The National Institute for Standards and Technology (NIST) initiated a standardization procedure for additional digital signatures and recently announced round-2 candidates for the PQ additional digital signature schemes. The multivariate digital signature scheme Unbalanced Oil and Vinegar (UOV) is one of the oldest post-quantum schemes and has been selected by NIST for Round 2. Although UOV is mathematically secure, several side-channel attacks (SCA) have been shown on the UOV or UOV-based...

NTRU-like constructions are among the most studied lattice-based schemes. The freedom of design of NTRU resulted in many variants in literature motivated by faster computations or more resistance against lattice attacks by changing the underlying algebra. To the best of our knowledge, BQTRU (DCC 2017), a noncommutative NTRU-like cryptosystem, is the fastest claimed variant of NTRU built over the quaternion algebra of the bivariate ring of polynomials. The key generation and the encryption of...

In response to the quantum threat, new post-quantum cryptographic algorithms will soon be deployed to replace existing public-key schemes. MAYO is a quantum-resistant digital signature scheme whose small keys and signatures make it suitable for widespread adoption, including on embedded platforms with limited security resources. This paper demonstrates two single-trace side-channel attacks on a MAYO implementation in ARM Cortex-M4 that recover a secret key with probabilities of 99.9% and...

In this work, we propose the first hardware implementation of Classic McEliece protected with countermeasures against Side-Channel Attacks (SCA) and Fault Injection Attacks (FIA). Classic Mceliece is one of the leading candidates for Key Encapsulation Mechanisms (KEMs) in the ongoing round 4 of the NIST standardization process for post-quantum cryptography. In particular, we implement a range of generic countermeasures against SCA and FIA, particularly protected the vulnerable operations...

Multivariate cryptography currently centres mostly around UOV-based signature schemes: All multivariate round 2 candidates in the selection process for additional digital signatures by NIST are either UOV itself or close variations of it: MAYO, QR-UOV, SNOVA, and UOV. Also schemes which have been in the focus of the multivariate research community, but are broken by now - like Rainbow and LUOV - are based on UOV. Both UOV and the schemes based on it have been frequently analyzed regarding...

We present the protected hardware implementation of the Module-Lattice-Based Digital Signature Standard (ML-DSA). ML-DSA is an extension of Dilithium 3.1, which is the winner of the Post Quantum Cryptography (PQC) competition in the digital signature category. The proposed design is based on the existing high-performance Dilithium 3.1 design. We implemented existing Dilithium masking gadgets in hardware, which were only implemented in software. The masking gadgets are integrated with the...

The Supersingular Isogeny Diffie-Hellman (SIDH) scheme is a public key cryptosystem that was submitted to the National Institute of Standards and Technology's competition for the standardization of post-quantum cryptography protocols. The private key in SIDH consists of an isogeny whose degree is a prime power. In July 2022, Castryck and Decru discovered an attack that completely breaks the scheme by recovering Bob's secret key, using isogenies between higher dimensional abelian varieties to...

A Timed Commitment (TC) with time parameter $t$ is hiding for time at most $t$, that is, commitments can be force-opened by any third party within time $t$. In addition to various cryptographic assumptions, the security of all known TC schemes relies on the sequentiality assumption of repeated squarings in hidden-order groups. The repeated squaring assumption is therefore a security bottleneck. In this work, we give a black-box construction of TCs from any time-lock puzzle (TLP) by...

Digital signature schemes based on multivariate- and code-based hard problems are promising alternatives for lattice-based signature schemes, due to their smaller signature size. Hence, several candidates in the ongoing additional standardization for quantum secure digital signature (DS) schemes by the National Institute of Standards and Technology (NIST) rely on such alternate hard problems. Gaussian Elimination (GE) is a critical component in the signing procedure of these schemes. In this...

Falcon is a winner of NIST's six-year post-quantum cryptography standardisation competition. Based on the celebrated full-domain-hash framework of Gentry, Peikert and Vaikuntanathan (GPV) (STOC'08), Falcon leverages NTRU lattices to achieve the most compact signatures among lattice-based schemes. Its security hinges on a Rényi divergence-based argument for Gaussian samplers, a core element of the scheme. However, the GPV proof, which uses statistical distance to argue closeness of...

With the advent of quantum computers, the security of cryptographic primitives, including digital signature schemes, has been compromised. To deal with this issue, some signature schemes have been introduced to resist against these computers. These schemes are known as post-quantum signature schemes. One group of these schemes is based on the hard problems of coding theory, called code-based cryptographic schemes. Several code-based signature schemes are inspired by the McEliece encryption...

