We propose a new NTRU-based Public-Key Encryption (PKE) scheme called $\mathsf{NTRU }\mathsf{PKE}$, which effectively incorporates the Fujisaki-Okamoto transformation for PKE (denoted as $\mathsf{FO}_{\mathsf{PKE}}$) to achieve chosen-ciphertext security in the Quantum Random Oracle Model (QROM). While $\mathsf{NTRUEncrypt}$, a first-round candidate in the NIST PQC standardization process, was proven to be chosen-ciphertext secure in the Random Oracle Model (ROM), it lacked corresponding...

Several cryptographic primitives, especially succinct proofs of various forms, transform the satisfaction of high-level properties to the existence of a polynomial quotient between a polynomial that interpolates a set of values with a cleverly arranged divisor. Some examples are SNARKs, like Groth16, and polynomial commitments, such as KZG. Such a polynomial division naively takes $O(n \log n)$ time with Fast Fourier Transforms, and is usually the asymptotic bottleneck for these...

Masking has become a widely applied and heavily researched method to protect cryptographic implementations against SCA attacks. The success of masking is primarily attributed to its strong theoretical foundation enabling it to formally prove security by modeling physical properties through so-called probing models. Specifically, the robust $d$-probing model enables us to prove the security for arbitrarily masked hardware circuits, manually or with the assistance of automated tools, even when...

We study the problem of generating public unbiased randomness in a distributed manner within the recent You Only Speak Once (YOSO) framework for stateless multiparty computation, introduced by Gentry et al. in CRYPTO 2021. Such protocols are resilient to adaptive denial-of-service attacks and are, by their stateless nature, especially attractive in permissionless environments. While most works in the YOSO setting focus on independent random corruptions, we consider YOSO protocols with...

Coercion is a challenging and multi-faceted threat that prevents people from expressing their will freely. Similarly, vote-buying does to undermine the foundation of free democratic elections. These threats are especially dire for remote electronic voting, which relies on voters to express their political will freely but happens in an uncontrolled environment outside the polling station and the protection of the ballot booth. However, electronic voting in general, both in-booth and remote,...

Oblivious Transfer (OT) is at the heart of secure computation and is a foundation for many applications in cryptography. Over two decades of work have led to extremely efficient protocols for evaluating OT instances in the preprocessing model, through a paradigm called OT extension. A few OT instances generated in an offline phase can be used to perform many OTs in an online phase efficiently, i.e., with very low communication and computational overheads. Specifically, traditional OT...

We present TaSSLE, a new lookup argument for decomposable tables with minimal commitment costs. The construction generalizes techniques introduced in Lasso (Eurocrypt '24) which take advantage of the internal structure present in such tables to avoid the need for any party to need to commit to, or even construct, the entire table. This allows the use of lookups against very large tables, with applications including new design strategies for "zero-knowledge virtual machines". We show that...

With the rise of generative AI technology, the media's credibility as a source of truth has been significantly compromised. This highlights the need to verify the authenticity of media and its originality. Ensuring the integrity of media during capture using the device itself presents a straightforward solution to this challenge. However, raw captured media often require certain refinements or redactions before publication. Zero-knowledge proofs (ZKP) offer a solution by allowing...

The Jacobi Symbol is an essential primitive in cryptographic applications such as primality testing, integer factorization, and various encryption schemes. By exploring the interdependencies among modular reductions within the algorithmic loop, we have developed a refined method that significantly enhances computational efficiency. Our optimized algorithm, implemented in the Rust language, achieves a performance increase of 72% over conventional textbook methods and is twice as fast as the...

A sequential function is, informally speaking, a function $f$ for which a massively parallel adversary cannot compute "substantially" faster than an honest user with limited parallel computation power. Sequential functions form the backbone of many primitives that are extensively used in blockchains such as verifiable delay functions (VDFs) and time-lock puzzles. Despite this widespread practical use, there has been little work studying the complexity or theory of sequential...

This paper presents a novel reduction from the average-case hardness of the Module Inhomogeneous Short Integer Solution (M-ISIS) problem to the worst-case hardness of the Closest Vector Problem (CVP) by defining and leveraging “perfect” lattices for cryptographic purposes. Perfect lattices, previously only theoretical constructs, are characterized by their highly regular structure, optimal density, and a central void, which we term the “Origin Cell.” The simplest Origin Cell is a...

