the analogues of the computational Diffie-Hellman (CDH) and discrete logarithm (DLog) problems for abelian group actions.
Galbraith, Panny, Smith and Vercauteren (Mathematical Cryptology '21) gave a quantum reduction of DLog to CDH, assuming a CDH oracle with perfect correctness. Montgomery and Zhandry (Asiacrypt '22, best paper award) showed...
On the bijectivity of the map $\chi$
Anna-Maurin Graner, Björn Kriepke, Lucas Krompholz, Gohar M. Kyureghyan
Foundations
We prove that for $n>1$ the map $\chi:\mathbb{F}_q^n \to \mathbb{F}_q^n$, defined by $y=\chi(x)$ with $y_i = x_i + x_{i+2}\cdot(1+x_{i+1})$ for $1\leq i \leq n$, is bijective if and only if
$q=2$ and $n$ is odd, as it was conjectured by Schoone and Daemen in 2023.
Adaptively-Sound Succinct Arguments for NP from Indistinguishability Obfuscation
Brent Waters, David J. Wu
Foundations
A succinct non-interactive argument (SNARG) for $\mathsf{NP}$ allows a prover to convince a verifier that an $\mathsf{NP}$ statement $x$ is true with a proof of size $o(|x| + |w|)$, where $w$ is the associated $\mathsf{NP}$ witness. A SNARG satisfies adaptive soundness if the malicious prover can choose the statement to prove after seeing the scheme parameters. In this work, we provide the first adaptively-sound SNARG for $\mathsf{NP}$ in the plain model assuming sub-exponentially-hard...
Finite Key OTP Functionality: Ciphers That Hold Off Attackers Smarter Than Their Designers
Gideon Samid
Foundations
The prevailing ciphers rely on the weak assumption that their attacker is not smarter than expected by their designers. The resultant crypto ecology favors the cryptographic powerhouses, and hinders cyber freedom, cyber privacy and cyber democracy. This weakness can be remedied by using the gold standard of cryptography -- One Time Pad, OTP. Alas, it comes with a prohibitive cost of a key as long as the message it encrypts. When the stakes are high enough users pay this high price because...
New self-orthogonal codes from weakly regular plateaued functions and their application in LCD codes
Melike Çakmak, Ahmet Sınak, Oğuz Yayla
Foundations
A linear code with few weights is a significant code family in coding theory. A linear code is considered self-orthogonal if contained within its dual code. Self-orthogonal codes have applications in linear complementary dual codes, quantum codes, etc. The construction of linear codes is an interesting research problem. There are various methods to construct linear codes, and one approach involves utilizing cryptographic functions defined over finite fields. The construction of linear codes...
Memory Checking Requires Logarithmic Overhead
Elette Boyle, Ilan Komargodski, Neekon Vafa
Foundations
We study the complexity of memory checkers with computational security and prove the first general tight lower bound.
Memory checkers, first introduced over 30 years ago by Blum, Evans, Gemmel, Kannan, and Naor (FOCS '91, Algorithmica '94), allow a user to store and maintain a large memory on a remote and unreliable server by using small trusted local storage. The user can issue instructions to the server and after every instruction, obtain either the correct value or a failure (but not...
R3PO: Reach-Restricted Reactive Program Obfuscation and its Application to MA-ABE
Kaartik Bhushan, Sai Lakshmi Bhavana Obbattu, Manoj Prabhakaran, Rajeev Raghunath
Foundations
In recent breakthrough results, novel use of garbled circuits yielded constructions for several primitives like Identity-Based Encryption (IBE) and 2-round secure multi-party computation, based on standard assumptions in public-key cryptography. While the techniques in these different results have many common elements, these works did not offer a modular abstraction that could be used across them.
Our main contribution is to introduce a novel notion of obfuscation, called Reach-Restricted...
Simpler and Faster BFV Bootstrapping for Arbitrary Plaintext Modulus from CKKS
Jaehyung Kim, Jinyeong Seo, Yongsoo Song
Foundations
Bootstrapping is a key operation in fully homomorphic encryption schemes that enables the evaluation of arbitrary multiplicative depth circuits.
In the BFV scheme, bootstrapping corresponds to reducing the size of accumulated noise in lower bits while preserving the plaintext in the upper bits.
The previous instantiation of BFV bootstrapping is achieved through the digit extraction procedure.
However, its performance is highly dependent on the plaintext modulus, so only a limited form...
On Hilbert-Poincaré series of affine semi-regular polynomial sequences and related Gröbner bases
Momonari Kudo, Kazuhiro Yokoyama
Foundations
Gröbner bases are nowadays central tools for solving various problems in commutative algebra and algebraic geometry.
A typical use of Gröbner bases is is the multivariate polynomial system solving, which enables us to construct algebraic attacks against post-quantum cryptographic protocols.
Therefore, the determination of the complexity of computing Gröbner bases is very important both in theory and in practice:
One of the most important cases is the case where input polynomials compose...
Constrained Pseudorandom Functions for Inner-Product Predicates from Weaker Assumptions
Sacha Servan-Schreiber
Foundations
In this paper, we build a framework for constructing Constrained Pseudorandom Functions (CPRFs) with inner-product constraint predicates, using ideas from subtractive secret sharing and related-key-attack security.
Our framework can be instantiated using a random oracle or any suitable Related-Key-Attack (RKA) secure pseudorandom function. We provide three instantiations of our framework:
1. an adaptively-secure construction in the random oracle model;
2. a selectively-secure...
Adaptive Distributional Security for Garbling Schemes with $\mathcal{O}(|x|)$ Online Complexity
Estuardo Alpírez Bock, Chris Brzuska, Pihla Karanko, Sabine Oechsner, Kirthivaasan Puniamurthy
Foundations
Garbling schemes allow to garble a circuit $C$ and an input $x$ such that $C(x)$ can be computed while hiding both $C$ and $x$. In the context of adaptive security, an adversary specifies the input to the circuit after seeing the garbled circuit, so that one can pre-process the garbling of $C$ and later only garble the input $x$ in the online phase. Since the online phase may be time-critical, it is an interesting question how much information needs to be transmitted in this phase and...
On Computing the Multidimensional Scalar Multiplication on Elliptic Curves
Walid Haddaji, Loubna Ghammam, Nadia El Mrabet, Leila Ben Abdelghani
Foundations
A multidimensional scalar multiplication ($d$-mul) consists of computing $[a_1]P_1+\cdots+[a_d]P_d$, where $d$ is an integer ($d\geq 2)$, $\alpha_1, \cdots, \alpha_d$ are scalars of size $l\in \mathbb{N}^*$ bits, $P_1, P_2, \cdots, P_d$ are points on an elliptic curve $E$. This operation ($d$-mul) is widely used in cryptography, especially in elliptic curve cryptographic algorithms.
Several methods in the literature allow to compute the $d$-mul efficiently (e.g., the bucket...
Lattice-Based Functional Commitments: Fast Verification and Cryptanalysis
Hoeteck Wee, David J. Wu
Foundations
A functional commitment allows a user to commit to an input $\mathbf{x} \in \{0,1\}^\ell$ and later open up the commitment to a value $y = f(\mathbf{x})$ with respect to some function $f$. In this work, we focus on schemes that support fast verification. Specifically, after a preprocessing step that depends only on $f$, the verification time as well as the size of the commitment and opening should be sublinear in the input length $\ell$, We also consider the dual setting where the user...