In parallel with the standardization of lattice-based cryptosystems, the research community in Post-quantum Cryptography focused on non-lattice-based hard problems for constructing public-key cryptographic primitives. The Linear Code Equivalence (LCE) Problem has gained attention regarding its practical applications and cryptanalysis. Recent advancements, including the LESS signature scheme and its candidacy in the NIST standardization for additional signatures, supported LCE as a...

Post-quantum cryptography (PQC) has rapidly evolved in response to the emergence of quantum computers, with the US National Institute of Standards and Technology (NIST) selecting four finalist algorithms for PQC standardization in 2022, including the Falcon digital signature scheme. The latest round of digital signature schemes introduced Hawk, both based on the NTRU lattice, offering compact signatures, fast generation, and verification suitable for deployment on resource-constrained...

A crucial ingredient for many cryptographic primitives such as key exchange protocols and advanced signature schemes is a commutative group action where the structure of the underlying group can be computed efficiently. SCALLOP provides such a group action, based on oriented supersingular elliptic curves. We present PEARL-SCALLOP, a variant of SCALLOP that changes several parameter and design choices, thereby improving on both efficiency and security and enabling feasible parameter...

We construct the first multi-input functional encryption (MIFE) and indistinguishability obfuscation (iO) schemes for pseudorandom functionalities, where the output of the functionality is pseudorandom for every input seen by the adversary. Our MIFE scheme relies on LWE and evasive LWE (Wee, Eurocrypt 2022 and Tsabary, Crypto 2022) for constant arity functions, and a strengthening of evasive LWE for polynomial arity. Thus, we obtain the first MIFE and iO schemes for a nontrivial...

With the recent standardization of post-quantum cryptographic algorithms, research efforts have largely remained centered on public key exchange and encryption schemes. Argument systems, which allow a party to efficiently argue the correctness of a computation, have received comparatively little attention regarding their quantum-resilient design. These computational integrity frameworks often rely on cryptographic assumptions, such as pairings or group operations, which are vulnerable to...

Classic McEliece is one of the three code-based candidates in the fourth round of the NIST post-quantum cryptography standardization process in the Key Encapsulation Mechanism category. As such, its decapsulation algorithm is used to recover the session key associated with a ciphertext using the private key. In this article, we propose a new side-channel attack on the syndrome computation in the decapsulation algorithm that recovers the private key, which consists of the private Goppa...

One of the main candidates of post-quantum cryptography is lattice-based cryptography. Its cryptographic security against quantum attackers is based on the worst-case hardness of lattice problems like the shortest vector problem (SVP), which asks to find the shortest non-zero vector in an integer lattice. Asymptotic quantum speedups for solving SVP are known and rely on Grover's search. However, to assess the security of lattice-based cryptography against these Grover-like quantum speedups,...

Cryptographic group actions are a leading contender for post-quantum cryptography, and have also been used in the development of quantum cryptographic protocols. In this work, we explore quantum group actions, which consist of a group acting on a set of quantum states. We show the following results: 1. In certain settings, statistical (even query bounded) security is impossible, analogously to post-quantum classical group actions. 2. We construct quantum state group actions and prove that...

Much work has been done recently on developing password-authenticated key exchange (PAKE) mechanisms with post-quantum security. However, modern guidance recommends the use of hybrid schemes—schemes which rely on the combined hardness of a post-quantum assumption, e.g., learning with Errors (LWE), and a more traditional assumption, e.g., decisional Diffie-Hellman. To date, there is no known hybrid PAKE construction, let alone a general method for achieving such. In this paper, we present...

The MPC-in-the-Head framework has been pro- posed as a solution for Non-Interactive Zero-Knowledge Arguments of Knowledge (NIZKAoK) due to its efficient proof generation. However, most existing NIZKAoK constructions using this approach require multiple MPC evaluations to achieve negligible soundness error, resulting in proof size and time that are asymptotically at least λ times the size of the circuit of the NP relation. In this paper, we propose a novel method to eliminate the need for...

In this paper we study several computational problems related to current post-quantum cryptosystems based on isogenies between supersingular elliptic curves. In particular we prove that the supersingular isogeny path and endomorphism ring problems are unconditionally equivalent under polynomial time reductions. We show that access to a factoring oracle is sufficient to solve the Quaternion path problem of KLPT and prove that these problems are equivalent, where previous results either...

SQIsign is a well-known post-quantum signature scheme due to its small combined signature and public-key size. However, SQIsign suffers from notably long signing times, and verification times are not short either. To improve this, recent research has explored both one-dimensional and two-dimensional variants of SQIsign, each with distinct characteristics. In particular, SQIsign2D's efficient signing and verification times have made it a focal point of recent research. However, the absence of...

