Zero-knowledge proofs allow one party to prove the truth of a statement without disclosing any extra information. Recent years have seen great improvements in zero-knowledge proofs. Among them, zero-knowledge SNARKs are notable for their compact and efficiently-verifiable proofs but face challenges with high prover costs for large-scale applications. To accelerate proof generation, Pianist (Liu et al., S&P 2024) proposes to distribute the proof generation process across multiple machines,...

A prominent countermeasure against side channel attacks, the hiding countermeasure, typically involves shuffling operations using a permutation algorithm. Especially in the era of Post-Quantum Cryptography, the importance of the hiding coun- termeasure is emphasized due to computational characteristics like those of lattice and code-based cryptography. In this context, swiftly and securely generating permutations has a critical impact on an algorithm’s security and efficiency. The widely...

In this note, we introduce the MATTER Tweakable Block Cipher, designed principally for low latency in low-area hardware implementations, but that can also be implemented in an efficient and compact way in software. MATTER is a 512-bit wide balanced Feistel network with three to six rounds, using the ASCON permutation as the round function. The Feistel network defines a keyed, non-tweakable core, which is made tweakable by using the encryption of the tweak as its key. Key and tweak are...

We construct two efficient post-quantum ring signatures with anonymity against full key exposure from isogenies, addressing limitations of existing isogeny-based ring signatures. First, we present an efficient concrete distinguisher for the SQIsign simulator when the signing key is provided using one transcript. This shows that turning SQIsign into an efficient full anonymous ring signature requires some new ideas. Second, we propose a variant of SQIsign that is resistant to the...

Resource-constrained devices such as wireless sensors and Internet of Things (IoT) devices have become ubiquitous in our digital ecosystem. These devices generate and handle a major part of our digital data. In the face of the impending threat of quantum computers on our public-key infrastructure, it is impossible to imagine the security and privacy of our digital world without integrating post-quantum cryptography (PQC) into these devices. Usually, due to the resource constraints of these...

Verifiable Random Functions (VRFs) are cryptographic primitives that generate unpredictable randomness along with proofs that are verifiable, a critical requirement for blockchain applications in decentralized finance, online gaming, and more. Existing VRF constructions often rely on centralized entities, creating security vulnerabilities. Distributed VRFs (DVRFs) offer a decentralized alternative but face challenges like large proof sizes or dependence on computationally expensive bilinear...

We present a novel cryptographic paradigm denoted ``cryptiny:'' Employing a single cryptographic value for several security goals, thus ``compacting'' the communication sent over a space-restricted (narrow) channel, while still proving security. Cryptiny is contrary to the classical cryptographic convention of using a separate cryptographic element for each security goal. Demonstrating the importance of cryptiny, we employ it for securing a critical IoT configuration in which a...

We reduce the number of bit operations required to implement AES to a new minimum, and also compute improvements to elements of some other ciphers. Exploring the algebra of AES allows choices of basis and streamlining of the nonlinear parts. We also compute a more efficient implementation of the linear part of each round. Similar computational optimizations apply to other cryptographic matrices and S-boxes. This work may be incorporated into a hardware AES implementation using minimal...

We present a variant of Function Secret Sharing (FSS) schemes tailored for point, comparison, and interval functions, featuring compact key sizes at the expense of additional comparison. While existing FSS constructions are primarily geared towards $2$-party scenarios, exceptions such as the work by Boyle et al. (Eurocrypt 2015) and Riposte (S&P 2015) have introduced FSS schemes for $p$-party scenarios ($p \geq 3$). This paper aims to achieve the most compact $p$-party FSS key size to date....

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...

We show that the smallness of message spaces can be used as a checksum allowing to hedge against CCA1 attacks in additively homomorphic encryption schemes. We first show that the additively homomorphic variant of Damgård's Elgamal provides IND-CCA1 security under the standard DDH assumption. Earlier proofs either required non-standard assumptions or only applied to hybrid versions of Damgård's Elgamal, which are not additively homomorphic. Our security proof builds on hash proof systems and...

End-to-End (E2E) encrypted messaging, which prevents even the service provider from learning communication contents, is gaining popularity. Since users care about maintaining access to their data even if their devices are lost or broken or just replaced, these systems are often paired with cloud backup solutions: Typically, the user will encrypt their messages with a fixed key, and upload the ciphertexts to the server. Unfortunately, this naive solution has many drawbacks. First, it often...

We construct a (compact) quantum fully homomorphic encryption (QFHE) scheme starting from any (compact) classical fully homomorphic encryption scheme with decryption in $\mathsf{NC}^{1}$, together with a dual-mode trapdoor function family. Compared to previous constructions (Mahadev, FOCS 2018; Brakerski, CRYPTO 2018) which made non-black-box use of similar underlying primitives, our construction provides a pathway to instantiations from different assumptions. Our construction uses the...