The MPC-in-the-Head (MPCitH) paradigm has recently gained traction as a foundation for post-quantum signature schemes, offering robust security without the need for trapdoors. Despite its strong security profile, MPCitH-based schemes suffer from high computational overhead and large signature sizes, limiting their practical application. This work addresses these inefficiencies by enhancing vector commitments within MPCitH-based schemes. We introduce the concept of vector semi-commitment,...

The field of Fully Homomorphic Encryption (FHE) has seen many theoretical and computational advances in recent years, bringing the technology closer to practicality than ever before. For this reason, practitioners from neighbouring fields such as machine learning have sought to understand FHE to provide privacy to their work. Unfortunately, selecting secure and efficient parameters in FHE is a daunting task due to the many interdependencies between the parameters involved. In this work, we...

Homomorphic encryption allows for computations on encrypted data without exposing the underlying plaintext, enabling secure and private data processing in various applications such as cloud computing and machine learning. This paper presents a comprehensive mathematical foundation for three prominent homomorphic encryption schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski-Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS), all based on the Ring Learning with Errors (RLWE) problem....

We study network-agnostic secure multiparty computation with perfect security. Traditionally MPC is studied assuming the underlying network is either synchronous or asynchronous. In a network-agnostic setting, the parties are unaware of whether the underlying network is synchronous or asynchronous. The feasibility of perfectly-secure MPC in synchronous and asynchronous networks has been settled a long ago. The landmark work of [Ben-Or, Goldwasser, and Wigderson, STOC'88] shows that $n...

Users increasingly store their data in the cloud, thereby benefiting from easy access, sharing, and redundancy. To additionally guarantee security of the outsourced data even against a server compromise, some service providers have started to offer end-to-end encrypted (E2EE) cloud storage. With this cryptographic protection, only legitimate owners can read or modify the data. However, recent attacks on the largest E2EE providers have highlighted the lack of solid foundations for this...

Masking is a widely adopted countermeasure against side-channel analysis (SCA) that protects cryptographic implementations from information leakage. However, current masking schemes often incur significant overhead in terms of electronic cost. RAMBAM, a recently proposed masking technique that fits elegantly with the AES algorithm, offers ultra-low latency/area by utilizing redundant representations of finite field elements. This paper presents a comprehensive generalization of RAMBAM and...

Security of blockchain technologies primarily relies on decentralization making them resilient against a subset of entities being taken down or corrupt. Blockchain scaling, crucial to decentralisation, has been addressed by architectural changes: i.e., the load of the nodes is reduced by parallelisation, called sharding or by taking computation load off the main blockchain via rollups. Both sharding and rollups have limitations in terms of decentralization and security. A crucial component...

Side channel attacks, and in particular timing attacks, are a fundamental obstacle to obtaining secure implementation of algorithms and cryptographic protocols, and have been widely researched for decades. While cryptographic definitions for the security of cryptographic systems have been well established for decades, none of these accepted definitions take into account the running time information leaked from executing the system. In this work, we give the foundation of new cryptographic...

Verifiable Delay Functions (VDF) are a class of cryptographic primitives aiming to guarantee a minimum computation time, even for an adversary with massive parallel computational power. They are useful in blockchain protocols, and several practical candidates have been proposed based on exponentiation in a large finite field: Sloth , Veedo, MinRoot. The underlying assumption of these constructions is that computing an exponentiation $x^e$ requires at least $\log_2 e$ sequential...

Extensible Markup Language (XML) is one of the most popular serialization languages. Since many security protocols are built using XML, it also provides cryptographic functionality. A central framework in this area is the Security Assertion Markup Language (SAML). This standard is one of the most widely used options for implementing Single Sign-On (SSO), which allows users to authenticate to different service providers using the credentials from a single identity provider. Like all other...

The Keyed Hashing and Asymmetric Nonce (KHAN) encryption algorithm is a novel cryptographic scheme that utilizes the unique properties of full reptend prime numbers. This paper details the algorithm, its theoretical foundations, and the rigorous proofs of its security properties. By leveraging the characteristics of cyclic sequences derived from full reptend primes, KHAN provides robust encryption with high resistance to cryptanalytic attacks.

The assumption that certain computations inherently require some sequential time has established itself as a powerful tool for cryptography. It allows for security and liveness guarantees in distributed protocols that are impossible to achieve with classical hardness assumptions. Unfortunately, many constructions from the realm of time-based cryptography are based on new and poorly understood hardness assumptions, which tend not to stand the test of time (cf. Leurent et al. 2023, Peikert &...