We extend the usual ideal action on oriented elliptic curves to a (Hermitian) module action on oriented (polarised) abelian varieties. Oriented abelian varieties are naturally enriched in $R$-modules, and our module action comes from the canonical power object construction on categories enriched in a closed symmetric monoidal category. In particular our action is canonical and gives a fully fledged symmetric monoidal action. Furthermore, we give algorithms to compute this action in practice,...

As the industry prepares for the transition to post-quantum secure public key cryptographic algorithms, vulnerability analysis of their implementations is gaining importance. A theoretically secure cryptographic algorithm should also be able to withstand the challenges of physical attacks in real-world environments. MAYO is a candidate in the ongoing first round of the NIST post-quantum standardization process for selecting additional digital signature schemes. This paper demonstrates three...

Keccak acts as the hash algorithm and eXtendable-Output Function (XOF) specified in the NIST standard drafts for Kyber and Dilithium. The Keccak output is highly correlated with sensitive information. While in RSA and ECDSA, hash-like components are only used to process public information, such as the message. The importance and sensitivity of hash-like components like Keccak are much higher in Kyber and Dilithium than in traditional public-key cryptography. However, few works study Keccak...

Isogeny-based cryptography is one of the candidates for post-quantum cryptography. Recently, many isogeny-based cryptosystems using isogenies between Kummer surfaces were proposed. Most of those cryptosystems use $(2,2)$-isogenies. However, to enhance the possibility of cryptosystems, higher degree isogenies, say $(\ell,\ell)$-isogenies for an odd $\ell$, is also crucial. For an odd $\ell$, the Lubicz-Robert gave a formula to compute $(\ell)^g$-isogenies in general dimension $g$. In this...

Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two promi- nent approaches, both heavily studied within the NIST standardization project. Code-based cryptography—most prominently exemplified by the McEliece cryptosystem—is based on the hardness of decoding random linear error-correcting codes. Despite the McEliece cryptosystem having been unbroken for several...

Are we there yet? Are we there yet? No, kids, the road to quantum-safety is long and sturdy. But let me tell you a story: Once upon a time, science discovered a great threat to Cryptography World: The scalable quantum computer! Nobody had ever seen one, but everyone understood it would break the mechanisms used to secure Internet communication since times of yore (or the late 20th century, anyway). The greatest minds from all corners of the land were gathered to invent, implement, and...

This article presents an in-depth study of isogeny-based cryptographic methods for the development of secure and scalable electronic voting systems. We address critical challenges such as voter privacy, vote integrity, and resistance to quantum attacks. Our work introduces novel cryptographic protocols leveraging isogenies, establishing a robust framework for post-quantum secure electronic voting. We provide detailed mathematical foundations, protocol designs, and security proofs,...

The Lattice Isomorphism Problem (LIP) was recently introduced as a new hardness assumption for post-quantum cryptography. The strongest known efficiently computable invariant for LIP is the genus of a lattice. To instantiate LIP-based schemes one often requires the existence of a lattice that (1) lies in some fixed genus, and (2) has some good geometric properties such as a high packing density or small smoothness parameter. In this work we show that such lattices exist. In particular,...

Recently, the construction of cryptographic schemes based on hard lattice problems has gained immense popularity. Apart from being quantum resistant, lattice-based cryptography allows a wide range of variations in the underlying hard problem. As cryptographic schemes can work in different environments under different operational constraints such as memory footprint, silicon area, efficiency, power requirement, etc., such variations in the underlying hard problem are very useful for designers...

Computationally hard problems based on coding theory, such as the syndrome decoding problem, have been used for constructing secure cryptographic schemes for a long time. Schemes based on these problems are also assumed to be secure against quantum computers. However, these schemes are often considered impractical for real-world deployment due to large key sizes and inefficient computation time. In the recent call for standardization of additional post-quantum digital signatures by the...

Zero-Knowledge (ZK) protocols have been a subject of intensive study due to their fundamental importance and versatility in modern cryptography. However, the inherently different nature of quantum information significantly alters the landscape, necessitating a re-examination of ZK designs. A crucial aspect of ZK protocols is their round complexity, intricately linked to $\textit{simulation}$, which forms the foundation of their formal definition and security proofs. In the...

Digital signature is a fundamental cryptographic primitive and is widely used in the real world. Unfortunately, the current digital signature standards like EC-DSA and RSA are not quantum-resistant. Among post-quantum cryptography (PQC), isogeny-based signatures preserve some advantages of elliptic curve cryptosystems, particularly offering small signature sizes. Currently, SQIsign and its variants are the most promising isogeny-based digital signature schemes. In this paper, we propose a...