Updatable, Aggregatable, Succinct Mercurial Vector Commitment from Lattice
Hongxiao Wang, Siu-Ming Yiu, Yanmin Zhao, Zoe L. Jiang
Foundations
Vector commitments (VC) and their variants attract a lot of attention due to their wide range of usage in applications such as blockchain and accumulator. Mercurial vector commitment (MVC), as one of the important variants of VC, is the core technique for building more complicated cryptographic applications, such as the zero-knowledge set (ZKS) and zero-knowledge elementary database (ZK-EDB). However, to the best of our knowledge, the only post-quantum MVC construction is trivially implied...
Towards general-purpose program obfuscation via local mixing
Ran Canetti, Claudio Chamon, Eduardo Mucciolo, Andrei Ruckenstein
Foundations
We explore the possibility of obtaining general-purpose obfuscation for all circuits by way of making only simple, local, functionality preserving random perturbations in the circuit structure. Towards this goal, we use the additional structure provided by reversible circuits, but no additional algebraic structure.
We start by formulating a new (and relatively weak) obfuscation task regarding the ability to obfuscate random circuits of bounded length. We call such obfuscators random...
On short digital signatures with Eulerian transformations
Vasyl Ustimenko
Foundations
Let n stands for the length of digital signatures with quadratic multivariate public rule in n variables. We construct postquantum secure procedure to sign O(n^t), t ≥1 digital documents with the signature of size n in time O(n^{3+t}). It allows to sign O(n^t), t <1 in time O(n^4). The procedure is defined in terms of Algebraic Cryptography. Its security rests on the semigroup based protocol of Noncommutative Cryptography referring to complexity of the decomposition of the collision...
Combinatorially Homomorphic Encryption
Yuval Ishai, Eyal Kushnir, Ron D. Rothblum
Foundations
Homomorphic encryption enables public computation over encrypted data. In the past few decades, homomorphic encryption has become a staple of both the theory and practice of cryptography. Nevertheless, while there is a general loose understanding of what it means for a scheme to be homomorphic, to date there is no single unifying minimal definition that captures all schemes.
In this work, we propose a new definition, which we refer to as combinatorially homomorphic encryption, which...
Hard Languages in $\mathsf{NP} \cap \mathsf{coNP}$ and NIZK Proofs from Unstructured Hardness
Riddhi Ghosal, Yuval Ishai, Alexis Korb, Eyal Kushilevitz, Paul Lou, Amit Sahai
Foundations
The existence of "unstructured" hard languages in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ is an intriguing open question. Bennett and Gill (SICOMP, 1981) asked whether $\mathsf{P}$ is separated from $\mathsf{NP} \cap \mathsf{coNP}$ relative to a random oracle, a question that remained open ever since. While a hard language in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ can be constructed in a black-box way from a one-way permutation, for which only few (structured) candidates exist, Bitansky et al....
The Planck Constant and Quantum Fourier Transformation
Zhengjun Cao, Zhenfu Cao
Foundations
Quantum Fourier Transformation (QFT) plays a key role in quantum computation theory. But its transform size has never been discussed. In practice, the Xilinx LogiCORE IP Fast Fourier Transform core has the maximum transform size $N=2^{16}$. Taking into account the Planck constant $\hbar=6.62607015\times 10^{-34}$ and the difficulty to physically implement basic operator $\left[ \begin{array}{cc} 1& 0\\ 0 & \exp(-2\pi\,i/N)\\ \end{array} \right]$ on a qubit, we think $N=2^{120}$ could be...
Monotone Policy BARGs from BARGs and Additively Homomorphic Encryption
Shafik Nassar, Brent Waters, David J. Wu
Foundations
A monotone policy batch $\mathsf{NP}$ language $\mathcal{L}_{\mathcal{R}, P}$ is parameterized by a monotone policy $P \colon \{0,1\}^k \to \{0,1\}$ and an $\mathsf{NP}$ relation $\mathcal{R}$. A statement $(x_1, \ldots, x_k)$ is a YES instance if there exists $w_1, \ldots, w_k$ where $P(\mathcal{R}(x_1, w_1), \ldots, \mathcal{R}(x_k, w_k)) = 1$. For example, we might say that an instance $(x_1, \ldots, x_k)$ is a YES instance if a majority of the statements are true. A monotone policy batch...
Protection Against Subversion Corruptions via Reverse Firewalls in the plain Universal Composability Framework
Paula Arnold, Sebastian Berndt, Jörn Müller-Quade, Astrid Ottenhues
Foundations
While many modern cryptographic primitives have stood the test of time, attacker have already begun to expand their attacks beyond classical cryptanalysis by specifically targeting implementations. One of the most well-documented classes of such attacks are subversion (or substitution) attacks, where the attacker replaces the Implementation of the cryptographic primitive in an undetectable way such that the subverted implementation leaks sensitive information of the user during a protocol...
Upgrading Fuzzy Extractors
Chloe Cachet, Ariel Hamlin, Maryam Rezapour, Benjamin Fuller
Foundations
Fuzzy extractors derive stable keys from noisy sources non-interactively (Dodis et al., SIAM Journal of Computing 2008). Since their introduction, research has focused on two tasks: 1) showing security for as many distributions as possible and 2) providing stronger security guarantees including allowing one to enroll the same value multiple times (reusability), security against an active attacker (robustness), and preventing leakage about the enrolled value (privacy).
Existing constructions...
Batch Arguments to NIZKs from One-Way Functions
Eli Bradley, Brent Waters, David J. Wu
Foundations
Succinctness and zero-knowledge are two fundamental properties in the study of cryptographic proof systems. Several recent works have formalized the connections between these two notions by showing how to realize non-interactive zero-knowledge (NIZK) arguments from succinct non-interactive arguments. Specifically, Champion and Wu (CRYPTO 2023) as well as Bitansky, Kamath, Paneth, Rothblum, and Vasudevan (ePrint 2023) recently showed how to construct a NIZK argument for NP from a...
The Splitting Field of $Y^n-2$, Two-Variable NTT and Lattice-Based Cryptography
Wenzhe Yang
Foundations
The splitting field $F$ of the polynomial $Y^n-2$ is an extension over $\mathbb{Q}$ generated by $\zeta_n=\exp(2 \pi \sqrt{-1} /n)$ and $\sqrt[n]{2}$. In this paper, we lay the foundation for applying the Order-LWE in the integral ring $\mathcal{R}=\mathbb{Z}[\zeta_n, \sqrt[n]{2}]$ to cryptographic uses when $n$ is a power-of-two integer. We explicitly compute the Galois group $\text{Gal}\left(F/\mathbb{Q} \right)$ and the canonical embedding of $F$, based on which we study the properties of...
Cryptography from Planted Graphs: Security with Logarithmic-Size Messages
Damiano Abram, Amos Beimel, Yuval Ishai, Eyal Kushilevitz, Varun Narayanan
Foundations
We study the following broad question about cryptographic primitives: is it possible to achieve security against an arbitrary $\mathsf{poly}(n)$-time adversary with $O(\log n)$-size messages? It is common knowledge that the answer is ``no'' unless information-theoretic security is possible. In this work, we revisit this question by considering the setting of cryptography with public information and computational security.
We obtain the following results, assuming variants of well-studied...
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...
Fully Parallel, One-Cycle Random Shuffling for Efficient Countermeasure in Post-Quantum Cryptography
Jong-Yeon Park, Dongsoo Lee, Seonggyeom Kim, Wonil lee, Bo Gyeong Kang, Kouichi Sakurai
Foundations
Hiding countermeasures are the most widely utilized techniques for thwarting side-channel attacks, and their significance has been further emphasized with the advent of Post Quantum Cryptography (PQC) algorithms, owing to the extensive use of vector operations. Commonly, the Fisher-Yates algorithm is adopted in hiding countermeasures with permuted operation for its security and efficiency in implementation, yet the inherently sequential nature of the algorithm imposes limitations on hardware...