Ring signatures, a cryptographic primitive introduced by Rivest, Shamir and Tauman (ASIACRYPT 2001), offer signer anonymity within dynamically formed user groups. Recent advancements have focused on lattice-based constructions to improve efficiency, particularly for large signing rings. However, current state-of-the-art solutions suffer from significant overhead, especially for smaller rings. In this work, we present a novel NTRU-based ring signature scheme, Gandalf, tailored towards...

We provide explicit radical $N$-isogeny formulae for all odd integers $N$. The formulae are compact closed-form expressions which require one $N$th root computation and $\mathcal{O}(N)$ basic field operations. The formulae are highly efficient to compute a long chain of $N$-isogenies, and have the potential to be extremely beneficial for speeding up certain cryptographic protocols such as CSIDH. Unfortunately, the formulae are conjectured, but we provide ample supporting evidence which...

In this work we introduce PERK a compact digital signature scheme based on the hardness of a new variant of the Permuted Kernel Problem (PKP). PERK achieves the smallest signature sizes for any PKP-based scheme for NIST category I security with 6 kB, while obtaining competitive signing and verification timings. PERK also compares well with the general state-of-the-art. To substantiate those claims we provide an optimized constant-time AVX2 implementation, a detailed performance analysis and...

The Module-NTRU problem, introduced by Cheon, Kim, Kim, Son (IACR ePrint 2019/1468), and Chuengsatiansup, Prest, Stehlé, Wallet, Xagawa (ASIACCS ’20), generalizes the versatile NTRU assump- tion. One of its main advantages lies in its ability to offer greater flexibil- ity on parameters, such as the underlying ring dimension. In this work, we present several lattice-based encryption schemes, which are IND-CPA (or OW-CPA) secure in the standard model based on the Module-NTRU and...

Fully Homomorphic Encryption (FHE) is a transformative technology that enables computations on encrypted data without requiring decryption, promising enhanced data privacy. However, its adoption has been limited due to significant performance overheads. Recent advances include the proposal of domain-specific, highly-parallel hardware accelerators designed to overcome these limitations. This paper introduces PICA, a comprehensive compiler framework designed to simplify the programming of...

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...

We introduce a new framework, POKE, to build cryptographic protocols from irrational isogenies using higher-dimensional representations. The framework enables two parties to manipulate higher-dimensional representations of isogenies to efficiently compute their pushforwards, and ultimately to obtain a shared secret. We provide three constructions based on POKE: the first is a PKE protocol, which is one of the most compact post-quantum PKEs and possibly the most efficient isogeny-based PKE...

In recent years, quantum technology has been rapidly developed. As security analyses for symmetric ciphers continue to emerge, many require an evaluation of the resources needed for the quantum circuit implementation of the encryption algorithm. In this regard, we propose the quantum circuit decision problem, which requires us to determine whether there exists a quantum circuit for a given permutation f using M ancilla qubits and no more than K quantum gates within the circuit depth D....

A cryptographic accumulator is a compact data structure for representing a set of elements coming from some domain. It allows for a compact proof of membership and, in the case of a universal accumulator, non-membership of an element x in the data structure. A dynamic accumulator, furthermore, allows elements to be added to and deleted from the accumulator. Previously known RSA-based dynamic accumulators were too slow in practice because they required that an element in the domain be...

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...

This paper introduces the first adaptively secure streaming functional encryption (sFE) scheme for P/Poly. sFE stands as an evolved variant of traditional functional encryption (FE), catering specifically to contexts with vast and/or dynamically evolving data sets. sFE is designed for applications where data arrives in a streaming fashion and is computed on in an iterative manner as the stream arrives. Unlike standard FE, in sFE: (1) encryption is possible without knowledge of the full data...

This work initiates the study of concrete registered functional encryption (Reg-FE) beyond ``all-or-nothing'' functionalities: - We build the first Reg-FE for linear function or inner-product evaluation (Reg-IPFE) from pairings. The scheme achieves adaptive IND-security under $k$-Lin assumption in the prime-order bilinear group. A minor modification yields the first Registered Inner-Product Encryption (Reg-IPE) scheme from $k$-Lin assumption. Prior work achieves the same security in...

Several Password Authenticated Key Exchange (PAKE) protocols have been recently proposed that leverage a Key-Encapsulation Mechanism (KEM) to create an efficient and easy-to-implement post-quantum secure PAKE. This line of work is driven by the intention of the National Institute of Standards and Technology (NIST) to soon standardize a lattice-based post-quantum KEM called $\mathsf{Kyber}$. In two recent works, Beguinet et al. (ACNS 2023) and Pan and Zeng (ASIACRYPT 2023) proposed generic...

Recent constructions of private information retrieval (PIR) have seen significant improvements in computational performance. However, these improvements rely on heavy offline preprocessing that is typically difficult in real-world applications. Motivated by the question of PIR with no offline processing, we introduce WhisPIR, a fully stateless PIR protocol with low per-query communication. WhisPIR clients are all ephemeral, meaning that they appear with only the protocol public parameters...

