This note reports new implementation results for the Falcon signature algorithm on an ARM Cortex-M4 microcontroller. Compared with our previous implementation (in 2019), runtime cost has been about halved.

We construct the first tightly secure signature schemes in the multi-user setting with adaptive corruptions from classical discrete logarithm, RSA, factoring, or post-quantum group action discrete logarithm assumption. In contrast to our scheme, the previous tightly secure schemes are based on the decisional assumption (e.g., (group action) DDH) or interactive search assumptions (e.g., one-more CDH). The security of our schemes is independent of the number of users, signing queries, and...

Designing post-quantum digital signatures is a very active research area at present, with several protocols being developed, based on a variety of mathematical assumptions. Many of these signatures schemes can be used as a basis to define more advanced schemes, such as ring or threshold signatures, where multiple parties are involved in the signing process. Unfortunately, the majority of these protocols only considers a static adversary, that must declare which parties to corrupt at the...

An anonymous credential (AC) system with partial disclosure allows users to prove possession of a credential issued by an issuer while selectively disclosing a subset of their attributes to a verifier in a privacy-preserving manner. In keyed-verification AC (KVAC) systems, the issuer and verifier share a secret key. Existing KVAC schemes rely on computationally expensive zero-knowledge proofs during credential presentation, with the presentation size growing linearly with the number of...

Secret handshakes, introduced by Balfanz et al. [3], allow users associated with various groups to determine if they share a common affiliation. These protocols ensure crucial properties such as fairness (all participants learn the result simultaneously), affiliation privacy (failed handshakes reveal no affiliation information), and result-hiding (even participants within a shared group cannot infer outcomes of unrelated handshakes). Over time, various secret-handshake schemes have been...

Blind signatures are an important primitive for privacy-preserving technologies. To date, highly efficient pairing-free constructions rely on the random oracle model, and additionally, a strong assumption, such as interactive assumptions or the algebraic group model. In contrast, for signatures we know many efficient constructions that rely on the random oracle model and standard assumptions. In this work, we develop techniques to close this gap. Compared to the most efficient...

We construct the first blind signature scheme that achieves all of the following properties simultaneously: - it is tightly secure under a standard (i.e., non-interactive, non-\(q\)-type) computational assumption, - it does not require pairings, - it does not rely on generic, non-black-box techniques (like generic NIZK proofs). The third property enables a reasonably efficient solution, and in fact signatures in our scheme comprise 10 group elements and 29...

We present a novel digital signature scheme grounded in non-commutative cryptography and implemented over a bilinear matrix group platform. At the core of our design is a unique equivocation function that obfuscates intermediate elements, effectively concealing outputs and minimizing observable information leakage. To the best of our knowledge, this is the first digital signature scheme to combine information-theoretic security with computational hardness, relying on a challenging instance...

In this work we state and prove an abstract version of the multi-forking lemma of Pointcheval and Stern from EUROCRYPT'96. Earlier, Bellare and Neven had given an abstract version of forking lemma for two-collisions (CCS'06). While the original purpose of the forking lemma was to prove security of signature schemes in the random oracle methodology, the abstract forking lemma can be used to obtain security proofs for multi-signatures, group signatures, and compilation of interactive protocols...

Group signature (GS) is a well-known cryptographic primitive providing anonymity and traceability. Several implication results have been given by mainly focusing on the several security levels of anonymity, e.g., fully anonymous GS implies public key encryption (PKE) and selfless anonymous GS can be constructed from one-way functions and non-interactive zero knowledge poofs, and so on. In this paper, we explore an winning condition of full traceability: an adversary is required to produce a...

One-more problems like One-More Discrete Logarithm (OMDL) and One-More Diffie--Hellman (OMDH) have found wide use in cryptography, due to their ability to naturally model security definitions for interactive primitives like blind signatures and oblivious PRF. Furthermore, a generalization of OMDH called Threshold OMDH (TOMDH) has proven useful for building threshold versions of interactive protocols. However, due to their complexity it is often unclear how hard such problems actually are,...

We present a novel protocol for two-party ECDSA that achieves two rounds (a single back-and-forth communication) at the cost of a single oblivious linear function evaluation (OLE). In comparison, the previous work of [DKLs18] (S&P 2018) achieves two rounds at the cost of three OLEs, while [BHL24] (Manuscript 2024) requires expensive zero-knowledge proofs on top of the OLE. We demonstrate this by proving that in the generic group model, any adversary capable of generating forgeries for our...