Reverie: an end-to-end accumulation scheme from Cyclefold
Lev Soukhanov
Foundations
Recent advances in SNARK recursion and incrementally-verifiable computation are vast, but most of the efforts seem to be focused on a particular design goal - proving the result of a large computation known completely in advance.
There are other possible applications, requiring different design tradeoffs. Particularly interesting direction is a case with a swarm of collaborating provers, communicating over a peer-to-peer network - which requires to also optimize the amount of data...
B2T: The Third Logical Value of a Bit
Dipesh, Vishesh Mishra, Urbi chatterjee
Foundations
Modern computing systems predominantly operate on the binary number system that accepts only ‘0’ or ‘1’ as logical values leading to computational homogeneity. But this helps in creating leakage patterns that can be exploited by adversaries to carry out hardware and software-level attacks. Recent research has shown that ternary systems, operating on three logical values (‘0′, ‘1', and ‘z') can surpass binary systems in terms of performance and security. In this paper, we first propose a...
Accountable Bulletin Boards: Definition and Provably Secure Implementation
Mike Graf, Ralf Küsters, Daniel Rausch, Simon Egger, Marvin Bechtold, Marcel Flinspach
Foundations
Bulletin boards (BB) are important cryptographic building blocks that, at their core, provide a broadcast channel with
memory. BBs are widely used within many security protocols, including secure multi-party computation protocols, e-voting systems, and electronic auctions. Even though the security of protocols crucially depends on the underlying BB, as also highlighted by recent works, the literature on constructing secure BBs is sparse. The so-far only provably secure BBs require trusted...
Different Flavours of HILL Pseudoentropy and Yao Incompressibility Entropy
Pihla Karanko
Foundations
There are two popular ways to measure computational entropy in cryptography: (HILL) pseudoentropy and (Yao) incompressibility entropy. Both of these computational entropy notions are based on a natural intuition.
- A random variable $X$ has $k$ bits of pseudoentropy if there exists a random variable $Y$ that has $k$ bits 'real' entropy and $Y$ is computationally indistinguishable from $X$.
- A random variable $X$ has $k$ bits of incompressibility entropy if $X$ cannot be efficiently...
A Simple and Efficient Framework of Proof Systems for NP
Yuyu Wang, Chuanjie Su, Jiaxin Pan, Yu Chen
Foundations
In this work, we propose a simple framework of constructing efficient non-interactive zero-knowledge proof (NIZK) systems for all NP. Compared to the state-of-the-art construction by Groth, Ostrovsky, and Sahai (J. ACM, 2012), our resulting NIZK system reduces the proof size and proving and verification cost without any trade-off, i.e., neither increasing computation cost, CRS size nor resorting to stronger assumptions.
Furthermore, we extend our framework to construct a batch argument...
A note on quantum approximate optimization algorithm
Zhengjun Cao
Foundations
The general quantum approximate optimization algorithm (QAOA)
produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer $p$ and the quality of approximation improves as $p$ is increased. In this note, we put some questions about the general QAOA. We also find the recursive QAOA for MaxCut problem is flawed because all quantum gates involved in the algorithm are single qubit gates. No any entangling gate is used, which results in...
Cycle Structure and Observability of Two Types of Galois NFSRs
Xianghan Wang, Jianghua Zhong, Dongdai Lin
Foundations
Nonlinear feedback shift registers (NFSRs) are used in many stream ciphers as their main building blocks. One security criterion for the design of a stream cipher is to assure its keystream has a long period. To meet this criterion, the NFSR used in a stream cipher must have a long state cycle. Further, to simultaneously avoid equivalent keys, the keystream's period is not compressed compared to the NFSR's state cycle length, which can be guaranteed if the NFSR is observable in the sense...
Unconditionally Secure Commitments with Quantum Auxiliary Inputs
Tomoyuki Morimae, Barak Nehoran, Takashi Yamakawa
Foundations
We show the following unconditional results on quantum commitments in two related yet different models:
1. We revisit the notion of quantum auxiliary-input commitments introduced by Chailloux, Kerenidis, and Rosgen (Comput. Complex. 2016) where both the committer and receiver take the same quantum state, which is determined by the security parameter,
as quantum auxiliary inputs. We show that computationally-hiding and statistically-binding quantum auxiliary-input commitments exist...
Unclonable Cryptography with Unbounded Collusions
Alper Çakan, Vipul Goyal
Foundations
Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program in a quantum state such that a user in possession of $k$ such states cannot create $k+1$ working copies. Introduced by Aaronson (CCC'09) over a decade ago, copy protection has proven to be notoriously hard to achieve.
In this work, we construct public-key encryption and functional encryption schemes whose secret keys are copy-protected against unbounded collusions in...
Ring-LWE Hardness Based on Non-invertible Ideals
Charanjit S. Jutla, Chengyu Lin
Foundations
We extend the known pseudorandomness of Ring-LWE to be based on lattices that do not correspond to any ideal of any order in the underlying number field. In earlier works of Lyubashevsky et al (EUROCRYPT 2010) and Peikert et al (STOC 2017), the hardness of RLWE was based on ideal lattices of ring of integers of number fields, which are known to be Dedekind domains. While these works extended Regev's (STOC 2005) quantum polynomial-time reduction for LWE, thus allowing more efficient and more...
Towards Unclonable Cryptography in the Plain Model
Céline Chevalier, Paul Hermouet, Quoc-Huy Vu
Foundations
By leveraging the no-cloning principle of quantum mechanics, unclonable cryptography enables us to achieve novel cryptographic protocols that are otherwise impossible classically. Two most notable examples of unclonable cryptography are quantum copy-protection and unclonable encryption. Most known constructions rely on the quantum random oracle model (as opposed to the plain model), in which all parties have access in superposition to a powerful random oracle.
Despite receiving a lot of...
Beyond MPC-in-the-Head: Black-Box Constructions of Short Zero-Knowledge Proofs
Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, Mor Weiss
Foundations
In their seminal work, Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC`07) presented the MPC-in-the-Head paradigm, which shows how to design Zero-Knowledge Proofs (ZKPs) from secure Multi-Party Computation (MPC) protocols. This paradigm has since then revolutionized and modularized the design of efficient ZKP systems, with far-reaching applications beyond ZKPs. However, to the best of our knowledge, all previous instantiations relied on fully-secure MPC protocols, and have not been able to...
On Instantiating Unleveled Fully-Homomorphic Signatures from Falsifiable Assumptions
Romain Gay, Bogdan Ursu
Foundations
We build the first unleveled fully homomorphic signature scheme in the standard model. Our scheme is not constrained by any a-priori bound on the depth of the functions that can be homomorphically evaluated, and relies on subexponentially-secure indistinguishability obfuscation, fully-homomorphic encryption and a non-interactive zero-knowledge (NIZK) proof system with composable zero-knowledge. Our scheme is also the first to satisfy the strong security notion of context-hiding for an...
Time-lock puzzles are unique cryptographic primitives that use computational complexity to keep information secret for some period of time, after which security expires. Unfortunately, current analysis techniques of time-lock primitives provide no sound mechanism to build multi-party cryptographic protocols which use expiring security as a building block. We explain in this paper that all other attempts at this subtle problem lack either composability, a fully consistent analysis, or...
In this paper, we consider two critical aspects of security in the distributed computing (DC) model: secure data shuffling and secure coded computing. It is imperative that any external entity overhearing the transmissions does not gain any information about the intermediate values (IVs) exchanged during the shuffling phase of the DC model. Our approach ensures IV confidentiality during data shuffling. Moreover, each node in the system must be able to recover the IVs necessary for computing...