In 2022, Wang et al. proposed the multivariate signature scheme SNOVA as a UOV variant over the non-commutative ring of $\ell \times \ell $ matrices over $\mathbb{F}_q$. This scheme has small public key and signature size and is a first round candidate of NIST PQC additional digital signature project. Recently, Ikematsu and Akiyama, and Li and Ding show that the core matrices of SNOVA with $v$ vinegar-variables and $o$ oil-variables are regarded as the representation matrices of UOV with...

Kyber was selected by NIST as a Post-Quantum Cryptography Key Encapsulation Mechanism standard. This means that the industry now needs to transition and adopt these new standards. One of the most demanding operations in Kyber is the modular arithmetic, making it a suitable target for optimization. This work offers a novel modular reduction design with the lowest area on Xilinx FPGA platforms. This novel design, through K-reduction and LUT-based reduction, utilizes 49 LUTs and 1 DSP...

Digital signatures are fundamental building blocks in various protocols to provide integrity and authenticity. The development of the quantum computing has raised concerns about the security guarantees afforded by classical signature schemes. CRYSTALS-Dilithium is an efficient post-quantum digital signature scheme based on lattice cryptography and has been selected as the primary algorithm for standardization by the National Institute of Standards and Technology. In this work, we present a...

In the post-quantum migration of TLS 1.3, an ephemeral Diffie-Hellman must be replaced with a post-quantum key encapsulation mechanism (KEM). At EUROCRYPT 2022, Huguenin-Dumittan and Vaudenay [EC:HugVau22] demonstrated that KEMs with standard CPA security are sufficient for the security of the TLS1.3 handshake. However, their result is only proven in the random oracle model (ROM), and as the authors comment, their reduction is very much non-tight and not sufficient to guarantee security in...

Embedded systems are flexible and cost-effective and thus have found a use case in almost every part of our daily lives. Due to their widespread use, they have also become valuable targets for cyber attacks. However, translating cutting-edge cyber security from servers and desktops to the embedded realm can be challenging due to the limited computational power and memory of embedded devices. Although quantum computing is still in early research and development, it threatens to break...

We propose Scloud+, a lattice-based key encapsulation mechanism (KEM) scheme. The design of Scloud+ is informed by the following two aspects. Firstly, Scloud+ is based on the hardness of algebraic-structure-free lattice problems, which avoids potential attacks brought by the algebraic structures. Secondly, Scloud+ provides sets of light weight parameters, which greatly reduce the complexity of computation and communication complexity while maintaining the required level of security.

Blind signatures represent a class of cryptographic primitives enabling privacy-preserving authentication with several applications such as e-cash or e-voting. It is still a very active area of research, in particular in the post-quantum setting where the history of blind signatures has been hectic. Although it started to shift very recently with the introduction of a few lattice-based constructions, all of the latter give up an important characteristic of blind signatures (size, efficiency,...

From 2022, Korean Post-Quantum Cryptography (KpqC) Competition has been held. Among the Round 1 algorithms of KpqC, eight algorithms were selected in December 2023. To evaluate the algorithms, the performance is critical factor. However, the performance of the algorithms submitted to KpqC was evaluated in different development environments. Consequently, it is difficult to compare the performance of each algorithm fairly, because the measurements were not conducted in the identical...

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...

Verifiable Timed Signatures (VTS) are cryptographic constructs that enable obtaining a signature at a specific time in the future and provide evidence that the signature is legitimate. This framework particularly finds utility in applications such as payment channel networks, multiparty signing operations, or multiparty computation, especially within blockchain architectures. Currently, VTS schemes are based on signature algorithms such as BLS signature, Schnorr signature, and ECDSA. These...

Compared to elliptic curve cryptography, a main drawback of lattice-based schemes is the larger size of their public keys and ciphertexts. A common procedure for compressing these objects consists essentially of dropping some of their least significant bits. Albeit effective for compression, there is a limit to the number of bits to be dropped before we get a noticeable decryption failure rate (DFR), which is a security concern. To address this issue, this paper presents a family of...

With the potential arrival of quantum computers, it is essential to build cryptosystems resistant to attackers with the computing power of a quantum computer. With Shor's algorithm, cryptosystems based on discrete logarithms and factorization become obsolete. Reason why NIST has launching two competitions in 2016 and 2023 to standardize post-quantum cryptosystems (such as KEM and signature ) based on problems supposed to resist attacks using quantum computers. EagleSign was prosed to NIT...

Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus, understanding their concrete security is critical. Most work on LWE security focuses on theoretical estimates of attack performance, which is important but may overlook attack nuances arising in real-world implementations. The sole existing concrete...

For more than two decades, pairings have been a fundamental tool for designing elegant cryptosystems, varying from digital signature schemes to more complex privacy-preserving constructions. However, the advancement of quantum computing threatens to undermine public-key cryptography. Concretely, it is widely accepted that a future large-scale quantum computer would be capable to break any public-key cryptosystem used today, rendering today's public-key cryptography obsolete and mandating the...

The progression of quantum computing is considered a potential threat to traditional cryptography system, highlighting the significance of post-quantum security in cryptographic systems. Regarding symmetric key encryption, the Grover algorithm can approximately halve the search complexity. Despite the absence of fully operational quantum computers at present, the necessity of assessing the security of symmetric key encryption against quantum computing continues to grow. In this paper, we...

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...

This article presents an innovative project for a Central Bank Digital Currency (CBDC) infrastructure. Focusing on security and reliability, the proposed architecture: (1) employs post-quantum cryptography (PQC) algorithms for long-term security, even against attackers with access to cryptographically-relevant quantum computers; (2) can be integrated with a Trusted Execution Environment (TEE) to safeguard the confidentiality of transaction contents as they are processed by third-parties; and...

The field of post-quantum cryptography (PQC) is continuously evolving. Many researchers are exploring efficient PQC implementation on various platforms, including x86, ARM, FPGA, GPU, etc. In this paper, we present an Efficient CryptOgraphy CRYSTALS (ECO-CRYSTALS) implementation on standard 64-bit RISC-V Instruction Set Architecture (ISA). The target schemes are two winners of the National Institute of Standards and Technology (NIST) PQC competition: CRYSTALS-Kyber and CRYSTALS-Dilithium,...

The rapid evolution of post-quantum cryptography, spurred by standardization efforts such as those led by NIST, has highlighted the prominence of lattice-based cryptography, notably exemplified by CRYSTALS-Kyber. However, concerns persist regarding the security of cryptographic implementations, particularly in the face of Side-Channel Attacks (SCA). The usage of operations like the Number Theoretic Transform (NTT) in CRYSTALS-Kyber introduces vulnerabilities to SCA, especially single-trace...

This paper presents extensions to the OpenTitan hardware root of trust that aim at enabling high-performance lattice-based cryptography. We start by carefully optimizing ML-KEM and ML-DSA - the two primary algorithms selected by NIST for standardization - in software targeting the OTBN accelerator. Based on profiling results of these implementations, we propose tightly integrated extensions to OTBN, specifically an interface from OTBN to OpenTitan's Keccak accelerator (KMAC core) and...

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...

Blockchain technology ensures accountability, transparency, and redundancy in critical applications, includ- ing IoT with embedded systems. However, the reliance on public-key cryptography (PKC) makes blockchain vulnerable to quantum computing threats. This paper addresses the urgent need for quantum-safe blockchain solutions by integrating Post- Quantum Cryptography (PQC) into blockchain frameworks. Utilizing algorithms from the NIST PQC standardization pro- cess, we aim to fortify...

As the use of the internet and digital devices has grown rapidly, keeping digital communications secure has become very important. Authenticated Key Agreement (AKA) protocols play a vital role in securing digital communications. These protocols enable the communicating parties to mutually authenticate and securely establish a shared secret key. The emergence of quantum computers makes many existing AKA protocols vulnerable to their immense computational power. Consequently, designing new...

As a prominent category of side-channel attacks (SCAs), plaintext-checking (PC) oracle-based SCAs offer the advantages of generality and operational simplicity on a targeted device. At TCHES 2023, Rajendran et al. and Tanaka et al. independently proposed the multiple-valued (MV) PC oracle, significantly reducing the required number of queries (a.k.a., traces) in the PC oracle. However, in practice, when dealing with environmental noise or inaccuracies in the waveform classifier, they...

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...

Isogeny-based schemes often come with special requirements on the field of definition of the involved elliptic curves. For instance, the efficiency of SQIsign, a promising candidate in the NIST signature standardisation process, requires a large power of two and a large smooth integer $T$ to divide $p^2-1$ for its prime parameter $p$. We present two new methods that combine previous techniques for finding suitable primes: sieve-and-boost and XGCD-and-boost. We use these methods to find...

The one-time pad cipher is renowned for its theoretical perfect security, yet its practical deployment is primarily hindered by the key-size and distribution challenge. This paper introduces a novel approach to key distribution called q-stream, designed to make symmetric-key cryptography, and the one-time pad cipher in particular, a viable option for contemporary secure communications, and specifically, post-quantum cryptography, leveraging quantum noise and combinatorics to ensure secure...