A group signatures allows a user to sign a message anonymously on behalf of a group and provides accountability by using an opening authority who can ``open'' a signature and reveal the signer's identity. Group signatures have been widely used in privacy-preserving applications including anonymous attestation and anonymous authentication. Fully dynamic group signatures allow new members to join the group and existing members to be revoked if needed. Symmetric-key based group signature...

We present a new construction of two-party, threshold ECDSA, building on a 2017 scheme of Lindell and improving his scheme in several ways. ECDSA signing is notoriously hard to distribute securely, due to non-linearities in the signing function. Lindell's scheme uses Paillier encryption to encrypt one party's key share and handle these non-linearities homomorphically, while elegantly avoiding any expensive zero knowledge proofs over the Paillier group during the signing process. However,...

In this paper we introduce the notion of encrypted RAM delegation. In an encrypted RAM delegation scheme, the prover creates a succinct proof for a group of two input strings $x_\mathsf{pb}$ and $x_\mathsf{pr}$, where $x_\mathsf{pb}$ corresponds to a large \emph{public} input and $x_\mathsf{pr}$ is a \emph{private} input. A verifier can check correctness of computation of $\mathcal{M}$ on $(x_\mathsf{pb}, x_\mathsf{pr})$, given only the proof $\pi$ and $x_\mathsf{pb}$. We design encrypted...

SNOVA is a post-quantum digital signature scheme based on multivariate polynomials. It is a first-round candidate in an ongoing NIST standardization process for post-quantum signatures, where it stands out for its efficiency and compactness. Since its initial submission, there have been several improvements to its security analysis, both on key recovery and forgery attacks. All these works reduce to solving a structured system of quadratic polynomials, which we refer to as SNOVA...

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...

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...

Non-interactive zero-knowledge proofs (NIZK) are essential building blocks in threshold cryptosystems like multiparty signatures, distributed key generation, and verifiable secret sharing, allowing parties to prove correct behavior without revealing secrets. Furthermore, universally composable (UC) NIZKs enable seamless composition in the larger cryptosystems. A popular way to construct NIZKs is to compile interactive protocols using the Fiat-Shamir transform. Unfortunately, Fiat-Shamir...

Multi-signature schemes are gaining significant interest due to their blockchain applications. Of particular interest are two-round schemes in the plain public-key model that offer key aggregation, and whose security is based on the hardness of the DLOG problem. Unfortunately, despite substantial recent progress, the security proofs of the proposed schemes provide rather insufficient concrete guarantees (especially for 256-bit groups). This frustrating situation has so far been approached...

A multi-signature scheme allows a list of signers to sign a common message. They are widely used in scenarios where the same message must be signed and transmitted by $N$ users, and, instead of concatenating $N$ individual signatures, employing a multi-signature can reduce the data to be sent. In recent years there have been numerous practical proposals in the discrete logarithm setting, such as MuSig2 (CRYPTO'21) for the Schnorr signature. Recently, these attempts have been extended to...

With the demand of cryptocurrencies, threshold ECDSA recently regained popularity. So far, several methods have been proposed to construct threshold ECDSA, including the usage of OT and homomorphic encryptions (HE). Due to the mismatch between the plaintext space and the signature space, HE-based threshold ECDSA always requires zero-knowledge range proofs, such as Paillier and Joye-Libert (JL) encryptions. However, the overhead of range proofs constitutes a major portion of the total...

Threshold signatures are one of the most important cryptographic primitives in distributed systems. The threshold Schnorr signature scheme, an efficient and pairing-free scheme, is a popular choice and is included in NIST's standards and recent call for threshold cryptography. Despite its importance, most threshold Schnorr signature schemes assume a static adversary in their security proof. A recent scheme proposed by Katsumata et al. (Crypto 2024) addresses this issue. However, it requires...

Compressing primitives such as accumulators and vector commitments, allow to rep- resent large data sets with some compact, ideally constant-sized value. Moreover, they support operations like proving membership or non-membership with minimal, ideally also constant- sized, storage and communication overhead. In recent years, these primitives have found numerous practical applications, with many constructions based on various hardness assumptions. So far, however, it has been elusive to...