In response to the evolving landscape of quantum computing and the heightened vulnerabilities in classical cryptographic systems, our paper introduces a comprehensive cryptographic framework. Building upon the pioneering work of Kuang et al., we present a unification of two innovative primitives: the Quantum Permutation Pad (QPP) for symmetric key encryption and the Homomorphic Polynomial Public Key (HPPK) for Key Encapsulation Mechanism (KEM) and Digital Signatures (DS). By harnessing...

Biscuit is a recent multivariate signature scheme based on the MPC-in-the-Head paradigm. It has been submitted to the NIST competition for additional signature schemes. Signatures are derived from a zero-knowledge proof of knowledge of the solution of a structured polynomial system. This extra structure enables efficient proofs and compact signatures. This short note demonstrates that it also makes these polynomial systems easier to solve than random ones. As a consequence, the original...

In this work, we propose two novel succinct one-out-of-many proofs from coding theory, which can be seen as extensions of the Stern's framework and Veron's framework from proving knowledge of a preimage to proving knowledge of a preimage for one element in a set, respectively. The size of each proof is short and scales better with the size of the public set than the code-based accumulator in \cite{nguyen2019new}. Based on our new constructions, we further present a logarithmic-size ring...

The present article explains how to generalize the hash function SwiftEC (in an elementary quasi-unified way) to any elliptic curve $E$ over any finite field $\mathbb{F}_{\!q}$ of characteristic $> 3$. The new result apparently brings the theory of hash functions onto elliptic curves to its logical conclusion. To be more precise, this article provides compact formulas that define a hash function $\{0,1\}^* \to E(\mathbb{F}_{\!q})$ (deterministic and indifferentible from a random oracle) with...

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...

Basic encryption and signature on lattices have comparable efficiency to their classical counterparts in terms of speed and key size. However, Identity-based Encryption (IBE) on lattices is much less efficient in terms of compactness, even when instantiated on ideal lattices and in the Random Oracle Model (ROM). This is because the underlying preimage sampling algorithm used to extract the users' secret keys requires huge public parameters. In this work, we specify a compact IBE...

This paper conducts a comprehensive benchmarking analysis of the performance of two innovative cryptographic schemes: Homomorphic Polynomial Public Key (HPPK)-Key Encapsulation Mechanism (KEM) and Digital Signature (DS), recently proposed by Kuang et al. These schemes represent a departure from traditional cryptographic paradigms, with HPPK leveraging the security of homomorphic symmetric encryption across two hidden rings without reliance on NP-hard problems. HPPK can be viewed as a...

Anonymous credentials are cryptographic mechanisms enabling users to authenticate themselves with a fine-grained control on the information they leak in the process. They have been the topic of countless papers which have improved the performance of such mechanisms or proposed new schemes able to prove ever-more complex statements about the attributes certified by those credentials. However, whereas these papers have studied in depth the problem of the information leaked by the credential...

This paper describes a way to protect medications against falsification, a long-standing problem in the world. We combine several existing technologies to achieve the stated goal. The building-blocks used are inherent physical randomness generated during the packaging process, artificial vision, short digital signatures and QR-codes.

Blind Signatures are a useful primitive for privacy preserving applications such as electronic payments, e-voting, anonymous credentials, and more. However, existing practical blind signature schemes based on standard assumptions require either pairings or lattices. We present the first practical construction of a round-optimal blind signature in the random oracle model based on standard assumptions without resorting to pairings or lattices. In particular, our construction is secure under...

This paper describes Biscuit, a new multivariate-based signature scheme derived using the MPC-in-the-Head (MPCitH) approach. The security of Biscuit is related to the problem of solving a set of structured quadratic algebraic equations. These equations are highly compact and can be evaluated using very few multiplications (one multiplication per equation). The core of Biscuit is a rather simple MPC protocol for secure multiplications using standard optimized multiplicative triples. This...

We present two new constructions for private information retrieval (PIR) in the classical setting where the clients do not need to do any preprocessing or store any database dependent information, and the server does not need to store any client-dependent information. Our first construction (HintlessPIR) eliminates the client preprocessing step from the recent LWE-based SimplePIR (Henzinger et. al., USENIX Security 2023) by outsourcing the "hint" related computation to the server,...

Homomorphic Encryption (HE) is one of the mainstream cryptographic tools used to enable secure outsourced computation. A typical task is secure matrix computation. Popular HE schemes are all based on the problem of Ring Learning with Errors (RLWE), where the messages are encrypted in a ring. In general, the ring dimension should be large to ensure security, which is often larger than the matrix size. Hence, exploiting the ring structure to make fast homomorphic matrix computation has been an...