Provable security based on a robust mathematical framework is the gold standard for security evaluation in cryptography. Several provable secure cryptosystems have been studied for public key cryptography. However, provably secure symmetric-key cryptography has received little attention. Although there are known provably secure symmetric-key cryptosystems based on the hardness of factorization and discrete logarithm problems, they are not only slower than conventional block ciphers but can...

Quantum computers can efficiently model and solve several challenging problems for classical computers, raising concerns about potential security reductions in cryptography. NIST is already considering potential quantum attacks in the development of post-quantum cryptography by estimating the quantum resources required for such quantum attacks. In this paper, we present quantum circuits for the NV sieve algorithm to solve the Shortest Vector Problem (SVP), which serves as the security...

In this work we tackle privacy concerns in biometric verification systems that typically require server-side processing of sensitive data (e.g., fingerprints and Iris Codes). Concretely, we design a solution that allows us to query whether a given Iris Code is similar to one contained in a given database, while all queries and datasets are being protected using secure multiparty computation (MPC). Addressing the substantial performance demands of operational systems like World ID and aid...

The discourse herein pertains to a directional encryption cryptosystem predicated upon logarithmic signatures interconnected via a system of linear equations (we call it LINE). A logarithmic signature serves as a foundational cryptographic primitive within the algorithm, characterized by distinct cryptographic attributes including nonlinearity, noncommutativity, unidirectionality, and factorizability by key. The confidentiality of the cryptosystem is contingent upon the presence of an...

Designing light clients for Proof-of-Work blockchains has been a foundational problem since Nakamoto's SPV construction in the Bitcoin paper. Over the years, communication was reduced from O(C) down to O(polylog(C)) in the system's lifetime C. We present Blink, the first provably secure O(1) light client that does not require a trusted setup.

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...

This paper presents a comprehensive security analysis of the Adh zero-knowledge proof system, a novel lattice-based, quantum-resistant proof of possession system. The Adh system offers compact key and proof sizes, making it suitable for real-world digital signature and public key agreement protocols. We explore its security by reducing it to the hardness of the Module-ISIS problem and introduce three new variants: Module-ISIS , Module-ISIS*, and Module-ISIS**. These constructions enhance...

Fully Homomorphic Encryption (FHE) is a powerful Privacy-Enhancing Technology (PET) that enables computations on encrypted data without having access to the secret key. While FHE holds immense potential for enhancing data privacy and security, creating its practical applications is associated with many difficulties. A significant barrier is the absence of easy-to-use, standardized components that developers can utilize as foundational building blocks. Addressing this gap requires...

Fully homomorphic encryption (FHE) allows for evaluating arbitrary functions over encrypted data. In Multi-party FHE applications, different parties encrypt their secret data and submit ciphertexts to a server, which, according to the application logic, performs homomorphic operations on them. For example, in a secret voting application, the tally is computed by summing up the ciphertexts encoding the votes. Valid encrypted votes are of the form $E(0)$ and $E(1)$. A malicious voter could...

Software solutions to address computational challenges are ubiquitous in our daily lives. One specific application area where software is often used is in embedded systems, which, like other digital electronic devices, are vulnerable to side-channel analysis attacks. Although masking is the most common countermeasure and provides a solid theoretical foundation for ensuring security, recent research has revealed a crucial gap between theoretical and real-world security. This shortcoming stems...

Zero-Knowledge Proof (ZKP) technology marks a revolutionary advancement in the field of cryptography, enabling the verification of certain information ownership without revealing any specific details. This technology, with its paradoxical yet powerful characteristics, provides a solid foundation for a wide range of applications, especially in enhancing the privacy and security of blockchain technology and other cryptographic systems. As ZKP technology increasingly becomes a part of the...

This paper introduces a high-performance and scalable hardware architecture designed for the Number-Theoretic Transform (NTT), a fundamental component extensively utilized in lattice-based encryption and fully homomorphic encryption schemes. The underlying rationale behind this research is to harness the advantages of the hypercube topology. This topology serves to significantly diminish the volume of data exchanges required during each iteration of the NTT, reducing it to a complexity of...

The elegant paradigm of Anamorphic Encryption (Persiano et al., Eurocrypt 2022) considers the question of establishing a private communication in a world controlled by a dictator. The challenge is to allow two users, sharing some secret anamorphic key, to exchange covert messages without the dictator noticing, even when the latter has full access to the regular secret keys. Over the last year several works considered this question and proposed constructions, novel extensions and...