Cryptography's most common use is secure communication---e.g. Alice can use encryption to hide the contents of the messages she sends to Bob (confidentiality) and can use signatures to assure Bob she sent these messages (authenticity). While one typically considers stateless security guarantees---for example a channel that Alice can use to send messages securely to Bob---one can also consider stateful ones---e.g. an interactive conversation between Alice, Bob and their friends where...

We describe a fully distributed KZG-based Snark instantiable with any pairing-friendly curve with a sufficiently large scalar field. In particular, the proof system is compatible with Cocks-Pinch or Brezing-Weng outer curves to the the widely used curves such as secp256k1, ED25519, BLS12-381 and BN254. This allows us to retain the fully parallelizable nature and the O(1) communication complexity of Pianist ([LXZ+23]) in conjunction with circumventing the huge overhead of non-native...

We propose a new cryptographic primitive called "batched identity-based encryption" (Batched IBE) and its thresholdized version. The new primitive allows encrypting messages with specific identities and batch labels, where the latter can represent, for example, a block number on a blockchain. Given an arbitrary subset of identities for a particular batch, our primitive enables efficient issuance of a single decryption key that can be used to decrypt all ciphertexts having identities that are...

Threshold signatures have been drawing lots of attention in recent years. Of particular interest are threshold signatures that are proven secure under adaptive corruptions (NIST Call 2023). Sadly, existing constructions with provable adaptive security suffer from at least one of the following drawbacks: (i) strong idealizations such as the algebraic group model (AGM), (ii) an unnatural restriction on the corruption threshold being $t/2$ where $t$ is the signing threshold, or (iii)...

Succinct arguments of knowledge allow an untrusted prover to establish that they know a witness for an NP relation. Many recent efficient constructions of such schemes work over arithmetic computations expressed in finite fields. Several common settings, however, have an extremely simple representation when expressed over the integers (e.g., RSA signatures/accumulators, range checks for committed values, computations over rational numbers). Efficient arguments of knowledge working natively...

We show that the widely-used Schnorr signature scheme meets existential unforgeability under chosen-message attack (EUF-CMA) in the random oracle model (ROM) if the circular discrete-logarithm (CDL) assumption, a new, non-interactive and falsifiable variant of the discrete-log (DL) problem we introduce, holds in the underlying group. Notably, our reduction is tight, meaning the constructed adversary against CDL has essentially the same running time and success probability as the assumed...

In scenarios where a seller holds sensitive data $x$, like employee / patient records or ecological data, and a buyer seeks to obtain an evaluation of specific function $f$ on this data, solutions in trustless digital environments like blockchain-based Web3 systems typically fall into two categories: (1) Smart contract-powered solutions and (2) cryptographic solutions leveraging tools such as adaptor signatures. The former approach offers atomic transactions where the buyer learns the...

Cryptographic group actions have gained significant attention in recent years for their application on post-quantum Sigma protocols and digital signatures. In NIST's recent additional call for post-quantum signatures, three relevant proposals are based on group actions: LESS, MEDS, and ALTEQ. This work explores signature optimisations leveraging a group's factorisation. We show that if the group admits a factorisation as a semidirect product of subgroups, the group action can be restricted...

Zero-Knowledge (ZK) protocols allow a prover to demonstrate the truth of a statement without disclosing additional information about the underlying witness. Code-based cryptography has a long history but did suffer from periods of slow development. Recently, a prominent line of research have been contributing to designing efficient code-based ZK from MPC-in-the-head (Ishai et al., STOC 2007) and VOLE-in-the head (VOLEitH) (Baum et al., Crypto 2023) paradigms, resulting in quite efficient...

We propose the first constructions of anonymous tokens with decentralized issuance. Namely, we consider a dynamic set of signers/issuers; a user can obtain a token from any subset of the signers, which is publicly verifiable and unlinkable to the issuance process. To realize this new primitive we formalize the notion of Blind Multi-Signatures (BMS), which allow a user to interact with multiple signers to obtain a (compact) signature; even if all the signers collude they are unable to link a...