Problems in the complexity class $NP$ are not all known to be solvable, but are verifiable given the solution, in polynomial time by a classical computer. The complexity class $BQP$ includes all problems solvable in polynomial time by a quantum computer. Prime factorization is in $NP$ class, and is also in $BQP$ class, owing to Shor's algorithm. The hardest of all problems within the $NP$ class are called $NP$-complete. If a quantum algorithm can solve an $NP$-complete problem in polynomial...
In this note, we improve the space-efficient variant of Regev's quantum factoring algorithm [Reg23] proposed by Ragavan and Vaikuntanathan [RV24] by constant factors in space and/or size. This allows us to bridge the significant gaps in concrete efficiency between the circuits by [Reg23] and [RV24]; [Reg23] uses far fewer gates, while [RV24] uses far fewer qubits. The main observation is that the space-efficient quantum modular exponentiation technique by [RV24] can be modified to...
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit relation between nonlinear complexities of finite-length binary sequences and their corresponding periodic sequences. Based on the relation, we propose two algorithms that can generate all periodic binary sequences with any prescribed nonlinear complexity.
In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of Shor's algorithm that requires far fewer quantum gates. His algorithm relies on a number-theoretic conjecture on the elements in $(\mathbb{Z}/N\mathbb{Z})^{\times}$ that can be written as short products of very small prime numbers. We prove a version of this conjecture using tools from analytic number theory such...
The traveling salesman problem is the problem of finding out the shortest route in a network of cities, that a salesman needs to travel to cover all the cities, without visiting the same city more than once. This problem is known to be $NP$-hard with a brute-force complexity of $O(N^N)$ or $O(N^{2N})$ for $N$ number of cities. This problem is equivalent to finding out the shortest Hamiltonian cycle in a given graph, if at least one Hamiltonian cycle exists in it. Quantum algorithms for this...
Vector commitments gain a lot of attention because of their wide usage in applications such as blockchain and accumulator. Mercurial vector commitments and mercurial functional commitments (MFC), as significant variants of VC, are the central techniques to construct more advanced cryptographic primitives such as zero-knowledge set and zero-knowledge functional elementary database (ZK-FEDB). However, the current MFC only supports linear functions, limiting its application, i.e. building the...
This paper considers an information theoretic model of secure integrated sensing and communication, represented as a wiretap channel with action dependent states. This model allows one to secure a part of the transmitted message against a sensed target that eavesdrops the communication, while allowing transmitter actions to change the channel statistics. An exact secrecy-distortion region is given for a physically-degraded channel. Moreover, a finite-length achievability region is...
In this work, we study the worst-case to average-case hardness of the Learning with Errors problem (LWE) under an alternative measure of hardness $−$ the maximum success probability achievable by a probabilistic polynomial-time (PPT) algorithm. Previous works by Regev (STOC 2005), Peikert (STOC 2009), and Brakerski, Peikert, Langlois, Regev, Stehle (STOC 2013) give worst-case to average-case reductions from lattice problems, specifically the approximate decision variant of the Shortest...
In a secret-sharing scheme, a secret is shared among $n$ parties such that the secret can be recovered by authorized coalitions, while it should be kept hidden from unauthorized coalitions. In this work we study secret-sharing for $k$-slice access structures, in which coalitions of size $k$ are either authorized or not, larger coalitions are authorized and smaller are unauthorized. Known schemes for these access structures had smaller shares for small $k$'s than for large ones; hence our...
The Number Theoretic Transform (NTT) is a powerful mathematical tool that has become increasingly important in developing Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE). Its ability to efficiently calculate polynomial multiplication using the convolution theorem with a quasi-linear complexity $O(n \log{n})$ instead of $O(n^2)$ when implemented with Fast Fourier Transform-style algorithms has made it a key component in modern cryptography. FFT-style NTT algorithm or fast-NTT...
In this paper, we investigate the computational complexity of the problem of solving a one-sided system of equations of degree two of a special form over the max-plus algebra. Also, we consider the asymptotic density of solvable systems of this form. Such systems have appeared during the analysis of some tropical cryptography protocols that were recently suggested. We show how this problem is related to the integer linear programming problem and prove that this problem is NP-complete. We...
Common random string model is a popular model in classical cryptography with many constructions proposed in this model. We study a quantum analogue of this model called the common Haar state model, which was also studied in an independent work by Chen, Coladangelo and Sattath (arXiv 2024). In this model, every party in the cryptographic system receives many copies of one or more i.i.d Haar states. Our main result is the construction of a statistically secure PRSG with: (a) the output...
In this article, we focus on deriving an easily implementable and efficient method of constructing units of the group ring of dihedral group. We provide a necessary and sufficient condition that relates the units in the group ring of dihedral group with the units in the group ring of cyclic group. Using this relation and the methods available for inversion in the group ring of the cyclic group, we introduce an algorithm to construct units efficiently and check its performance experimentally.
Cryptographic agility, or crypto-agility, is a design feature that enables agile updates to new cryptographic algorithms and standards without the need to modify or replace the surrounding infrastructure. This paper examines the prerequisites for crypto-agility and proposes its desired design feature. More specifically, we investigate the design characteristics of widely deployed cybersecurity paradigms, i.e., zero trust, and apply its design feature to crypto-agility, achieving greater...
Biextensions associated to line bundles on abelian varieties allows to reinterpret the usual Weil, Tate, Ate, optimal Ate, \ldots, pairings as monodromy pairings. We introduce a cubical arithmetic, derived from the canonical cubical torsor structure of these line bundles, to obtain an efficient arithmetic of these biextensions. This unifies and extends Miller's standard algorithm to compute pairings along with other algorithms like elliptic nets and theta functions, and allows to adapt...
We present new secure multi-party computation protocols for linear algebra over a finite field, which improve the state-of-the-art in terms of security. We look at the case of \emph{unconditional security with perfect correctness}, i.e., information-theoretic security without errors. We notably propose an expected constant-round protocol for solving systems of $m$ linear equations in $n$ variables over $\mathbb{F}_q$ with expected complexity $O(k(n^{2.5} + m^{2.5}+n^2m^{0.5}))$ where $k >...
We explore a very simple distribution of unitaries: random (binary) phase -- Hadamard -- random (binary) phase -- random computational-basis permutation. We show that this distribution is statistically indistinguishable from random Haar unitaries for any polynomial set of orthogonal input states (in any basis) with polynomial multiplicity. This shows that even though real-valued unitaries cannot be completely pseudorandom (Haug, Bharti, Koh, arXiv:2306.11677), we can still obtain some...
We construct perfect zero-knowledge probabilistically checkable proofs (PZK-PCPs) for every language in #P. This is the first construction of a PZK-PCP for any language outside BPP. Furthermore, unlike previous constructions of (statistical) zero-knowledge PCPs, our construction simultaneously achieves non-adaptivity and zero knowledge against arbitrary (adaptive) polynomial-time malicious verifiers. Our construction consists of a novel masked sumcheck PCP, which uses the...
Quantum Fourier Transformation (QFT) needs to construct the rotation gates with extremely tiny angles. Since it is impossible to physically manipulate such tiny angles (corresponding to extremely weak energies), those gates should be replaced by some scaled and controllable gates. The version of QFT is called banded QFT (BQFT), and can be mathematically specified by Kronecker product and binary fraction. But the systemic errors of BQFT has never been heuristically estimated. In this...