Direct Anonymous Attestation (DAA) is a cryptographic protocol that enables users with a Trusted Platform Module (TPM) to authenticate without revealing their identity. Thus, DAA emerged as a good privacy-enhancing solution. Current standards have security based on factorization and discrete logarithm problem making them vulnerable to quantum computer attacks. Recently, a number of lattice-based DAA has been propose in the literature to start transition to quantum-resistant cryptography. In...

Lattice-based cryptography has emerged as a promising new candidate to build cryptographic primitives. It offers resilience against quantum attacks, enables fully homomorphic encryption, and relies on robust theoretical foundations. Zero-knowledge proofs (ZKPs) are an essential primitive for various privacy-preserving applications. For example, anonymous credentials, group signatures, and verifiable oblivious pseudorandom functions all require ZKPs. Currently, the majority of ZKP systems are...

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...

Transport Layer Security ( TLS ) is foundational for safeguarding client-server communication. However, it does not extend integrity guarantees to third-party verification of data authenticity. If a client wants to present data obtained from a server, it cannot convince any other party that the data has not been tampered with. TLS oracles ensure data authenticity beyond the client-server TLS connection, such that clients can obtain data from a server and ensure provenance to any third...

We define a (small) augmentation to the FROST threshold signature scheme that additionally allows for re-randomizable public and secret keys. We build upon the notion of re-randomizable keys in the literature, but tailor this capability when the signing key is secret-shared among a set of mutually trusted parties. We do not make any changes to the plain FROST protocol, but instead define additional algorithms to allow for randomization of the threshold public key and participant’s individual...

Verifiable Random Functions (VRFs) play a pivotal role in Proof of Stake (PoS) blockchain due to their applications in secret leader election protocols. However, the original definition by Micali, Rabin and Vadhan is by itself insufficient for such applications. The primary concern is that adversaries may craft VRF key pairs with skewed output distribution, allowing them to unfairly increase their winning chances. To address this issue David, Gaži, Kiayias and Russel (2017/573) proposed a...

The Bitcoin ecosystem has continued to evolve beyond its initial promises of decentralization, transparency, and security. Recent advancements have notably been made with the integration of Layer-2 solutions, which address scalability issues by offloading transactions from the main blockchain. This facilitates faster and more cost-effective transactions while maintaining integrity. The advent of inscriptions and ordinal protocols has further broadened the spectrum of capabilities, enabling...

In this paper, we explore a novel Zero-knowledge Virtual Machine (zkVM) framework leveraging succinct, non-interactive zero-knowledge proofs for verifiable computation over any code. Our approach divides program execution proof into two stages. In the first stage, the process breaks down program execution into segments, identifying and grouping identical sections. These segments are then proved through data-parallel circuits that allow for varying amounts of duplication. In the subsequent...

We introduce a new cryptographic primitive, called Sybil-Resilient Anonymous (SyRA) signatures, which enable users to generate, on demand, unlinkable pseudonyms tied to any given context, and issue signatures on behalf of these pseudonyms. Concretely, given a personhood relation, an issuer (who may be a distributed entity) enables users to prove their personhood and extract an associated long-term key, which can then be used to issue signatures for any given context and message....

We devise algorithms for finding equivalences of trilinear forms over finite fields modulo linear group actions. Our focus is on two problems under this umbrella, Matrix Code Equivalence (MCE) and Alternating Trilinear Form Equivalence (ATFE), since their hardness is the foundation of the NIST round-$1$ signature candidates MEDS and ALTEQ respectively. We present new algorithms for MCE and ATFE, which are further developments of the algorithms for polynomial isomorphism and alternating...

Inspired by range-check trick from recent Latticefold paper we construct elliptic-curve based IVC capable of simulating non-native arithmetic efficiently. We explain the general principle (which can be applied to both Protostar and Hypernova), and describe the Wrongfield ARithmetic for Protostar folding in details. Our construction supports circuits over mutilple non-native fields simultaneously and allows interfacing between them using range-checked elements. WARPfold...

Nonlocal games are a foundational tool for understanding entanglement and constructing quantum protocols in settings with multiple spatially separated quantum devices. In this work, we continue the study initiated by Kalai et al. (STOC '23) of compiled nonlocal games, played between a classical verifier and a single cryptographically limited quantum device. Our main result is that the compiler proposed by Kalai et al. is sound for any two-player XOR game. A celebrated theorem of Tsirelson...

In differential-like attacks, the process typically involves extending a distinguisher forward and backward with probability 1 for some rounds and recovering the key involved in the extended part. Particularly in rectangle attacks, a holistic key recovery strategy can be employed to yield the most efficient attacks tailored to a given distinguisher. In this paper, we treat the distinguisher and the extended part as an integrated entity and give a one-step framework for finding rectangle...