Blind signatures have garnered significant attention in recent years, with several efficient constructions in the random oracle model relying on well-understood assumptions. However, this progress does not apply to pairing-free cyclic groups: fully secure constructions over cyclic groups rely on pairings, remain inefficient, or depend on the algebraic group model or strong interactive assumptions. To address this gap, Chairattana-Apirom, Tessaro, and Zhu (CTZ, Crypto 2024) proposed a new...

The recent works of Ananth et al. (ITCS 2022) and Bartusek et al. (Eurocrypt 2023) initiated the study of pre-constrained cryptography which achieves meaningful security even against the system authority. In this work we significantly expand this area by defining several new primitives and providing constructions from simple, standard assumptions as follows. - Pre-Constrained Encryption. We define a weaker notion of pre-constrained encryption (PCE), as compared to the work of Ananth et...

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...

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...

Blind signature schemes enable a user to obtain a digital signature on a message from a signer without revealing the message itself. Among the most fundamental examples of such a scheme is blind Schnorr, but recent results show that it does not satisfy the standard notion of security against malicious users, One-More Unforgeability (OMUF), as it is vulnerable to the ROS attack. However, blind Schnorr does satisfy the weaker notion of sequential OMUF, in which only one signing session is open...

In a fully non-interactive multi-signature, resp. aggregate-signature scheme (fNIM, resp. fNIA), signatures issued by many signers on the same message, resp. on different messages, can be succinctly ``combined'', resp. ``aggregated''. fNIMs are used in the Ethereum consensus protocol, to produce the certificates of validity of blocks which are to be verified by billions of clients. fNIAs are used in some PBFT-like consensus protocols, such as the production version of Diem by Aptos, to...

T-out-of-N threshold signatures have recently seen a renewed interest, with various types now available, each offering different tradeoffs. However, one property that has remained elusive is adaptive security. When we target thresholdizing existing efficient signatures schemes based on the Fiat-Shamir paradigm such as Schnorr, the elusive nature becomes clear. This class of signature schemes typically rely on the forking lemma to prove unforgeability. That is, an adversary is rewound and...

Ring signatures are one of the crucial cryptographic primitives used in the design of privacy-preserving systems. Such a signature scheme allows a signer to anonymously sign a message on behalf of a spontaneously formed group. It not only ensures the authenticity of the message but also conceals the true signer within the group. An important extension of ring signatures is linkable ring signatures, which prevent a signer from signing twice without being detected (under some constraints)....

In this work we first present an explicit forking lemma that distills the information-theoretic essence of the high-moment technique introduced by Rotem and Segev (CRYPTO '21), who analyzed the security of identification protocols and Fiat-Shamir signature schemes. Whereas the technique of Rotem and Segev was particularly geared towards two specific cryptographic primitives, we present a stand-alone probabilistic lower bound, which does not involve any underlying primitive or idealized...

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...

Asynchronous Remote Key Generation (ARKG) is a primitive introduced by Frymann et al. at ACM CCS 2020. It enables a sender to generate a new public key $pk'$ for a receiver ensuring only it can, at a later time, compute the corresponding private key $sk'$. These key pairs are indistinguishable from freshly generated ones and can be used in various public-key cryptosystems such as digital signatures and public-key encryption. ARKG has been explored for applications in WebAuthn credential...

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...

We introduce a new cryptographic primitive called symmetric signcryption, which differs from traditional signcryption because the sender and recipient share a secret key. We prove that a natural composition of symmetric encryption and signatures achieves strong notions of security against attackers that can learn and control many keys. We then identify that the core encryption algorithm of the Keybase encrypted messaging protocol can be modeled as a symmetric signcryption scheme. We prove...

Ring signatures allow members of a group (called "ring") to sign a message anonymously within the group, which is chosen ad hoc at the time of signing (the members do not need to have interacted before). In this paper, we propose a physical version of ring signatures. Our signature is based on one-out-of-many signatures, a method used in many real cryptographic ring signatures. It consists of boxes containing coins locked with padlocks that can only be opened by a particular group member. To...

We introduce SQIsign2D-West, a variant of SQIsign using two-dimensional isogeny representations. SQIsignHD was the first variant of SQIsign to use higher dimensional isogeny representations. Its eight-dimensional variant is geared towards provable security but is deemed unpractical. Its four-dimensional variant is geared towards efficiency and has significantly faster signing times than SQIsign, but slower verification owing to the complexity of the four-dimensional representation. Its...