Targeted Denial-of-Service (DoS) attacks have been a practical concern for permissionless blockchains. Potential solutions, such as random sampling, are adopted by blockchains. However, the associated security guarantees have only been informally discussed in prior work. This is due to the fact that existing adversary models are either not fully capturing this attack or giving up certain design choices (as in the sleepy model or asynchronous network model), or too strong to be...
With the ongoing advances in machine learning (ML), cybersecurity solutions and security primitives are becoming increasingly vulnerable to successful attacks. Strong physically unclonable functions (PUFs) are a potential solution for providing high resistance to such attacks. In this paper, we propose a generalized attack model that leverages multiple chips jointly to minimize the cloning error. Our analysis shows that the entropy rate over different chips is a relevant measure to the new...
Only a handful candidates for computational assumptions that imply secure key-agreement protocols (KA) are known, and even fewer are believed to be quantum safe. In this paper, we present a new hardness assumption---the worst-case hardness of a promise problem related to an interactive version of Kolmogorov Complexity. Roughly speaking, the promise problem requires telling apart tuples of strings $(\pi,x,y)$ with relatively (w.r.t. $K(\pi)$) low time-bounded Interactive Kolmogorov...
We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions. In more detail: - Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not...
Evolving secret-sharing schemes, defined by Komargodski, Naor, and Yogev [TCC 2016B, IEEE Trans. on Info. Theory 2018], are secret-sharing schemes in which there is no a-priory bound on the number of parties. In such schemes, parties arrive one by one; when a party arrives, the dealer gives it a share and cannot update this share in later stages. The requirement is that some predefined sets (called authorized sets) should be able to reconstruct the secret, while other sets should learn no...
Sponge hashing is a novel class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a short digest which consists of a subset of the final output bits. While much is known about the post-quantum security of the sponge...
A compilation of various notes written over the years on some algorithms on abelian varieties.
While classic result in the 1980s establish that one-way functions (OWFs) imply the existence of pseudorandom generators (PRGs) which in turn imply pseudorandom functions (PRFs), the constructions (most notably the one from OWFs to PRGs) is complicated and inefficient. Consequently, researchers have developed alternative \emph{direct} constructions of PRFs from various different concrete hardness assumptions. In this work, we continue this thread of work and demonstrate the first direct...
This paper presents a heuristic ideal obfuscation scheme based on the learning problem, which di ers from that of Jain, Lin, and Luo [JLLW23]. The paper adopts a method similar to Brakerski, Dottling, Garg, and Malavolta [BDGM22, BDGM20] for constructing iO. It first introduces a variant of the LWR problem and proves its pseudorandomness. Based on the variant of the LWR problem, it constructs LHE, then combines it with sFHE constructed from the LWE problem to further construct the ideal...
Garbling schemes are one of the most fundamental objects in cryptography and have been studied extensively due to their broad applicability. The state-of-the-art is a construction in which XOR gates are free and AND gates require $3\kappa/2+\mathcal{O}(1)$ bits per gate, due to Rosulek and Roy (CRYPTO'21). An important technique in their garbling is slicing, which partitions the labels into two equal-length slices. In this paper, we explore the feasibility of the slicing technique for...
This work models a secure integrated sensing and communication (ISAC) system as a broadcast channel with action-dependent channel states and output feedback. The transmitted message is split into a common and a secure message, both of which must be recovered at the legitimate receiver, while the secure message needs to be kept secret from the eavesdropper. The transmitter actions, such as beamforming vector design, affect the corresponding state distribution at each channel use. The action...
A $t$-multi-collision-resistant hash function ($t$-MCRH) is a family of shrinking functions for which it is computationally hard to find $t$ distinct inputs mapping to the same output for a function sampled from this family. Several works have shown that $t$-MCRHs are sufficient for many of the applications of collision-resistant hash functions (CRHs), which correspond to the special case of $t = 2$. An important question is hence whether $t$-MCRHs for $t > 2$ are fundamentally weaker...
One of the most basic problems for studying the "price of privacy over time" is the so called private counter problem, introduced by Dwork et al. (2010) and Chan et al. (2010). In this problem, we aim to track the number of events that occur over time, while hiding the existence of every single event. More specifically, in every time step $t\in[T]$ we learn (in an online fashion) that $\Delta_t\geq 0$ new events have occurred, and must respond with an estimate $n_t\approx\sum_{j=1}^t...
Collision-resistant hashing, a fundamental primitive in modern cryptography, ensures that there is no efficient way to find distinct inputs that produce the same hash value. This property underpins the security of various cryptographic applications, making it crucial to understand its complexity. The complexity of this problem is well-understood in the classical setting and $\Theta(N^{1/2})$ queries are needed to find a collision. However, the advent of quantum computing has introduced new...
Recent work has introduced the "Quantum-Computation Classical-Communication" (QCCC) (Chung et. al.) setting for cryptography. There has been some evidence that One Way Puzzles (OWPuzz) are the natural central cryptographic primitive for this setting (Khurana and Tomer). For a primitive to be considered central it should have several characteristics. It should be well behaved (which for this paper we will think of as having amplification, combiners, and universal constructions); it...
We put forward a new approach for achieving non-interactive zero-knowledge proofs (NIKZs) from the learning with errors (LWE) assumption (with subexponential modulus to noise ratio). We provide a LWE-based construction of a hidden bits generator that gives rise to a NIZK via the celebrated hidden bits paradigm. A noteable feature of our construction is its simplicity. Our construction employs lattice trapdoors, but beyond that uses only simple operations. Unlike prior solutions we do not...
Side channel attacks are devastating attacks targeting cryptographic implementations. To protect against these attacks, various countermeasures have been proposed -- in particular, the so-called masking scheme. Masking schemes work by hiding sensitive information via secret sharing all intermediate values that occur during the evaluation of a cryptographic implementation. Over the last decade, there has been broad interest in designing and formally analyzing such schemes. The random probing...
Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. One of the strongest and most well-studied adversarial tampering models is $2$-split-state tampering. Here, a codeword is split into two parts which are stored in physically distant servers, and the adversary can then...
A leakage-resilient circuit for $f:\{0,1\}^n\to\{0,1\}^m$ is a randomized Boolean circuit $C$ mapping a randomized encoding of an input $x$ to an encoding of $y=f(x)$, such that applying any leakage function $L\in \cal L$ to the wires of $C$ reveals essentially nothing about $x$. A leakage-tolerant circuit achieves the stronger guarantee that even when $x$ and $y$ are not protected by any encoding, the output of $L$ can be simulated by applying some $L'\in \cal L$ to $x$ and $y$ alone....
The incentive-compatibility properties of blockchain transaction fee mechanisms have been investigated with passive block producers that are motivated purely by the net rewards earned at the consensus layer. This paper introduces a model of active block producers that have their own private valuations for blocks (representing, for example, additional value derived from the application layer). The block producer surplus in our model can be interpreted as one of the more common colloquial...
We present a novel circuit bootstrapping algorithm that outperforms the state-of-the-art TFHE method with 9.9× speedup and 15.6× key size reduction. These improvements can be attributed to two technical contributions. Firstly, we redesigned the circuit bootstrapping workflow to operate exclusively under the ring ciphertext type, which eliminates the need of conversion between LWE and RLWE ciphertexts. Secondly, we improve the LMKC+ blind rotation algorithm by reducing the number of...
Uniformly random unitaries, i.e., unitaries drawn from the Haar measure, have many useful properties, but cannot be implemented efficiently. This has motivated a long line of research into random unitaries that ``look'' sufficiently Haar random while also being efficient to implement. Two different notions of derandomisation have emerged: $t$-designs are random unitaries that information-theoretically reproduce the first $t$ moments of the Haar measure, and pseudorandom unitaries (PRUs)...