The Tensor Isomorphism Problem (TIP) has been shown to be equivalent to the matrix code equivalence problem, making it an interesting candidate on which to build post-quantum cryptographic primitives. These hard problems have already been used in protocol development. One of these, MEDS, is currently in Round 1 of NIST's call for additional post-quantum digital signatures. In this work, we consider the TIP for a special class of tensors. The hardness of the decisional version of this...

Asynchronous complete secret sharing (ACSS) is a foundational primitive in the design of distributed algorithms and cryptosystems that require secrecy. Dual-threshold ACSS permits a dealer to distribute a secret to a collection of $n$ servers so that everyone holds shares of a polynomial containing the dealer's secret. This work contributes a new ACSS protocol, called Haven , that uses packing and batching to make asymptotic and concrete advances in the design and application of ACSS for...

Zero-knowledge circuits are frequently required to prove gadgets that are not optimised for the constraint system in question. A particularly daunting task is to embed foreign arithmetic such as Boolean operations, field arithmetic, or public-key cryptography. We construct techniques for offloading foreign arithmetic from a zero-knowledge circuit including: (i) equality of discrete logarithms across different groups; (ii) scalar multiplication without requiring elliptic curve...

We present a concretely efficient and simple extractable witness encryption scheme for KZG polynomial commitments. It allows to encrypt a message towards a triple $(\mathsf{com}, \alpha, \beta)$, where $\mathsf{com}$ is a KZG commitment for some polynomial $f$. Anyone with an opening for the commitment attesting $f(\alpha) = \beta$ can decrypt, but without knowledge of a valid opening the message is computationally hidden. Our construction is simple and highly efficient. The ciphertext is...

Byzantine Agreement (BA) allows a set of $n$ parties to agree on a value even when up to $t$ of the parties involved are corrupted. While previous works have shown that, for $\ell$-bit inputs, BA can be achieved with the optimal communication complexity $\mathcal{O}(\ell n)$ for sufficiently large $\ell$, BA only ensures that honest parties agree on a meaningful output when they hold the same input, rendering the primitive inadequate for many real-world applications. This gave rise to...

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...

We study blockchain-based provably anonymous payment systems between light clients. Such clients interact with the blockchain through full nodes, who can see what the light clients read and write. The goal of our work is to enable light clients to perform anonymous payments, while maintaining privacy even against the full nodes through which they interact with the blockchain. We formalize the problem in the universal composability model and present a provably secure solution to it. In...

Secure multi-party computation (MPC) allows a set of $n$ parties to jointly compute a function over their private inputs. The seminal works of Ben-Or, Canetti and Goldreich [STOC '93] and Ben-Or, Kelmer and Rabin [PODC '94] settled the feasibility of MPC over asynchronous networks. Despite the significant line of work devoted to improving the communication complexity, current protocols with information-theoretic security and optimal resilience $t<n/3$ communicate $\Omega(n^4C)$ field...

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,...

This paper introduces an algorithm to efficiently break the Decisional Diffie-Hellman (DDH) assumption in totally non-maximal imaginary quadratic orders, specifically when $\Delta_1 = 3$, and $f$ is non-prime with knowledge of a single factor. Inspired by Shanks and Dedekind's work on 3-Sylow groups, we generalize their observations to undermine DDH security.

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...

Threshold signatures improve both availability and security of digital signatures by splitting the signing key into $N$ shares handed out to different parties. Later on, any subset of at least $T$ parties can cooperate to produce a signature on a given message. While threshold signatures have been extensively studied in the pre-quantum setting, they remain sparse from quantum-resilient assumptions. We present the first efficient lattice-based threshold signatures with signature size 13...

The use of zero-knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARK) and similar types of proofs has become increasingly popular as a solution for improving scalability, privacy, and interoperability of blockchain systems. However, even with the most advanced proving systems, verifying a single SNARK proof can require a significant amount of computational resources making it expensive to be performed on-chain. This becomes a noticeable bottleneck in scaling SNARK-based...

In recent years, the number of third-party services that can access highly-sensitive data has increased steadily, e.g., in the financial sector, in eGovernment applications, or in high-assurance identity services. Protocols that enable this access must provide strong security guarantees. A prominent and widely employed protocol for this purpose is the OpenID Foundation's FAPI protocol. The FAPI protocol is already in widespread use, e.g., as part of the UK's Open Banking standards and...