We propose a new lattice-based sublinear argument for R1CS that not only achieves efficiency in concrete proof size but also demonstrates practical performance in both proof generation and verification. To reduce the proof size, we employ a new encoding method for large prime fields, resulting in a compact proof for R1CS over such fields. We also devise a new proof technique that randomizes the input message. This results in fast proof generation performance, eliminating rejection...

Given two linear codes, the code equivalence problem asks to find an isometry mapping one code into the other. The problem can be described in terms of group actions and, as such, finds a natural application in signatures derived from a Zero-Knowledge Proof system. A recent paper, presented at Asiacrypt 2023, showed how a proof of equivalence can be significantly compressed by describing how the isometry acts only on an information set. Still, the resulting signatures are far from being...

Isogeny-based cryptography is one of the candidates for post-quantum cryptography. One of the benefits of using isogeny-based cryptography is its compactness. In particular, a key exchange scheme SIDH allowed us to use a $4\lambda$-bit prime for the security parameter $\lambda$. Unfortunately, SIDH was broken in 2022 by some studies. After that, some isogeny-based key exchange and public key encryption schemes have been proposed; however, most of these schemes use primes whose sizes are...

Identity-based matchmaking encryption (IB-ME) [Ateniese et al. Crypto 2019] allows users to communicate privately in an anonymous and authenticated manner. After the seminal paper by Ateniese et al., a lot of work has been done on the security and construction of IB-ME. In this work, we revisit the security definitions of IB-ME and provide improved constructions of it. First, we classify the existing security notions of IB-ME, systematically categorizing privacy into three categories (CPA,...

Homomorphic Encryption (HE) presents a promising solution to securing neural networks for Machine Learning as a Service (MLaaS). Despite its potential, the real-time applicability of current HE-based solutions remains a challenge, and the diversity in network structures often results in inefficient implementations and maintenance. To address these issues, we introduce a unified and compact network structure for real-time inference in convolutional neural networks based on HE. We further...

In this paper, we improve the cube attack by exploiting low-degree factors of the superpoly w.r.t. certain "special" index set of cube (ISoC). This can be viewed as a special case of the correlation cube attack proposed at Eurocrypt 2018, but under our framework more beneficial equations on the key variables can be obtained in the key-recovery phase. To mount our attack, one has two challenging problems: (1) effectively recover algebraic normal form of the superpoly and extract out its...

Data formats used for cryptographic inputs have historically been the source of many attacks on cryptographic protocols, but their security guarantees remain poorly studied. One reason is that, due to their low-level nature, formats often fall outside of the security model. Another reason is that studying all of the uses of all of the formats within one protocol is too difficult to do by hand, and requires a comprehensive, automated framework. We propose a new framework, “Comparse”, that...

In this paper, we initiate the study of the Rank Decoding (RD) problem and LRPC codes with blockwise structures in rank-based cryptosystems. First, we introduce the blockwise errors ($\ell$-errors) where each error consists of $\ell$ blocks of coordinates with disjoint supports, and define the blockwise RD ($\ell$-RD) problem as a natural generalization of the RD problem whose solutions are $\ell$-errors (note that the standard RD problem is actually a special $\ell$-RD problem with...

Count-Min Sketch (CMS) and HeavyKeeper (HK) are two realizations of a compact frequency estimator (CFE). These are a class of probabilistic data structures that maintain a compact summary of (typically) high-volume streaming data, and provides approximately correct estimates of the number of times any particular element has appeared. CFEs are often the base structure in systems looking for the highest-frequency elements (i.e., top-$K$ elements, heavy hitters, elephant flows). ...

IoT devices collect privacy-sensitive data, e.g., in smart grids or in medical devices, and send this data to cloud servers for further processing. In order to ensure confidentiality as well as authenticity of the sensor data in the untrusted cloud environment, we consider a transciphering scenario between embedded IoT devices and multiple cloud servers that perform secure multi-party computation (MPC). Concretely, the IoT devices encrypt their data with a lightweight symmetric cipher and...

Publicly Verifiable Secret Sharing (PVSS) is a fundamental primitive that allows to share a secret $S$ among $n$ parties via a publicly verifiable transcript $T$. Existing (efficient) PVSS are only proven secure against static adversaries who must choose who to corrupt ahead of a protocol execution. As a result, any protocol (e.g., a distributed randomness beacon) that builds on top of such a PVSS scheme inherits this limitation. To overcome this barrier, we revisit the security of PVSS...

We propose two generic constructions of public-key encryption (PKE) with tight simulation-based selective-opening security against chosen-ciphertext attacks (SIM-SO-CCA) in the random oracle model. Our constructions can be instantiated with a small constant number of elements in the ciphertext, ignoring smaller contributions from symmetric-key encryption. That is, they have compact ciphertexts. Furthermore, three of our instantiations have compact public keys as well. Known (almost)...