Pseudorandom Quantum States (PRS) were introduced by Ji, Liu and Song as quantum analogous to Pseudorandom Generators. They are an ensemble of states efficiently computable but computationally indistinguishable from Haar random states. Subsequent works have shown that some cryptographic primitives can be constructed from PRSs. Moreover, recent classical and quantum oracle separations of PRS from One-Way Functions strengthen the interest in a purely quantum alternative building block for...
We consider a secure integrated sensing and communication (ISAC) scenario, in which a signal is transmitted through a state-dependent wiretap channel with one legitimate receiver with which the transmitter communicates and one honest-but-curious target that the transmitter wants to sense. The secure ISAC channel is modeled as two state-dependent fast-fading channels with correlated Rayleigh fading coefficients and independent additive Gaussian noise components. Delayed channel outputs are...
This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the lower bounds of variants of the discrete logarithm (DL) problem: the multiple-instance DL and one-more DL problems (and their mixture). We also re-prove the unknown-order GGM lower bounds, such as the order finding, root extraction, and repeated squaring. -...
Decentralized Storage Networks (DSNs) represent a paradigm shift in data storage methodology, distributing and housing data across multiple network nodes rather than relying on a centralized server or data center architecture. The fundamental objective of DSNs is to enhance security, reinforce reliability, and mitigate censorship risks by eliminating a single point of failure. Leveraging blockchain technology for functions such as access control, ownership validation, and transaction...
We study how to construct hash functions that can securely instantiate the Fiat-Shamir transformation against bounded-depth adversaries. The motivation is twofold. First, given the recent fruitful line of research of constructing cryptographic primitives against bounded-depth adversaries under worst-case complexity assumptions, and the rich applications of Fiat-Shamir, instantiating Fiat-Shamir hash functions against bounded-depth adversaries under worst-case complexity assumptions might...
We construct an adaptively sound SNARGs in the plain model with CRS relying on the assumptions of (subexponential) indistinguishability obfuscation (iO), subexponential one-way functions and a notion of lossy functions we call length parameterized lossy functions. Length parameterized lossy functions take in separate security and input length parameters and have the property that the function image size in lossy mode depends only on the security parameter. We then show a novel way of...
As blockchains like Ethereum continue to grow, clients with limited resources can no longer store the entire chain. Light nodes that want to use the blockchain, without verifying that it is in a good state overall, can just download the block headers without the corresponding block contents. As those light nodes may eventually need some of the block contents, they would like to ensure that they are in principle available. Data availability sampling, introduced by Bassam et al., is a...
Users bid in a transaction fee mechanism (TFM) to get their transactions included and confirmed by a blockchain protocol. Roughgarden (EC'21) initiated the formal treatment of TFMs and proposed three requirements: user incentive compatibility (UIC), miner incentive compatibility (MIC), and a form of collusion-resilience called OCA-proofness. Ethereum's EIP-1559 mechanism satisfies all three properties simultaneously when there is no contention between transactions, but loses the UIC property...
We show that key exchange and two-party computation are exactly equivalent to monoid actions with certain structural and hardness properties. To the best of our knowledge, this is the first "natural" characterization of the mathematical structure inherent to any key exchange or two-party computation protocol, and the first explicit proof of the necessity of mathematical structure for public-key cryptography. We then utilize these characterizations to show a new black-box separation result,...
We construct pseudorandom error-correcting codes (or simply pseudorandom codes), which are error-correcting codes with the property that any polynomial number of codewords are pseudorandom to any computationally-bounded adversary. Efficient decoding of corrupted codewords is possible with the help of a decoding key. We build pseudorandom codes that are robust to substitution and deletion errors, where pseudorandomness rests on standard cryptographic assumptions. Specifically,...
Nova is a new type of recursive proof system that uses folding scheme as its core building block. This brilliant idea of folding relations can significantly reduce recursion overhead. In this paper, we study some issues related to Nova's soundness proof that relies on the soundness of the folding scheme in a recursive manner. First, its proof strategy, due to its recursive nature, inevitably expands the running time of the recursive extractor polynomially for each additional recursive...
A zero-knowledge proof enables a prover to convince a verifier that $x \in S$, without revealing anything beyond this fact. By running a zero-knowledge proof $k$ times, it is possible to prove (still in zero-knowledge) that $k$ separate instances $x_1,\dots,x_k$ are all in $S$. However, this increases the communication by a factor of $k$. Can one do better? In other words, is (non-trivial) zero-knowledge batch verification for $S$ possible? Recent works by Kaslasi et al. (TCC 2020,...
Universal computational extractors (UCEs), introduced by Bellare, Hoang, and Keelveedhi [BHK13], can securely replace random oracles in various applications, including KDM-secure encryption, deterministic encryption, RSA-OAEP, etc. Despite its usefulness, constructing UCE in the standard model is challenging. The only known positive result is given by Brzuska and Mittelbach [BM14], who construct UCE with strongly computationally unpredictable one-query source assuming indistinguishability...
Cleve's celebrated result (STOC'86) showed that a strongly fair multi-party coin-toss is impossible in the presence of majority-sized coalitions. Recently, however, a fascinating line of work studied a relaxed fairness notion called \emph{game-theoretic fairness}, which guarantees that no coalition should be incentivized to deviate from the prescribed protocol. A sequence of works has explored the feasibility of game-theoretic fairness for \emph{two-sided} coin-toss, and indeed...
Quantum devices offer a highly useful function - that is generating random numbers in a non-deterministic way since the measurement of a quantum state is not deterministic. This means that quantum devices can be constructed that generate qubits in a uniform superposition and then measure the state of those qubits. If the preparation of the qubits in a uniform superposition is unbiased, then quantum computers can be used to create high entropy, secure random numbers. Typically, preparing and...
Typical results in multi-party computation (in short, MPC) capture faulty parties by assuming a threshold adversary corrupting parties actively and/or fail-corrupting. These corruption types are, however, inadequate for capturing correct parties that might suffer temporary network failures and/or localized faults - these are particularly relevant for MPC over large, global scale networks. Omission faults and general adversary structures have been proposed as more suitable alternatives....
Trusted setup is commonly used for non-interactive proof and argument systems. However, there is no guarantee that the setup parameters in these systems are generated in a trustworthy manner. Building upon previous works, we conduct a systematic study of non-interactive zero-knowledge arguments in the common reference string model where the authority running the trusted setup might be corrupted. We explore both zero-knowledge and soundness properties in this setting. - We consider a new...
Abelian group actions appear in several areas of cryptography, especially isogeny-based post-quantum cryptography. A natural problem is to relate the analogues of the computational Diffie-Hellman (CDH) and discrete logarithm (DLog) problems for abelian group actions. Galbraith, Panny, Smith and Vercauteren (Mathematical Cryptology '21) gave a quantum reduction of DLog to CDH, assuming a CDH oracle with perfect correctness. Montgomery and Zhandry (Asiacrypt '22, best paper award) showed...
We prove that for $n>1$ the map $\chi:\mathbb{F}_q^n \to \mathbb{F}_q^n$, defined by $y=\chi(x)$ with $y_i = x_i + x_{i+2}\cdot(1+x_{i+1})$ for $1\leq i \leq n$, is bijective if and only if $q=2$ and $n$ is odd, as it was conjectured by Schoone and Daemen in 2023.