Software obfuscation is a powerful tool to protect the intellectual property or secret keys inside programs. Strong software obfuscation is crucial in the context of untrusted execution environments (e.g., subject to malware infection) or to face potentially malicious users trying to reverse-engineer a sensitive program. Unfortunately, the state-of-the-art of pure software-based obfuscation (including white-box cryptography) is either insecure or infeasible in practice. This work...

Decentralized applications (DApps), which are innovative blockchain-powered software systems designed to serve as the fundamental building blocks for the next generation of Internet services, have witnessed exponential growth in recent years. This paper thoroughly compares and analyzes two blockchain-based decentralized storage networks (DSNs), which are crucial foundations for DApp and blockchain ecosystems. The study examines their respective mechanisms for data persistence, strategies for...

ZK-SNARKs, a fundamental component of privacy-oriented payment systems, identity protocols, or anonymous voting systems, are advanced cryptographic protocols for verifiable computation: modern SNARKs allow to encode the invariants of a program, expressed as an arithmetic circuit, in an appropriate constraint language from which short, zero-knowledge proofs for correct computations can be constructed. One of the most important computations that is run through SNARK systems is the...

In today's systems, privacy is often at odds with utility: users that reveal little information about themselves get restricted functionality, and service providers mistrust them. In practice, systems tip to either full anonymity (e.g. Monero), or full utility (e.g. Bitcoin). Well-known cryptographic primitives for bridging this gap exist: anonymous credentials (AC) let users disclose a subset of their credentials' attributes, revealing to service providers "just what they need"; group...

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...

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...

Decentralized Finance (DeFi) has witnessed remarkable growth and innovation, with Decentralized Exchanges (DEXes) playing a pivotal role in shaping this ecosystem. As numerous DEX designs emerge, challenges such as price inefficiency and lack of user privacy continue to prevail. This paper introduces a novel DEX design, termed COMMON, that addresses these two predominant challenges. COMMON operates as an order book, natively integrated with a shielded token pool, thus providing anonymity to...

In May 2020, Zoom Video Communications, Inc. (Zoom) announced a multi-step plan to comprehensively support end-to-end encrypted (E2EE) group video calls and subsequently rolled out basic E2EE support to customers in October 2020. In this work we provide the first formal security analysis of Zoom's E2EE protocol, and also lay foundation to the general problem of E2EE group video communication. We observe that the vast security literature analyzing asynchronous messaging does not translate...

The Learning with Errors (LWE) problem has been widely utilized as a foundation for numerous cryptographic tools over the years. In this study, we focus on an algebraic variant of the LWE problem called Group ring LWE (GR-LWE). We select group rings (or their direct summands) that underlie specific families of finite groups constructed by taking the semi-direct product of two cyclic groups. Unlike the Ring-LWE problem described in \cite{lyubashevsky2010ideal}, the multiplication operation in...

Multi-signatures allow for compressing many signatures for the same message that were generated under independent keys into one small aggregated signature. This primitive is particularly useful for proof-of-stake blockchains, like Ethereum, where the same block is signed by many signers, who vouch for the block's validity. Being able to compress all signatures for the same block into a short string significantly reduces the on-chain storage costs, which is an important efficiency metric...

Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocols---in particular, when communication can be sublinear in the circuit representation size of the desired function. Significant advances have been made affirmatively answering this question within the two-party setting, based on a...

The Snowden's revelations kick-started a community-wide effort to develop cryptographic tools against mass surveillance. In this work, we propose to add another primitive to that toolbox: Fail-Stop Signatures (FSS) [EC'89]. FSS are digital signatures enhanced with a forgery-detection mechanism that can protect a PPT signer from more powerful attackers. Despite the fascinating concept, research in this area stalled after the '90s. However, the ongoing transition to post-quantum...

In this paper, inspired by the work of Beyne and Rijmen at CRYPTO 2022, we explore the accurate probability of $d$-differential in the fixed-key model. The theoretical foundations of our method are based on a special matrix $-$ quasi-$d$-differential transition matrix, which is a natural extension of the quasidifferential transition matrix. The role of quasi-$d$-differential transition matrices in polytopic cryptananlysis is analogous to that of correlation matrices in linear cryptanalysis....

Deep learning-based profiling side-channel analysis has gained widespread adoption in academia and industry due to its ability to uncover secrets protected by countermeasures. However, to exploit this capability, an adversary must have access to a clone of the targeted device to obtain profiling measurements and know secret information to label these measurements. Non-profiling attacks avoid these constraints by not relying on secret information for labeled data. Instead, they attempt all...