EagleSign is one of the 40 “Round 1 Additional Signatures” that is accepted for consideration in the supplementary round of the Post-Quantum Cryptography standardization process, organized by NIST. Its design is based on structured lattices, and it boasts greater simplicity and performance compared to the two lattice signatures already selected for standardization: Falcon and Dilithium. In this paper, we show that those claimed advantages come at the cost of security. More precisely, we...

Enhanced pqsigRM is a code-based hash-and-sign scheme proposed to the second National Institute of Standards and Technology call for post-quantum signatures. The scheme is based on the $(U,U+V)$-construction and it enjoys remarkably small signature lengths, about $1$KBytes for a security level of $128$ bits. Unfortunately we show that signatures leak information about the underlying $(U,U+V)$-structure. It allows to retrieve the private-key with~$100, 000$ signatures.

In 2018, Mouha et al. (IEEE Trans. Reliability, 2018) performed a post-mortem investigation of the correctness of reference implementations submitted to the SHA3 competition run by NIST, finding previously unidentified bugs in a significant portion of them, including two of the five finalists. Their innovative approach allowed them to identify the presence of such bugs in a black-box manner, by searching for counterexamples to expected cryptographic properties of the implementations under...

Oblivious transfer (OT) is a fundamental cryptographic protocol that plays a crucial role in secure multi-party computation (MPC). Most practical OT protocols by, e.g., Naor and Pinkas (SODA'01) or Chou and Orlandi (Latincrypt'15), are based on Diffie-Hellman (DH)-like assumptions and not post-quantum secure. In contrast, many other components of MPC protocols, including garbled circuits and secret sharings, are post-quantum secure. The reliance on non-post-quantum OT protocols presents a...

Anticipating the advent of large quantum computers, NIST started a worldwide competition in 2016 aiming to define the next cryptographic standards. HQC is one of these post-quantum schemes still in contention, with three others already standardized. In 2022, Guo et al. introduced a timing attack that exploited an inconsistency in HQC rejection sampling function to recover its secret key in 866,000 calls to an oracle. The authors of HQC updated its specification by applying an algorithm to...

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...

It is fundamental that executing cryptographic software must not leak secrets through side-channels. For software-visible side-channels, it was long believed that "constant-time" programming would be sufficient as a systematic countermeasure. However, this belief was shattered in 2018 by attacks exploiting speculative execution—so called Spectre attacks. Recent work shows that language support suffices to protect cryptographic code with minimal overhead against one class of such attacks,...

$SPHINCS^+$, one of the Post-Quantum Cryptography Digital Signature Algorithms (PQC-DSA) selected by NIST in the third round, features very short public and private key lengths but faces significant performance challenges compared to other post-quantum cryptographic schemes, limiting its suitability for real-world applications. To address these challenges, we propose the GPU-based paRallel Accelerated $SPHINCS^+$ (GRASP), which leverages GPU technology to enhance the efficiency of...

Oblivious Transfer (OT) is a fundamental cryptographic protocol with applications in secure Multi-Party Computation, Federated Learning, and Private Set Intersection. With the advent of quantum computing, it is crucial to develop unconditionally secure core primitives like OT to ensure their continued security in the post-quantum era. Despite over four decades since OT's introduction, the literature has predominantly relied on computational assumptions, except in cases using unconventional...

Internet of Medical Things (IoMT) has gained significant research focus in both academic and medical institutions. Nevertheless, the sensitive data involved in IoMT raises concerns regarding user validation and data privacy. To address these concerns, certificateless signcryption (CLSC) has emerged as a promising solution, offering authenticity, confidentiality, and unforgeability. Unfortunately, most existing CLSC schemes are impractical for IoMT due to their heavy computational and storage...

This work expands the machinery we have for isogeny-based cryptography in genus 2 by developing a toolbox of several essential algorithms for Kummer surfaces, the dimension-2 analogue of $x$-only arithmetic on elliptic curves. Kummer surfaces have been suggested in hyper-elliptic curve cryptography since at least the 1980s and recently these surfaces have reappeared to efficiently compute $(2,2)$-isogenies. We construct several essential analogues of techniques used in one-dimensional...

The current cryptographic frameworks like RSA, ECC, and AES are potentially under quantum threat. Quantum cryptographic and post-quantum cryptography are being extensively researched for securing future information. The quantum computer and quantum algorithms are still in the early developmental stage and thus lack scalability for practical application. As a result of these challenges, most researched PQC methods are lattice-based, code-based, ECC isogeny, hash-based, and multivariate...