Universal verifiability is a must-to-have for electronic voting schemes. It is essential to ensure honest behavior of all the players during the whole process, together with the eligibility. However, it should not endanger the privacy of the individual votes, which is another major requirement. Whereas the first property prevents attacks during the voting process, privacy of the votes should hold forever, which has been called everlasting privacy. A classical approach for universal...

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

The elliptic curve-based Enhanced Privacy ID (EPID) signature scheme is broadly used for hardware enclave attestation by many platforms that implement Intel Software Guard Extensions (SGX) and other devices. This scheme has also been included in the Trusted Platform Module (TPM) specifications and ISO/IEC standards. However, it is insecure against quantum attackers. While research into quantum-resistant EPID has resulted in several lattice-based schemes, Boneh et al. have initiated the study...

Direct Anonymous Attestation (DAA) was designed for the Trusted Platform Module (TPM) and versions using RSA and elliptic curve cryptography have been included in the TPM specifications and in ISO/IEC standards. These standardised DAA schemes have their security based on the factoring or discrete logarithm problems and are therefore insecure against quantum attackers. Research into quantum-resistant DAA has resulted in several lattice-based schemes. Now in this paper, we propose the first...

Group signatures and their variants have been widely used in privacy-sensitive scenarios such as anonymous authentication and attestation. In this paper, we present a new post-quantum group signature scheme from symmetric primitives. Using only symmetric primitives makes the scheme less prone to unknown attacks than basing the design on newly proposed hard problems whose security is less well-understood. However, symmetric primitives do not have rich algebraic properties, and this makes it...

Delegatable Anonymous Credentials (DAC) are an enhanced Anonymous Credentials (AC) system that allows credential owners to use credentials anonymously, as well as anonymously delegate them to other users. In this work, we introduce a new concept called Delegatable Attribute-based Anonymous Credentials with Chainable Revocation (DAAC-CR), which extends the functionality of DAC by allowing 1) fine-grained attribute delegation, 2) issuers to restrict the delegation capabilities of the delegated...

Cumplido, María et al. have recently shown that the Wang-Hu digital signature is not secure and has presented a potential attack on the root extraction problem. The effectiveness of generic attacks on solving this problem for braids is still uncertain and it is unknown if it is possible to create braids that require exponential time to solve these problems. In 2023, Lin and al. has proposed a post-quantum signature scheme similar to the Wang-Hu scheme that is proven to be able to withstand...

Threshold signatures have recently seen a renewed interest due to applications in cryptocurrency while NIST has released a call for multi-party threshold schemes, with a deadline for submission expected for the first half of 2025. So far, all lattice-based threshold signatures requiring less than two-rounds are based on heavy tools such as (fully) homomorphic encryption (FHE) and homomorphic trapdoor commitments (HTDC). This is not unexpected considering that most efficient two-round...

A verifiable delay function $\texttt{VDF}(x,T)\rightarrow (y,\pi)$ maps an input $x$ and time parameter $T$ to an output $y$ together with an efficiently verifiable proof $\pi$ certifying that $y$ was correctly computed. The function runs in $T$ sequential steps, and it should not be possible to compute $y$ much faster than that. The only known practical VDFs use sequential squaring in groups of unknown order as the sequential function, i.e., $y=x^{2^T}$. There are two constructions for...

Threshold Schnorr signatures are seeing increased adoption in practice, and offer practical defenses against single points of failure. However, one challenge with existing randomized threshold Schnorr signature schemes is that signers must carefully maintain secret state across signing rounds, while also ensuring that state is deleted after a signing session is completed. Failure to do so will result in a fatal key-recovery attack by re-use of nonces. While deterministic threshold...

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...

$n$-out-of-$n$ distributed signatures are a special type of threshold $t$-out-of-$n$ signatures. They are created by a group of $n$ signers, each holding a share of the secret key, in a collaborative way. This kind of signatures has been studied intensively in recent years, motivated by different applications such as reducing the risk of compromising secret keys in cryptocurrencies. Towards maintaining security in the presence of quantum adversaries, Damgård et al. (J Cryptol 35(2), 2022)...