A succinct non-interactive argument (SNARG) for $\mathsf{NP}$ allows a prover to convince a verifier that an $\mathsf{NP}$ statement $x$ is true with a proof of size $o(|x| + |w|)$, where $w$ is the associated $\mathsf{NP}$ witness. A SNARG satisfies adaptive soundness if the malicious prover can choose the statement to prove after seeing the scheme parameters. In this work, we provide the first adaptively-sound SNARG for $\mathsf{NP}$ in the plain model assuming sub-exponentially-hard...
The prevailing ciphers rely on the weak assumption that their attacker is not smarter than expected by their designers. The resultant crypto ecology favors the cryptographic powerhouses, and hinders cyber freedom, cyber privacy and cyber democracy. This weakness can be remedied by using the gold standard of cryptography -- One Time Pad, OTP. Alas, it comes with a prohibitive cost of a key as long as the message it encrypts. When the stakes are high enough users pay this high price because...
A linear code with few weights is a significant code family in coding theory. A linear code is considered self-orthogonal if contained within its dual code. Self-orthogonal codes have applications in linear complementary dual codes, quantum codes, etc. The construction of linear codes is an interesting research problem. There are various methods to construct linear codes, and one approach involves utilizing cryptographic functions defined over finite fields. The construction of linear codes...
We study the complexity of memory checkers with computational security and prove the first general tight lower bound. Memory checkers, first introduced over 30 years ago by Blum, Evans, Gemmel, Kannan, and Naor (FOCS '91, Algorithmica '94), allow a user to store and maintain a large memory on a remote and unreliable server by using small trusted local storage. The user can issue instructions to the server and after every instruction, obtain either the correct value or a failure (but not...
In recent breakthrough results, novel use of garbled circuits yielded constructions for several primitives like Identity-Based Encryption (IBE) and 2-round secure multi-party computation, based on standard assumptions in public-key cryptography. While the techniques in these different results have many common elements, these works did not offer a modular abstraction that could be used across them. Our main contribution is to introduce a novel notion of obfuscation, called Reach-Restricted...
Bootstrapping is a key operation in fully homomorphic encryption schemes that enables the evaluation of arbitrary multiplicative depth circuits. In the BFV scheme, bootstrapping corresponds to reducing the size of accumulated noise in lower bits while preserving the plaintext in the upper bits. The previous instantiation of BFV bootstrapping is achieved through the digit extraction procedure. However, its performance is highly dependent on the plaintext modulus, so only a limited form...
Gröbner bases are nowadays central tools for solving various problems in commutative algebra and algebraic geometry. A typical use of Gröbner bases is is the multivariate polynomial system solving, which enables us to construct algebraic attacks against post-quantum cryptographic protocols. Therefore, the determination of the complexity of computing Gröbner bases is very important both in theory and in practice: One of the most important cases is the case where input polynomials compose...
In this paper, we build a framework for constructing Constrained Pseudorandom Functions (CPRFs) with inner-product constraint predicates, using ideas from subtractive secret sharing and related-key-attack security. Our framework can be instantiated using a random oracle or any suitable Related-Key-Attack (RKA) secure pseudorandom function. We provide three instantiations of our framework: 1. an adaptively-secure construction in the random oracle model; 2. a selectively-secure...
Garbling schemes allow to garble a circuit $C$ and an input $x$ such that $C(x)$ can be computed while hiding both $C$ and $x$. In the context of adaptive security, an adversary specifies the input to the circuit after seeing the garbled circuit, so that one can pre-process the garbling of $C$ and later only garble the input $x$ in the online phase. Since the online phase may be time-critical, it is an interesting question how much information needs to be transmitted in this phase and...
A multidimensional scalar multiplication ($d$-mul) consists of computing $[a_1]P_1+\cdots+[a_d]P_d$, where $d$ is an integer ($d\geq 2)$, $\alpha_1, \cdots, \alpha_d$ are scalars of size $l\in \mathbb{N}^*$ bits, $P_1, P_2, \cdots, P_d$ are points on an elliptic curve $E$. This operation ($d$-mul) is widely used in cryptography, especially in elliptic curve cryptographic algorithms. Several methods in the literature allow to compute the $d$-mul efficiently (e.g., the bucket...
A functional commitment allows a user to commit to an input $\mathbf{x} \in \{0,1\}^\ell$ and later open up the commitment to a value $y = f(\mathbf{x})$ with respect to some function $f$. In this work, we focus on schemes that support fast verification. Specifically, after a preprocessing step that depends only on $f$, the verification time as well as the size of the commitment and opening should be sublinear in the input length $\ell$, We also consider the dual setting where the user...
Vector commitments (VC) and their variants attract a lot of attention due to their wide range of usage in applications such as blockchain and accumulator. Mercurial vector commitment (MVC), as one of the important variants of VC, is the core technique for building more complicated cryptographic applications, such as the zero-knowledge set (ZKS) and zero-knowledge elementary database (ZK-EDB). However, to the best of our knowledge, the only post-quantum MVC construction is trivially implied...
We explore the possibility of obtaining general-purpose obfuscation for all circuits by way of making only simple, local, functionality preserving random perturbations in the circuit structure. Towards this goal, we use the additional structure provided by reversible circuits, but no additional algebraic structure. We start by formulating a new (and relatively weak) obfuscation task regarding the ability to obfuscate random circuits of bounded length. We call such obfuscators random...
Let n stands for the length of digital signatures with quadratic multivariate public rule in n variables. We construct postquantum secure procedure to sign O(n^t), t ≥1 digital documents with the signature of size n in time O(n^{3+t}). It allows to sign O(n^t), t <1 in time O(n^4). The procedure is defined in terms of Algebraic Cryptography. Its security rests on the semigroup based protocol of Noncommutative Cryptography referring to complexity of the decomposition of the collision...
Homomorphic encryption enables public computation over encrypted data. In the past few decades, homomorphic encryption has become a staple of both the theory and practice of cryptography. Nevertheless, while there is a general loose understanding of what it means for a scheme to be homomorphic, to date there is no single unifying minimal definition that captures all schemes. In this work, we propose a new definition, which we refer to as combinatorially homomorphic encryption, which...
The existence of "unstructured" hard languages in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ is an intriguing open question. Bennett and Gill (SICOMP, 1981) asked whether $\mathsf{P}$ is separated from $\mathsf{NP} \cap \mathsf{coNP}$ relative to a random oracle, a question that remained open ever since. While a hard language in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ can be constructed in a black-box way from a one-way permutation, for which only few (structured) candidates exist, Bitansky et al....
Quantum Fourier Transformation (QFT) plays a key role in quantum computation theory. But its transform size has never been discussed. In practice, the Xilinx LogiCORE IP Fast Fourier Transform core has the maximum transform size $N=2^{16}$. Taking into account the Planck constant $\hbar=6.62607015\times 10^{-34}$ and the difficulty to physically implement basic operator $\left[ \begin{array}{cc} 1& 0\\ 0 & \exp(-2\pi\,i/N)\\ \end{array} \right]$ on a qubit, we think $N=2^{120}$ could be...
A monotone policy batch $\mathsf{NP}$ language $\mathcal{L}_{\mathcal{R}, P}$ is parameterized by a monotone policy $P \colon \{0,1\}^k \to \{0,1\}$ and an $\mathsf{NP}$ relation $\mathcal{R}$. A statement $(x_1, \ldots, x_k)$ is a YES instance if there exists $w_1, \ldots, w_k$ where $P(\mathcal{R}(x_1, w_1), \ldots, \mathcal{R}(x_k, w_k)) = 1$. For example, we might say that an instance $(x_1, \ldots, x_k)$ is a YES instance if a majority of the statements are true. A monotone policy batch...