$\mathrm{SPHINCS^{+}}$ is a post-quantum signature scheme that, at the time of writing, is being standardized as $\mathrm{SLH\text{-}DSA}$. It is the most conservative option for post-quantum signatures, but the original tight proofs of security were flawed—as reported by Kudinov, Kiktenko and Fedorov in 2020. In this work, we formally prove a tight security bound for $\mathrm{SPHINCS^{+}}$ using the EasyCrypt proof assistant, establishing greater confidence in the general security of the...

We present an efficient quantum algorithm for solving the semidirect discrete logarithm problem (SDLP) in any finite group. The believed hardness of the semidirect discrete logarithm problem underlies more than a decade of works constructing candidate post-quantum cryptographic algorithms from nonabelian groups. We use a series of reduction results to show that it suffices to consider SDLP in finite simple groups. We then apply the celebrated Classification of Finite Simple Groups to...

A popular way to build post-quantum signature schemes is by first constructing an identification scheme (IDS) and applying the Fiat-Shamir transform to it. In this work we tackle two open questions related to the general applicability of techniques around this approach that together allow for efficient post-quantum signatures with optimal security bounds in the QROM. First we consider a recent work by Aguilar-Melchor, Hülsing, Joseph, Majenz, Ronen, and Yue (Asiacrypt'23) that showed...

Interactive proofs are a cornerstone of modern cryptography and as such used in many areas, from digital signatures to multy-party computation. Often the knowledge error $\kappa$ of an interactive proof is not small enough, and thus needs to be reduced. This is usually achieved by repeating the interactive proof in parallel t times. Recently, it was shown that parallel repetition of any $(k_1, \ldots , k_\mu)$-special-sound multi-round public-coin interactive proof reduces the knowledge...

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...

Direct Anonymous Attestation (DAA) allows a (host) device with a Trusted Platform Module (TPM) to prove that it has a certified configuration of hardware and software whilst preserving the privacy of the device. All deployed DAA schemes are based on classical security assumptions. Despite a long line of works proposing post-quantum designs, the vast majority give only theoretical schemes and where concrete parameters are computed, their efficiency is far from practical. Our first...

Multivariate Cryptography is one of the main candidates for Post-quantum Cryptography. Multivariate schemes are usually constructed by applying two secret affine invertible transformations $\mathcal S,\mathcal T$ to a set of multivariate polynomials $\mathcal{F}$ (often quadratic). The secret polynomials $\mathcal{F}$ posses a trapdoor that allows the legitimate user to find a solution of the corresponding system, while the public polynomials $\mathcal G=\mathcal S\circ\mathcal...

In this paper we propose verifiable secret sharing (VSS) schemes secure for any honest majority in the synchronous model, and that only use symmetric-key cryptographic tools, therefore having plausibly post-quantum security. Compared to the state-of-the-art scheme with these features (Atapoor et al., Asiacrypt `23), our main improvement lies on the complexity of the ``optimistic'' scenario where the dealer and all but a small number of receivers behave honestly in the sharing phase: in this...

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...

In this paper, we present three types of variations of the ALTEQ cryptosystem, a recent submission to the NIST's additional call for signatures. We name these Dangerous Variations of ALTEQ (DVA), as there is always a certain danger in stepping out of usual constructions, although we attempt to maintain heuristic security. First, we present DVA-GG (Graph Generalization), that can be seen as a more abstract point-of-view on the operations done in ALTEQ and encourages more research on the...

In this paper, we introduce a new probability function parameter in the instantiations of the Goldreich-Micali-Wigderson with Fiat-Shamir and unbalanced challenges used in ALTEQ, a recent NIST PQC candidate in the call for additional signatures. This probability set at 100% does not bring any changes in the scheme, but modifies the public challenge generation process when below 100%, by injecting potential rejections in otherwise completely valid inputs. From a theoretical point of view,...

In this paper, we study the robustness of Kyber, the Learning With Errors (LWE)-based Key Encapsulation Mechanism (KEM) chosen for standardization by NIST, against key mismatch attacks. We demonstrate that Kyber's security levels can be compromised with a few mismatch queries by striking a balance between the parallelization level and the cost of lattice reduction for post-processing. This highlights the imperative need to strictly prohibit key reuse in CPA-secure Kyber. We further...

An important proof technique in the random oracle model involves reprogramming it on hard to predict inputs and arguing that an attacker cannot detect that this occurred. In the quantum setting, a particularly challenging version of this considers adaptive reprogramming wherein the points to be reprogrammed (or output values they should be programmed to) are dependent on choices made by the adversary. Frameworks for analyzing adaptive reprogramming were given by, e.g., by Unruh (CRYPTO...