Structure-preserving signatures (SPS) have emerged as an important cryptographic building block, as their compatibility with the Groth-Sahai (GS) NIZK framework allows to construct protocols under standard assumptions with reasonable efficiency. Over the last years there has been a significant interest in the design of threshold signature schemes. However, only very recently Crites et al. (ASIACRYPT 2023) have introduced threshold SPS (TSPS) along with a fully non-interactive construction....

Linkable ring signatures are an important cryptographic primitive for anonymized applications, such as e-voting, e-cash and confidential transactions. To eliminate backdoor and overhead in a trusted setup, transparent setup in the discrete logarithm or pairing settings has received considerable attention in practice. Recent advances have improved the proof sizes and verification efficiency of linkable ring signatures with a transparent setup to achieve logarithmic bounds. Omniring (CCS '19)...

Verifiable random functions (VRFs) are pseudorandom functions with the addition that the function owner can prove that a generated output is correct (i.e., generated correctly relative to a committed key). In this paper we introduce the notion of an exponent-VRF (eVRF): a VRF that does not provide its output $y$ explicitly, but instead provides $Y = y \cdot G$, where $G$ is a generator of some finite cyclic group (or $Y=g^y$ in multiplicative notation). We construct eVRFs from DDH and from...

With the rapidly evolving landscape of cryptography, blockchain technology has advanced to cater to diverse user requirements, leading to the emergence of a multi-chain ecosystem featuring various use cases characterized by distinct transaction speed and decentralization trade-offs. At the heart of this evolution lies digital signature schemes, responsible for safeguarding blockchain-based assets such as ECDSA, Schnorr, and EdDSA, among others. However, a critical gap exists in the...

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

EdDSA, standardized by both IRTF and NIST, is a variant of the well-known Schnorr signature scheme based on Edwards curves, benefitting from stateless and deterministic derivation of nonces (i.e., it does not require a reliable source of randomness or state continuity). Recently, NIST called for multi-party threshold EdDSA signatures in one mode of verifying such nonce derivation via zero-knowledge (ZK) proofs. However, it is challenging to translate the stateless and deterministic benefits...

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

This paper introduces the notion of registered attribute-based signature (registered ABS). Distinctly different from classical attribute-based signature (ABS), registered ABS allows any user to generate their own public/secret key pair and register it with the system. The key curator is critical to keep the system flowing, which is a fully transparent entity that does not retain secrets. Our results can be summarized as follows. -This paper provides the first definition of registered...

Threshold variants of the Schnorr signature scheme have recently been at the center of attention due to their applications to cryptocurrencies. However, existing constructions for threshold Schnorr signatures among a set of $n$ parties with corruption threshold $t_c$ suffer from at least one of the following drawbacks: (i) security only against static (i.e., non-adaptive) adversaries, (ii) cubic or higher communication cost to generate a single signature, (iii) strong synchrony assumptions...

In recent years, decentralized computing has gained popularity in various domains such as decentralized learning, financial services and the Industrial Internet of Things. As identity privacy becomes increasingly important in the era of big data, safeguarding user identity privacy while ensuring the security of decentralized computing systems has become a critical challenge. To address this issue, we propose ADC (Anonymous Decentralized Computing) to achieve anonymity in decentralized...

The Linear Code Equivalence (LCE) Problem has received increased attention in recent years due to its applicability in constructing efficient digital signatures. Notably, the LESS signature scheme based on LCE is under consideration for the NIST post-quantum standardization process, along with the MEDS signature scheme that relies on an extension of LCE to the rank metric, namely the Matrix Code Equivalence (MCE) Problem. Building upon these developments, a family of signatures with...

The recent surge of distribute technologies caused an increasing interest towards threshold signature protocols, that peaked with the recent NIST First Call for Multi-Party Threshold Schemes. Since its introduction, the Fiat-Shamir Transform has been the most popular way to design standard digital signature schemes. Many threshold signature schemes are designed in a way that recalls the structure of digital signatures created using Fiat Shamir, by having the signers generate a common...

Equivalence class signatures (EQS; Asiacrypt '14), sign vectors of elements from a bilinear group. Anyone can transform a signature on a vector to a signature on any multiple of that vector; signatures thus authenticate equivalence classes. A transformed signature/message pair is indistinguishable from a random signature on a random message. EQS have been used to efficiently instantiate (delegatable) anonymous credentials, (round-optimal) blind signatures, ring and group signatures,...