While many modern cryptographic primitives have stood the test of time, attacker have already begun to expand their attacks beyond classical cryptanalysis by specifically targeting implementations. One of the most well-documented classes of such attacks are subversion (or substitution) attacks, where the attacker replaces the Implementation of the cryptographic primitive in an undetectable way such that the subverted implementation leaks sensitive information of the user during a protocol...
Fuzzy extractors derive stable keys from noisy sources non-interactively (Dodis et al., SIAM Journal of Computing 2008). Since their introduction, research has focused on two tasks: 1) showing security for as many distributions as possible and 2) providing stronger security guarantees including allowing one to enroll the same value multiple times (reusability), security against an active attacker (robustness), and preventing leakage about the enrolled value (privacy). Existing constructions...
Succinctness and zero-knowledge are two fundamental properties in the study of cryptographic proof systems. Several recent works have formalized the connections between these two notions by showing how to realize non-interactive zero-knowledge (NIZK) arguments from succinct non-interactive arguments. Specifically, Champion and Wu (CRYPTO 2023) as well as Bitansky, Kamath, Paneth, Rothblum, and Vasudevan (ePrint 2023) recently showed how to construct a NIZK argument for NP from a...
The splitting field $F$ of the polynomial $Y^n-2$ is an extension over $\mathbb{Q}$ generated by $\zeta_n=\exp(2 \pi \sqrt{-1} /n)$ and $\sqrt[n]{2}$. In this paper, we lay the foundation for applying the Order-LWE in the integral ring $\mathcal{R}=\mathbb{Z}[\zeta_n, \sqrt[n]{2}]$ to cryptographic uses when $n$ is a power-of-two integer. We explicitly compute the Galois group $\text{Gal}\left(F/\mathbb{Q} \right)$ and the canonical embedding of $F$, based on which we study the properties of...
We study the following broad question about cryptographic primitives: is it possible to achieve security against an arbitrary $\mathsf{poly}(n)$-time adversary with $O(\log n)$-size messages? It is common knowledge that the answer is ``no'' unless information-theoretic security is possible. In this work, we revisit this question by considering the setting of cryptography with public information and computational security. We obtain the following results, assuming variants of well-studied...
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...
Hiding countermeasures are the most widely utilized techniques for thwarting side-channel attacks, and their significance has been further emphasized with the advent of Post Quantum Cryptography (PQC) algorithms, owing to the extensive use of vector operations. Commonly, the Fisher-Yates algorithm is adopted in hiding countermeasures with permuted operation for its security and efficiency in implementation, yet the inherently sequential nature of the algorithm imposes limitations on hardware...
Recent advances in SNARK recursion and incrementally-verifiable computation are vast, but most of the efforts seem to be focused on a particular design goal - proving the result of a large computation known completely in advance. There are other possible applications, requiring different design tradeoffs. Particularly interesting direction is a case with a swarm of collaborating provers, communicating over a peer-to-peer network - which requires to also optimize the amount of data...
Modern computing systems predominantly operate on the binary number system that accepts only ‘0’ or ‘1’ as logical values leading to computational homogeneity. But this helps in creating leakage patterns that can be exploited by adversaries to carry out hardware and software-level attacks. Recent research has shown that ternary systems, operating on three logical values (‘0′, ‘1', and ‘z') can surpass binary systems in terms of performance and security. In this paper, we first propose a...
Bulletin boards (BB) are important cryptographic building blocks that, at their core, provide a broadcast channel with memory. BBs are widely used within many security protocols, including secure multi-party computation protocols, e-voting systems, and electronic auctions. Even though the security of protocols crucially depends on the underlying BB, as also highlighted by recent works, the literature on constructing secure BBs is sparse. The so-far only provably secure BBs require trusted...
There are two popular ways to measure computational entropy in cryptography: (HILL) pseudoentropy and (Yao) incompressibility entropy. Both of these computational entropy notions are based on a natural intuition. - A random variable $X$ has $k$ bits of pseudoentropy if there exists a random variable $Y$ that has $k$ bits 'real' entropy and $Y$ is computationally indistinguishable from $X$. - A random variable $X$ has $k$ bits of incompressibility entropy if $X$ cannot be efficiently...
In this work, we propose a simple framework of constructing efficient non-interactive zero-knowledge proof (NIZK) systems for all NP. Compared to the state-of-the-art construction by Groth, Ostrovsky, and Sahai (J. ACM, 2012), our resulting NIZK system reduces the proof size and proving and verification cost without any trade-off, i.e., neither increasing computation cost, CRS size nor resorting to stronger assumptions. Furthermore, we extend our framework to construct a batch argument...
The general quantum approximate optimization algorithm (QAOA) produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer $p$ and the quality of approximation improves as $p$ is increased. In this note, we put some questions about the general QAOA. We also find the recursive QAOA for MaxCut problem is flawed because all quantum gates involved in the algorithm are single qubit gates. No any entangling gate is used, which results in...
Nonlinear feedback shift registers (NFSRs) are used in many stream ciphers as their main building blocks. One security criterion for the design of a stream cipher is to assure its keystream has a long period. To meet this criterion, the NFSR used in a stream cipher must have a long state cycle. Further, to simultaneously avoid equivalent keys, the keystream's period is not compressed compared to the NFSR's state cycle length, which can be guaranteed if the NFSR is observable in the sense...
We show the following unconditional results on quantum commitments in two related yet different models: 1. We revisit the notion of quantum auxiliary-input commitments introduced by Chailloux, Kerenidis, and Rosgen (Comput. Complex. 2016) where both the committer and receiver take the same quantum state, which is determined by the security parameter, as quantum auxiliary inputs. We show that computationally-hiding and statistically-binding quantum auxiliary-input commitments exist...
Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program in a quantum state such that a user in possession of $k$ such states cannot create $k+1$ working copies. Introduced by Aaronson (CCC'09) over a decade ago, copy protection has proven to be notoriously hard to achieve. In this work, we construct public-key encryption and functional encryption schemes whose secret keys are copy-protected against unbounded collusions in...
We extend the known pseudorandomness of Ring-LWE to be based on lattices that do not correspond to any ideal of any order in the underlying number field. In earlier works of Lyubashevsky et al (EUROCRYPT 2010) and Peikert et al (STOC 2017), the hardness of RLWE was based on ideal lattices of ring of integers of number fields, which are known to be Dedekind domains. While these works extended Regev's (STOC 2005) quantum polynomial-time reduction for LWE, thus allowing more efficient and more...
By leveraging the no-cloning principle of quantum mechanics, unclonable cryptography enables us to achieve novel cryptographic protocols that are otherwise impossible classically. Two most notable examples of unclonable cryptography are quantum copy-protection and unclonable encryption. Most known constructions rely on the quantum random oracle model (as opposed to the plain model), in which all parties have access in superposition to a powerful random oracle. Despite receiving a lot of...
In their seminal work, Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC`07) presented the MPC-in-the-Head paradigm, which shows how to design Zero-Knowledge Proofs (ZKPs) from secure Multi-Party Computation (MPC) protocols. This paradigm has since then revolutionized and modularized the design of efficient ZKP systems, with far-reaching applications beyond ZKPs. However, to the best of our knowledge, all previous instantiations relied on fully-secure MPC protocols, and have not been able to...
We build the first unleveled fully homomorphic signature scheme in the standard model. Our scheme is not constrained by any a-priori bound on the depth of the functions that can be homomorphically evaluated, and relies on subexponentially-secure indistinguishability obfuscation, fully-homomorphic encryption and a non-interactive zero-knowledge (NIZK) proof system with composable zero-knowledge. Our scheme is also the first to satisfy the strong security notion of context-hiding for an...