In this paper, we present NEV -- a faster and smaller NTRU Encryption using Vector decoding, which is provably IND-CPA secure in the standard model under the decisional NTRU and RLWE assumptions over the cyclotomic ring $R_q = \mathbb{Z}_q[X]/(X^n 1)$. Our main technique is a novel and non-trivial way to integrate a previously known plaintext encoding and decoding mechanism into the provably IND-CPA secure NTRU variant by Stehl\'e and Steinfeld (Eurocrypt 2011). Unlike the original NTRU...

LV16/Lin17 IO schemes are famous progresses towards simplifying obfuscation mechanism. In fact, these two schemes only constructed two compact functional encryption (CFE) algorithms, while other things were taken to the AJ15 IO frame or BV15 IO frame. CFE algorithms are inserted into the AJ15 IO frame or BV15 IO frame to form a complete IO scheme. We stated the invalidity of LV16/Lin17 IO schemes. More detailedly, under reasonable assumption “real white box (RWB)” LV16/Lin17 CFE algorithms...

Threshold signatures are digital signatures that support the multi-party signature generation such that a number of parties initially share a signing key and more than a threshold number of parties gather to generate a signature. In this paper, we propose a non-interactive decentralized threshold signature (NIDTS) scheme that supports the non-interactive and transparent key setup based on BLS signatures. Our NIDTS scheme has the following properties. 1) The key setup process is completely...

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular, persistent homology (PH) takes in data (e.g., point clouds, images, time series) and derives compact representations of latent topological structures, known as persistence diagrams (PDs). Because PDs enjoy inherent noise tolerance, are interpretable and provide a...

Hash functions are a crucial component in incrementally verifiable computation (IVC) protocols and applications. Among those, recursive SNARKs and folding schemes require hash functions to be both fast in native CPU computations and compact in algebraic descriptions (constraints). However, neither SHA-2/3 nor newer algebraic constructions, such as Poseidon, achieve both requirements. In this work we overcome this problem in several steps. First, for certain prime field domains we propose a...

Anonymous credentials (AC) have emerged as a promising privacy-preserving solu- tion for user-centric identity management. They allow users to authenticate in an anonymous and unlinkable way such that only required information (i.e., attributes) from their credentials are re- vealed. With the increasing push towards decentralized systems and identity, e.g., self-sovereign identity (SSI) and the concept of verifiable credentials, this also necessitates the need for suit- able AC systems. For...

The Mobius transform is a linear circuit used to compute the evaluations of a Boolean function over all points on its input domain. The operation is very useful in finding the solution of a system of polynomial equations over GF(2) for obvious reasons. However the operation, although linear, needs exponential number of logic operations (around $n\cdot 2^{n-1}$ bit xors) for an $n$-variable Boolean function. As such, the only known hardware circuit to efficiently compute the Mobius transform...

Practical Identity Based Encryption (IBE) schemes use the costly bilinear pairing computation. Clifford Cock proposed an IBE based on quadratic residuosity in 2001 which does not use bilinear pairing but was not efficient in practice, due to the large ciphertext size. In 2007, Boneh et al. proposed the first space efficient IBE that was also based on quadratic residuosity problem. It was an improvement over Cock's scheme but still the time required for encryption was quartic in the security...

Searchable Symmetric Encryption (SSE) supports efficient keyword searches over encrypted outsourced document collections while minimizing information leakage. All practically efficient SSE schemes supporting conjunctive queries rely crucially on quantum-broken cryptographic assumptions (such as discrete-log hard groups) to achieve compact storage and fast query processing. On the other hand, quantum-safe SSE schemes based on purely symmetric-key crypto-primitives either do not support...

Lossy trapdoor functions (LTFs) constitute a useful and versatile cryptographic building block. LTFs have found applications in various types of encryption schemes, are closely connected to statistically secure oblivious transfer protocols, and have led to the first constructions of group-based trapdoor functions. However, with one recent exception, all known group-based LTFs are comparatively inefficient, and in particular suffer from large images. In this work, we attempt to explain this...

Selective opening (SO) security is a security notion for public-key encryption schemes that captures security against adaptive corruptions of senders. SO security comes in chosen-plaintext (SO-CPA) and chosen-ciphertext (SO-CCA) variants, neither of which is implied by standard security notions like IND-CPA or IND-CCA security. In this paper, we present the first SO-CCA secure encryption scheme that combines the following two properties: (1) it has a constant ciphertext expansion...

Group actions are fundamental mathematical tools, with a long history of use in cryptography. Indeed, the action of finite groups at the basis of the discrete logarithm problem is behind a very large portion of modern cryptographic systems. With the advent of post-quantum cryptography, however, the method for building protocols shifted towards a different paradigm, centered on the difficulty of discerning 'noisy' objects, as is the case for lattices, codes, and multivariate systems. This...