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...

A Proof of Exponentiation (PoE) allows a prover to efficiently convince a verifier that $y=x^e$ in some group of unknown order. PoEs are the basis for practical constructions of Verifiable Delay Functions (VDFs), which, in turn, are important for various higher-level protocols in distributed computing. In applications such as distributed consensus, many PoEs are generated regularly, motivating protocols for secure aggregation of batches of statements into a few statements to improve the...

The transition to post-quantum cryptography has been an enormous challenge and effort for cryptographers over the last decade, with impressive results such as the future NIST standards. However, the latter has so far only considered central cryptographic mechanisms (signatures or KEM) and not more advanced ones, e.g., targeting privacy-preserving applications. Of particular interest is the family of solutions called blind signatures, group signatures and anonymous credentials, for which...

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...

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

Threshold signature schemes have gained prominence in enhancing the security and flexibility of digital signatures, allowing a group of participants to collaboratively create signatures while maintaining a predefined threshold of participants for validity. However, conventional threshold signatures treat all participants equally, lacking the capability to accommodate hierarchical structures often seen in real-world applications. Hierarchical Threshold Signature Schemes (HTSS) naturally...

An accountable subgroup multi-signature (ASM) is a multi-signature that allows any subgroup of potential signers to jointly sign a message such that the subgroup of co-signers are accountable for the resulting signature and their identities are identifiable to any verifier. In this paper, we pro- pose a novel lattice-based accountable subgroup multi-signature scheme, i.e., vMS2, by combining the group setup method of recently proposed vASM scheme and Damgard et al.’s lattice-based MS2...

Let n stands for the length of digital signatures with quadratic multivariate public rule in n variables. We construct postquantum secure procedure to sign O(n^t), t ≥1 digital documents with the signature of size n in time O(n^{3+t}). It allows to sign O(n^t), t <1 in time O(n^4). The procedure is defined in terms of Algebraic Cryptography. Its security rests on the semigroup based protocol of Noncommutative Cryptography referring to complexity of the decomposition of the collision...

A monotone policy batch $\mathsf{NP}$ language $\mathcal{L}_{\mathcal{R}, P}$ is parameterized by a monotone policy $P \colon \{0,1\}^k \to \{0,1\}$ and an $\mathsf{NP}$ relation $\mathcal{R}$. A statement $(x_1, \ldots, x_k)$ is a YES instance if there exists $w_1, \ldots, w_k$ where $P(\mathcal{R}(x_1, w_1), \ldots, \mathcal{R}(x_k, w_k)) = 1$. For example, we might say that an instance $(x_1, \ldots, x_k)$ is a YES instance if a majority of the statements are true. A monotone policy batch...

In this paper, we study the design of efficient signature and public-key encryption (PKE) schemes in the presence of both leakage and tampering attacks. Firstly, we formalize the strong leakage and tamper-resilient (sLTR) security model for signature, which provides strong existential unforgeability, and deals with bounded leakage and restricted tampering attacks, as a counterpart to the sLTR security introduced by Sun et al. (ACNS 2019) for PKE. Then, we present direct constructions...

We find an efficient method to solve the semidirect discrete logarithm problem (SDLP) over finite nonabelian groups of order $p^3$ and exponent $p^2$ for certain exponentially large parameters. This implies an attack on SPDH-Sign, a signature scheme based on the SDLP, for such parameters. We also take a step toward proving the quantum polynomial time equivalence of SDLP and SCDH.

The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in \mathrm{End}(G)$, and $h=\prod_{i=0}^{t-1}\sigma^i(g)$ for some integer $t$, the SDLP$(G,\sigma)$, for $g$ and $h$, asks to determine $t$. As Shor's algorithm crucially depends on commutativity, it is believed not to be applicable to the SDLP. Previously, the...

We study digital signatures with revocation capabilities and show two results. First, we define and construct digital signatures with revocable signing keys from the LWE assumption. In this primitive, the signing key is a quantum state which enables a user to sign many messages and yet, the quantum key is also revocable, i.e., it can be collapsed into a classical certificate which can later be verified. Once the key is successfully revoked, we require that the initial recipient of the key...