This paper presents a procedure to construct parameterized families of prime-order endomorphism-equipped elliptic curves that are defined over the scalar field of pairing-friendly elliptic curve families such as Barreto–Lynn–Scott (BLS), Barreto–Naehrig (BN) and Kachisa–Schaefer–Scott (KSS), providing general formulas derived from the curves’ seeds. These so-called “embedded curves” are of major interest in SNARK applications that prove statements involving elliptic curve arithmetic...

This paper re-analyzes the algorithm proposed by Guedes, Assis, and Lula in 2012, which they claimed that the algorithm can break Blum-Micali Pseudorandom number generator in polynomial time. We used a 5×5 transformation matrix instead of the original 2×2 transformation matrix, which can include terms that they missed in their analysis. We proved that their proposed algorithm cannot break the pseudorandom number generator, because during the amplitude amplification process, two iterations of...

Finding isogenies between supersingular elliptic curves is a natural algorithmic problem which is known to be equivalent to computing the curves' endomorphism rings. When the isogeny is additionally required to have a specific known degree $d$, the problem appears to be somewhat different in nature, yet its hardness is also required in isogeny-based cryptography. Let $E_1,E_2$ be supersingular elliptic curves over $\mathbb{F}_{p^2}$. We present improved classical and quantum...

Ethereum is a decentralized and permissionless network offering several attractive features. However, block proposers in Ethereum can exploit the order of transactions to extract value. This phenomenon, known as maximal extractable value (MEV), not only disrupts the optimal functioning of different protocols but also undermines the stability of the underlying consensus mechanism. In this work, we present a new method to alleviate the MEV problem by separating transaction inclusion and...

Goldwasser-Kalai-Rothblum protocol (GKR) for layered circuits is a sumcheck-based argument of knowledge for layered circuits, running in $\sim 2\mu \ell$ amount of rounds, where $\ell$ is the amount of layers and $\mu$ is the average layer logsize. For a layer $i$ of size $2^{\mu_i}$ the main work consists of running a sumcheck protocol of the form \[\underset{x,y}{\sum} \text{Add}_i(x,y,z)(f(x) f(y)) \text{Mul}_i(x,y,z)f(x)f(y)\] over a $2^{2\mu_i}$-dimensional cube, where...

While secure multi-party computation (MPC) protects the privacy of inputs and intermediate values of a computation, differential privacy (DP) ensures that the output itself does not reveal too much about individual inputs. For this purpose, MPC can be used to generate noise and add this noise to the output. However, securely generating and adding this noise is a challenge considering real-world implementations on finite-precision computers, since many DP mechanisms guarantee privacy only...

Zero-Knowledge Proofs (ZKPs), especially Succinct Non-interactive ARguments of Knowledge (SNARKs), have garnered significant attention in modern cryptographic applications. Given the multitude of emerging tools and libraries, assessing their strengths and weaknesses is nuanced and time-consuming. Often, claimed results are generated in isolation, and omissions in details render them irreproducible. The lack of comprehensive benchmarks, guidelines, and support frameworks to navigate the ZKP...

Dual attacks aiming at decoding generic linear codes have been found recently to outperform for certain parameters information set decoding techniques which have been for $60$ years the dominant tool for solving this problem and choosing the parameters of code-based cryptosystems. However, the analysis of the complexity of these dual attacks relies on some unproven assumptions that are not even fully backed up with experimental evidence. These dual attacks can actually be viewed as the...

Blind signatures serve as a foundational tool for privacy-preserving applications and have recently seen renewed interest due to new applications in blockchains and privacy-authentication tokens. With this, constructing practical round-optimal (i.e., signing consists of the minimum two rounds) blind signatures in the random oracle model (ROM) has been an active area of research, where several impossibility results indicate that either the ROM or a trusted setup is inherent. In this work,...

This study delves into secure computations for set intersections using fully homomorphic encryption (FHE) within the semi-honest setting. Our protocols facilitate joint computations between two parties, each holding a set of inputs denoted as $N_s$ and $N_r$ in size, respectively. The primary objective is to determine various functionalities, such as intersection size and sum, while maintaining data confidentiality. These functionalities extend the classic private set intersection (PSI) and...

This paper introduces Sigmabus, a technique designed to enhance the efficiency of zero-knowledge circuits by relocating computationally expensive operations outside the circuit. Specifically, Sigmabus focuses on moving elliptic curve group operations, typically proven with expensive non-native field arithmetic, to external computations. By leveraging Sigma protocols, elliptic curve group operations are proven outside the circuit, while additional constraints are applied to the circuit to...