NIST has already published the first round of submissions for additional post-quantum signature schemes and the only isogeny-based candidate is SQIsign. It boasts the most compact key and signature sizes among all post-quantum signature schemes. However, its current implementation does not address side-channel resistance. This work is the first to identify a potential side-channel vulnerability in SQIsign. At certain steps within the signing procedure, it relies on Cornacchia’s algorithm...

The Supersingular Isogeny Diffie-Hellman (SIDH) protocol has been the main and most efficient isogeny-based encryption protocol, until a series of breakthroughs led to a polynomial-time key-recovery attack. While some countermeasures have been proposed, the resulting schemes are significantly slower and larger than the original SIDH. In this work, we propose a new countermeasure technique that leads to significantly more efficient and compact protocols. To do so, we introduce the...

Isogeny-based cryptography is famous for its short key size. As one of the most compact digital signatures, SQIsign (Short Quaternion and Isogeny Signature) is attractive among post-quantum cryptography, but it is inefficient compared to other post-quantum competitors because of complicated procedures in the ideal-to-isogeny translation, which is the efficiency bottleneck of the signing phase. In this paper, we recall the current implementation of SQIsign and mainly focus on how to improve...

Recently, NIST has announced Kyber, a lattice-based key encapsulation mechanism (KEM), as a post-quantum standard. However, it is not the most efficient scheme among the NIST's KEM finalists. Saber enjoys more compact sizes and faster performance, and Mera et al. (TCHES '21) further pushed its efficiency, proposing a shorter KEM, Sable. As KEM are frequently used on the Internet, such as in TLS protocols, it is essential to achieve high efficiency while maintaining sufficient security....

Lattice gadgets and the associated algorithms are the essential building blocks of lattice-based cryptography. In the past decade, they have been applied to build versatile and powerful cryptosystems. However, the practical optimizations and designs of gadget-based schemes generally lag their theoretical constructions. For example, the gadget-based signatures have elegant design and capability of extending to more advanced primitives, but they are far less efficient than other lattice-based...

Functional encryption (FE) is a primitive where the holder of a master secret key can control which functions a user can evaluate on encrypted data. It is a powerful primitive that even implies indistinguishability obfuscation (iO), given sufficiently compact ciphertexts (Ananth-Jain, CRYPTO'15 and Bitansky-Vaikuntanathan, FOCS'15). However, despite being extensively studied, there are FE schemes, such as function-hiding inner-product FE (Bishop-Jain-Kowalczyk, AC'15,...

In cryptocurrencies, all transactions are public. For their adoption, it is important that these transactions, while publicly verifiable, do not leak information about the identity and the balances of the transactors. For UTXO-based cryptocurrencies, there are well-established approaches (e.g., ZCash) that guarantee full privacy to the transactors. Full privacy in UTXO means that each transaction is anonymous within the set of all private transactions ever posted on the...

Indistinguishability obfuscation (IO) is at the frontier of cryptography research for several years. LV16/Lin17 obfuscation schemes are famous progresses towards simplifying obfuscation mechanism. In fact, these two schemes only constructed two compact functional encryption (CFE) algorithms, while other things were taken to AJ15 IO frame or BV15 IO frame. That is, CFE algorithms are inserted into AJ15 IO frame or BV15 IO frame to form a complete IO scheme. The basic structure of two CFE...

The hard mathematical problems that assure the security of our current public-key cryptography (RSA, ECC) are broken if and when a quantum computer appears rendering them ineffective for use in the quantum era. Lattice based cryptography is a novel approach to public key cryptography, of which the mathematical investigation (so far) resists attacks from quantum computers. By choosing a module learning with errors (MLWE) algorithm as the next standard, National Institute of Standard \&...

Lattice-based cryptosystems are some of the primary post-quantum secure alternatives to the asymmetric cryptography that is used today. These lattice-based cryptosystems typically rely on the hardness of some version of either the NTRU or the LWE problem. In this paper, we present the NTWE problem, a natural combination of the NTRU and LWE problems, and construct a new lattice-based cryptosystem based on the hardness of the NTWE problem. As with the NTRU and LWE problems, the NTWE problem...

The functional bootstrap in FHEW/TFHE allows for fast table lookups on ciphertexts and is a powerful tool for privacy-preserving computations. However, the functional bootstrap suffers from two limitations: the negacyclic constraint of the lookup table (LUT) and the limited ability to evaluate large-precision LUTs. To overcome the first limitation, several full-domain functional bootstraps (FDFB) have been developed, enabling the evaluation of arbitrary LUTs. Meanwhile, algorithms based on...

Threshold signatures protect the signing key by sharing it among a group of signers so that an adversary must corrupt a threshold number of signers to be able to forge signatures. Existing threshold signatures with succinct signatures and constant verification times do not work if signers have different weights. Such weighted settings are seeing increasing importance in decentralized systems, especially in the Proof-of-Stake blockchains. This paper presents a new paradigm for threshold...