Multi-signatures allow to combine individual signatures from different signers on the same message into a short aggregated signature. Newer schemes further allow to aggregate the individual public keys, such that the combined signature gets verified against a short aggregated key. This makes them a versatile alternative to threshold or distributed signatures: the aggregated key can serve as group key, and signatures under that key can only be computed with the help of all signers. What makes...

Digital signatures is a cryptographic protocol that can provide the added assurances of identity, status, proof of origin of an electronic document, and can acknowledge informed consent by the signer. Lattice based assumptions have seen a certain rush in recent years to fulfil the desire to expand the hardness assumption beyond factoring or discrete logarithm problem on which digital signatures can rely. In this article, we cover the recent progress made in digital signatures based on...

VOX has been submitted to the NIST Round 1 Additional Signature of the Post-Quantum Signature Competition in June 2023. VOX is a strengthened variant of UOV which uses the Quotient-Ring (QR) setting to reduce the public-key size. At the end of August 2023, Furue and Ikamatsu posted on the NIST mailing-list a post, indicating that the parameters of VOX can be attacked efficiently using the rectangular attack in the QR setting. In this note, we explain the attack in the specific case of...

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...

We present the first concurrently-secure blind signatures making black-box use of a pairing-free group for which unforgeability, in the random oracle model, can be proved {\em without} relying on the algebraic group model (AGM), thus resolving a long-standing open question. Prior pairing-free blind signatures without AGM proofs have only been proved secure for bounded concurrency, relied on computationally expensive non-black-box use of NIZKs, or had complexity growing with the number of...

GLS254 is an elliptic curve defined over a finite field of characteristic 2; it contains a 253-bit prime order subgroup, and supports an endomorphism that can be efficiently computed and helps speed up some typical operations such as multiplication of a curve element by a scalar. That curve offers on x86 and ARMv8 platforms the best known performance for elliptic curves at the 128-bit security level. In this paper we present a number of new results related to GLS254: - We describe...

Ring signature (RS) allows users to demonstrate to verifiers their membership within a specified group (ring) without disclosing their identities. Based on this, RS can be used as a privacy protection technology for users' identities in blockchain. However, there is currently a lack of RS schemes that are fully applicable to the blockchain applications: Firstly, users can only spend a UTXO once, and the current RS schemes are not yet perfect in a one-time manner. At the same time, the...

Cryptographic applications often require proving statements about hidden secrets satisfying certain circuit relations. Moreover, these proofs must often be generated obliviously, i.e., without knowledge of the secret. This work presents a new technique called --- FRI on hidden values --- for efficiently proving such statements. This technique enables a polynomial commitment scheme for values hidden inside linearly homomorphic primitives, such as linearly homomorphic encryption, linearly...

Blind signatures allow the issuing of signatures on messages chosen by the user so that they ensure $\mathit{blindness}$ of the message against the signer. Moreover, a malicious user cannot output $\ell+1$ signatures while only finishing $\ell$ signing sessions. This notion, called $\mathit{one}$-$\mathit{more}$ unforgeability, comes in two flavors supporting either $\mathit{sequential}$ or $\mathit{concurrent}$ sessions. In this paper, we investigate the security of a class of blind...

Threshold signatures are one of the most important cryptographic primitives in distributed systems. A popular choice of threshold signature scheme is the BLS threshold signature introduced by Boldyreva (PKC'03). Some attractive properties of Boldyreva's threshold signature are that the signatures are unique and short, the signing process is non-interactive, and the verification process is identical to that of non-threshold BLS. These properties have resulted in its practical adoption in...

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...

Electronic voting is one of the most interesting application of modern cryptography, as it involves many innovative tools (such as homomorphic public-key encryption, non-interactive zero-knowledge proofs, and distributed cryptography) to guarantee several a priori contradictory security properties: the integrity of the tally and the privacy of the individual votes. While many efficient solutions exist for honest-but-curious voters, that follow the official procedure but try to learn more...

Sparkle is the first threshold signature scheme in the pairing-free discrete logarithm setting (Crites, Komlo, Maller, Crypto 2023) to be proven secure under adaptive corruptions. However, without using the algebraic group model, Sparkle's proof imposes an undesirable restriction on the adversary. Namely, for a signing threshold $t<n$, the adversary is restricted to corrupt at most $t/2$ parties. In addition, Sparkle's proof relies on a strong one-more assumption. In this work, we...