Succinct arguments allow a prover to convince a verifier of the validity of any statement in a language, with minimal communication and verifier's work. Among other approaches, lattice-based protocols offer solid theoretical foundations, post-quantum security, and a rich algebraic structure. In this work, we present some new approaches to constructing efficient lattice-based succinct arguments. Our main technical ingredient is a new commitment scheme based on vanishing polynomials, a notion...

The supersingular Endomorphism Ring problem is the following: given a supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of this problem is foundational for isogeny-based cryptography. The One Endomorphism problem only asks to find a single non-scalar endomorphism. We prove that these two problems are equivalent, under probabilistic polynomial time reductions. We prove a number of consequences. First, assuming the hardness of the endomorphism ring...

The presumed hardness of the Shortest Vector Problem for ideal lattices (Ideal-SVP) has been a fruitful assumption to understand other assumptions on algebraic lattices and as a security foundation of cryptosystems. Gentry [CRYPTO'10] proved that Ideal-SVP enjoys a worst-case to average-case reduction, where the average-case distribution is the uniform distribution over the set of inverses of prime ideals of small algebraic norm (below $d^{O(d)}$ for cyclotomic fields, here $d$ refers to...

Motivated by the extended deployment of authenticated data structures (e.g., Merkle Patricia Tries) for verifying massive amounts of data in blockchain systems, we begin a systematic study of the I/O efficiency of such systems. We first explore the fundamental limitations of memory checking, a previously-proposed abstraction for verifiable storage, in terms of its locality---a complexity measure that we introduce for the first time and is defined as the number of non-contiguous memory...

The Algorand consensus protocol is interesting both in theory and in practice. On the theoretical side, to achieve adaptive security, it introduces the novel idea of player replaceability, where each step of the protocol is executed by a different randomly selected committee whose members remain secret until they send their first and only message. The protocol provides consistency under arbitrary network conditions and liveness under intermittent network partitions. On the practical side,...

Physical attacks are well-known threats to cryptographic implementations. While countermeasures against passive Side-Channel Analysis (SCA) and active Fault Injection Analysis (FIA) exist individually, protecting against their combination remains a significant challenge. A recent attempt at achieving joint security has been published at CCS 2022 under the name CINI-MINIS. The authors introduce relevant security notions and aim to construct arbitrary-order gadgets that remain trivially...

Broadcast protocols enable a set of $n$ parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, a fruitful line of work harnessed randomization and cryptography to achieve low-communication broadcast protocols with sub-quadratic total communication and with "balanced" sub-linear communication cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most...

Modern e-voting systems provide what is called verifiability, i.e., voters are able to check that their votes have actually been counted despite potentially malicious servers and voting authorities. Some of these systems, called tally-hiding systems, provide increased privacy by revealing only the actual election result, e.g., the winner of the election, but no further information that is supposed to be kept secret. However, due to these very strong privacy guarantees, supporting complex...

Liskov, Rivest and Wagner laid the theoretical foundations for tweakable block ciphers (TBC). In a seminal paper, they proposed two (up to) birthday-bound secure design strategies --- LRW1 and LRW2 --- to convert any block cipher into a TBC. Several of the follow-up works consider cascading of LRW-type TBCs to construct beyond-the-birthday bound (BBB) secure TBCs. Landecker et al. demonstrated that just two-round cascading of LRW2 can already give a BBB security. Bao et al. undertook a...

Distributed key management (DKM) services are multi-party services that allow their users to outsource the generation, storage, and usage of cryptographic private keys, while guaranteeing that none of the involved service providers learn the private keys in the clear. This is typically achieved through distributed key generation (DKG) protocols, where the service providers generate the keys on behalf of the users in an interactive protocol, and each of the servers stores a share of each key...

Both threshold and blind signatures have, individually, received a considerable amount of attention. However little is known about their combination, i.e., a threshold signature which is also blind, in that no coalition of signers learns anything about the message being signed or the signature being produced. Several applications of blind signatures (e.g., anonymous tokens) would benefit from distributed signing as a means to increase trust in the service and hence reduce the risks of key...

In this paper, we present a new quantum-resistant weak Verifiable Delay Function based on a purely algebraic construction. Its delay depends on computing a large-degree isogeny between elliptic curves, whereas its verification relies on the computation of isogenies between products of two elliptic curves. One of its major advantages is its expected fast verification time. However, it is important to note that the practical implementation of our theoretical framework poses significant...