Secure Multi-Party Computation (MPC) is continuously becoming more and more practical. Many optimizations have been introduced, making MPC protocols more suitable for solving real-world problems. However, the MPC protocols and optimizations are usually implemented as a standalone proof of concept or in an MPC framework and are tightly coupled with special-purpose circuit formats, such as Bristol Format. This makes it very hard and time-consuming to re-use algorithmic advances and implemented...

We present a framework for building practical anonymous credential schemes based on the hardness of lattice problems. The running time of the prover and verifier is independent of the number of users and linear in the number of attributes. The scheme is also compact in practice, with the proofs being as small as a few dozen kilobytes for arbitrarily large (say up to $2^{128}$) users with each user having several attributes. The security of our scheme is based on a new family of lattice...

The universal thresholdizer, introduced at CRYPTO'18, is a cryptographic scheme that transforms any cryptosystem into a threshold variant, thereby enhancing its applicability in threshold cryptography. It enables black-box construction of one-round threshold signature schemes based on the Learning with Errors problem, and similarly, facilitates one-round threshold ciphertext-attack secure public key encryption when integrated with non-threshold schemes. Current constructions of universal...

Lattice-based cryptography has laid the foundation of various modern-day cryptosystems that cater to several applications, including post-quantum cryptography. For structured lattice-based schemes, polynomial arithmetic is a fundamental part. In several instances, the performance optimizations come from implementing compact multipliers due to the small range of the secret polynomial coefficients. However, this optimization does not easily translate to side-channel protected implementations...

Proof of Storage-time (PoSt) is a cryptographic primitive that enables a server to demonstrate non-interactive continuous avail- ability of outsourced data in a publicly verifiable way. This notion was first introduced by Filecoin to secure their Blockchain-based decentral- ized storage marketplace, using expensive SNARKs to compact proofs. Recent work [2] employs the notion of trapdoor delay function to address the problem of compact PoSt without SNARKs. This approach however entails...

The concept of using Lookup Tables (LUTs) instead of Boolean circuits is well-known and been widely applied in a variety of applications, including FPGAs, image processing, and database management systems. In cryptography, using such LUTs instead of conventional gates like AND and XOR results in more compact circuits and has been shown to substantially improve online performance when evaluated with secure multi-party computation. Several recent works on secure floating-point computations and...

We propose the first aggregate signature scheme such that: (1) its security is based on the standard lattice assumptions in the random oracle model; (2) the aggregate signature size is logarithmic; (3) it is not one-time; and (4) it supports non-interactive aggregation. To obtain such a scheme, we combine the most compact SNARK (Succinct Non-interactive ARgument of Knowledge) system and a SNARK-friendly signature scheme. As a result, our aggregated signature size is sufficiently compact. For...

Preimage sampling is a fundamental tool in lattice-based cryptography, and its performance directly impacts that of the cryptographic mechanisms relying on it. In 2012, Micciancio and Peikert proposed a new way of generating trapdoors (and an associated preimage sampling procedure) with very interesting features. Unfortunately, in some applications such as digital signatures, the performance may not be as competitive as other approaches like Fiat-Shamir with Aborts. In an effort to improve...

Bounded-collusion identity-based encryption (BC-IBE) is a variant of identity-based encryption, where an adversary obtains user secrete keys corresponding to at most $d$ identities. From results of existing work, it is proven that BC-IBE can be constructed from public key encryption (PKE) with several properties. In particular, we focus on post-quantum PKE schemes submitted to the NIST PQC competition, as the underlying PKE of BC-IBE schemes. This is because post-quantum cryptography is one...

We introduce SQIsignHD, a new post-quantum digital signature scheme inspired by SQIsign. SQIsignHD exploits the recent algorithmic breakthrough underlying the attack on SIDH, which allows to efficiently represent isogenies of arbitrary degrees as components of a higher dimensional isogeny. SQIsignHD overcomes the main drawbacks of SQIsign. First, it scales well to high security levels, since the public parameters for SQIsignHD are easy to generate: the characteristic of the underlying field...

A \emph{witness map} deterministically maps a witness $w$ of some NP statement $x$ into computationally sound proof that $x$ is true, with respect to a public common reference string (CRS). In other words, it is a deterministic, non-interactive, computationally sound proof system in the CRS model. A \emph{unique witness map} (UWM) ensures that for any fixed statement $x$, the witness map should output the same \emph{unique} proof for $x$, no matter what witness $w$ it is applied to. More...

Actively secure two-party computation (2PC) is one of the canonical building blocks in modern cryptography. One main goal for designing actively secure 2PC protocols is to reduce the communication overhead, compared to semi-honest 2PC protocols. In this paper, we make significant progress in closing this gap by proposing two new actively secure constant-round 2PC protocols, one with one-way communication of $2\kappa 5$ bits per AND gate (for $\kappa$-bit computational security and any...