The BUFF transform, due to Cremers et al. (S&P'21), is a generic transformation for digital signature scheme, with the purpose of obtaining additional security guarantees beyond unforgeability: exclusive ownership, message-bound signatures, and non-resignability. Non-resignability (which essentially challenges an adversary to re-sign an unknown message for which it only obtains the signature) turned out to be a delicate matter, as recently Don et al. (CRYPTO'24) showed that the initial...

In computer arithmetic operations, the Number Theoretic Transform (NTT) plays a significant role in the efficient implementation of cyclic and nega-cyclic convolutions with the application of multiplying large integers and large degree polynomials. Multiplying polynomials is a common operation in lattice-based cryptography. Hence, the NTT is a core component of several lattice-based cryptographic algorithms. Two well-known examples are the key encapsulation mechanism Kyber and the...

The Deuring correspondence is a correspondence between supersingular elliptic curves and quaternion orders. Under this correspondence, an isogeny between elliptic curves corresponds to a quaternion ideal. This correspondence plays an important role in isogeny-based cryptography and several algorithms to compute an isogeny corresponding to a quaternion ideal (ideal-to-isogeny algorithms) have been proposed. In particular, SQIsign is a signature scheme based on the Deuring correspondence and...

Isogeny-based cryptography is cryptographic schemes whose security is based on the hardness of a mathematical problem called the isogeny problem, and is attracting attention as one of the candidates for post-quantum cryptography. A representative isogeny-based cryptography is the signature scheme called SQIsign, which was submitted to the NIST PQC standardization competition. SQIsign has attracted much attention because of its very short signature and key size among the candidates for the...

With the rise of quantum computing, the security of traditional cryptographic systems, especially those vulnerable to quantum attacks, is under threat. While public key cryptography has been widely studied in post-quantum security, symmetric-key cryptography has received less attention. This paper explores using the Ajtai-Micciancio hash function, based on the Short Integer Solution (SIS) problem, as a pseudorandom function in the Luby-Rackoff cipher. Since lattice-based problems like SIS...

Multivariate public key cryptography (MPKC) is one of the most promising alternatives to build quantum-resistant signature schemes, as evidenced in NIST's call for additional post-quantum signature schemes. The main assumption in MPKC is the hardness of the Multivariate Quadratic (MQ) problem, which seeks for a common root to a system of quadratic polynomials over a finite field. Although the Crossbred algorithm is among the most efficient algorithm to solve MQ over small fields, its...

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...

In 2017, Petzoldt, Szepieniec, and Mohamed proposed a blind signature scheme, based on multivariate cryptography. This construction has been expanded on by several other works. This short paper shows that their construction is susceptible to an efficient polynomial-time attack. The problem is that the authors implicitly assumed that for a random multivariate quadratic map $\mathcal{R}:\mathbb{F}_q^m \rightarrow \mathbb{F}_q^m$ and a collision-resistant hash function $H: \{0,1\}^* \rightarrow...

The advent of quantum computing technology will compromise many of the current cryptographic algorithms, especially public-key cryptography, which is widely used to protect digital information. Most algorithms on which we depend are used worldwide in components of many different communications, processing, and storage systems. Once access to practical quantum computers becomes available, all public-key algorithms and associated protocols will be vulnerable to criminals, competitors, and...

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...

This work shows how FALCON can achieve the Beyond UnForgeability Features (BUFF) introduced by Cremers et al. (S&P'21) more efficiently than by applying the generic BUFF transform. Specifically, we show that applying a transform of Pornin and Stern (ACNS'05), dubbed PS-3 transform, already suffices for FALCON to achieve BUFF security. For FALCON, this merely means to include the public key in the hashing step in signature generation and verification, instead of hashing only the nonce and the...

FALCON is candidate for standardization of the new Post Quantum Cryptography (PQC) primitives by the National Institute of Standards and Technology (NIST). However, it remains a challenge to define efficient countermeasures against side-channel attacks (SCA) for this algorithm. FALCON is a lattice-based signature that relies on rational numbers which is unusual in the cryptography field. While recent work proposed a solution to mask the addition and the multiplication, some roadblocks...

In white-box cryptography, early protection techniques have fallen to the automated Differential Computation Analysis attack (DCA), leading to new countermeasures and attacks. A standard side-channel countermeasure, Ishai-Sahai-Wagner's masking scheme (ISW, CRYPTO 2003) prevents Differential Computation Analysis but was shown to be vulnerable in the white-box context to the Linear Decoding Analysis attack (LDA). However, recent quadratic and cubic masking schemes by Biryukov-Udovenko...