An oblivious pseudorandom function, or OPRF, is an important primitive that is used to build many advanced cryptographic protocols. Despite its relevance, very few post-quantum solutions exist. In this work, we propose a novel OPRF protocol that is post-quantum, verifiable, round-optimal, and moderately compact. Our protocol is based on a previous SIDH-based construction by Boneh, Kogan, and Woo, which was later shown to be insecure due to an attack on its one-more unpredictability. We...

In this paper we characterize all $2n$-bit-to-$n$-bit Pseudorandom Functions (PRFs) constructed with the minimum number of calls to $n$-bit-to-$n$-bit PRFs and arbitrary number of linear functions. First, we show that all two-round constructions are either classically insecure, or vulnerable to quantum period-finding attacks. Second, we categorize three-round constructions depending on their vulnerability to these types of attacks. This allows us to identify classes of constructions that...

We give a construction of a 2-round blind signature scheme based on the hardness of standard lattice problems (Ring/Module-SIS/LWE and NTRU) with a signature size of 22 KB. The protocol is round-optimal and has a transcript size that can be as small as 60 KB. This blind signature is around $4$ times shorter than the most compact lattice-based scheme based on standard assumptions of del Pino and Katsumata (Crypto 2022) and around $2$ times shorter than the scheme of Agrawal et al. (CCS 2022)...

Privacy-preserving neural network based on secure multi-party computation (MPC) enables multiple parties to jointly train neural network models without revealing sensitive data. In privacy-preserving neural network, the high communication costs of securely computing non-linear functions is the primary performance bottleneck. For commonly used non-linear functions, such as ReLU, existing work adopts an offline-online computation paradigm and utilizes distributed comparison function (DCF) to...

We introduce a new notion of {\em multiverse threshold signatures} (MTS). In an MTS scheme, multiple universes -- each defined by a set of (possibly overlapping) signers, their weights, and a specific security threshold -- can co-exist. A universe can be (adaptively) created via a non-interactive asynchronous setup. Crucially, each party in the multiverse holds constant-sized keys and releases compact signatures with size and computation time both independent of the number of universes....

Multi-signature is a protocol where a set of signatures jointly sign a message so that the final signature is significantly shorter than concatenating individual signatures together. Recently, it finds applications in blockchain, where several users want to jointly authorize a payment through a multi-signature. However, in this setting, there is no centralized authority and it could suffer from a rogue key attack where the attacker can generate his own keys arbitrarily. Further, to...

On-line/off-line encryption schemes enable the fast encryption of a message from a pre-computed coupon. The paradigm was put forward in the case of digital signatures. This work introduces a compact public-key additively homomorphic encryption scheme. The scheme is semantically secure under the decisional composite residuosity (DCR) assumption. Compared to Paillier cryptosystem, it merely requires one or two integer additions in the on-line phase and no increase in the ciphertext size. This...

Secure cryptographic storage is one of the most important issues that both businesses and end-users take into account before moving their data to either centralized clouds or blockchain-based decen- tralized storage marketplace. Recent work [4 ] formalizes the notion of Proof of Storage-Time (PoSt) which enables storage servers to demonstrate non-interactive continuous availability of outsourced data in a publicly verifiable way. The work also proposes a stateful compact PoSt...

To mitigate cybersecurity breaches, secure communication is crucial for the Internet of Things (IoT) environment. Data integrity is one of the most significant characteristics of security, which can be achieved by employing cryptographic hash functions. In view of the demand from IoT applications, the National Institute of Standards and Technology (NIST) initiated a standardization process for lightweight hash functions. This work presents field-programmable gate array (FPGA) implementations...

In 2009, Lyubashevsky proposed a lattice-based signature scheme by applying the Fiat-Shamir transformation and proved its security under the generalized compact knapsack (GCK) problem. This scheme has a simple structure but has large signature and key sizes due to the security requirement of their security reduction. Dilithium, which was submitted to the NIST Post-Quantum Cryptography standardization and selected as one of the final candidates, is an improvement of the Lyubashevsky's...

NTRU was the first practical public key encryption scheme constructed on a lattice over a polynomial-based ring and has been considered secure against significant cryptanalytic attacks over the past few decades. However, NTRU and its variants suffer from several drawbacks, including difficulties in achieving worst-case correctness error in a moderate modulus, inconvenient sampling distributions for messages, and relatively slower algorithms compared to other lattice-based schemes. In...

Private comparison schemes constructed on homomorphic encryption offer the noninteractive, output expressive and parallelizable features, and have advantages in communication bandwidth and performance. In this paper, we propose cuXCMP, which allows negative and float inputs, offers fully output expressive feature, and is more extensible and practical compared to XCMP (AsiaCCS 2018). Meanwhile, we introduce several memory-centric optimizations of the constant term extraction kernel tailored for...