The MPC-in-the-head introduced in [IKOS07] has established itself as an important paradigm to design efficient digital signatures. It has been leveraged in the Picnic scheme [CDG+ 20] that reached the third round of the NIST PQC Standardization process. It has also been used in [Beu20] to introduce the Proof of Knowledge (PoK) with Helper paradigm. This construction permits to design shorter signatures but induces a non negligible performance overhead as it uses cut-and-choose. In this paper, we introduce the PoK leveraging structure paradigm along with its associated challenge space amplification technique. Our new approach to design PoK brings some improvements over the PoK with Helper one. Indeed, we show how one can substitute the Helper in these constructions by leveraging the underlying structure of the considered problem. This approach does not suffer from the performance overhead inherent to the PoK with Helper paradigm hence offers different trade-offs between security, signature sizes and performances. We also present four new post-quantum signature schemes. The first one is based on a new PoK with Helper for the Syndrome Decoding problem. It relies on ideas from [BGKM22] and [FJR21] and improve the latter using a new technique that can be seen as performing some cut-and-choose with a meet in the middle approach. The three other signatures are based on our new PoK leveraging structure approach and as such illustrate its versatility. We provide new PoK related to the Permuted Kernel Problem (PKP), Syndrome Decoding (SD) problem and Rank Syndrome Decoding (RSD) problem. In practice, these PoK lead to comparable or shorter signatures than existing ones. Indeed, considering (public key + signature), we get sizes below 9kB for our signature related to the PKP problem, below 15kB for our signature related to the SD problem and below 7kB for our signature related to the RSD problem.
The MPC-in-the-head introduced in [IKOS07] has established itself as an important paradigm to design efficient digital signatures. It has been leveraged in the Picnic scheme [CDG+ 20] that reached the third round of the NIST PQC Standardization process. It has also been used in [Beu20] to introduce the Proof of Knowledge (PoK) with Helper paradigm. This construction permits to design shorter signatures but induces a non negligible performance overhead as it uses cut-and-choose. In this paper, we introduce the PoK leveraging structure paradigm along with its associated challenge space amplification technique. Our new approach to design PoK brings some improvements over the PoK with Helper one. Indeed, we show how one can substitute the Helper in these constructions by leveraging the underlying structure of the considered problem. This approach does not suffer from the performance overhead inherent to the PoK with Helper paradigm hence offers different trade-offs between security, signature sizes and performances. We also present four new post-quantum signature schemes. The first one is based on a new PoK with Helper for the Syndrome Decoding problem. It relies on ideas from [BGKM22] and [FJR21] and improve the latter using a new technique that can be seen as performing some cut-and-choose with a meet in the middle approach. The three other signatures are based on our new PoK leveraging structure approach and as such illustrate its versatility. We provide new PoK related to the Permuted Kernel Problem (PKP), Syndrome Decoding (SD) problem and Rank Syndrome Decoding (RSD) problem. In practice, these PoK lead to comparable or shorter signatures than existing ones. Indeed, considering (public key + signature), we get sizes below 9kB for our signature related to the PKP problem, below 15kB for our signature related to the SD problem and below 7kB for our signature related to the RSD problem.
Quantum computing poses significant challenges to traditional zero-knowledge proof schemes based on number-theoretic assumptions. As a result, code-based cryptography has attracted increasing attention for its resistance against quantum computing. In this paper, we study the Rank Syndrome Decoding problem (RSD) and investigate its ZK proof formulation within the MPC-in-the-Head framework. To prove the possession of a secret witness, we reformulate the secret witness as a mixed-field matrix multiplication preserving the rank constraint, and then obtain a representation that aligns naturally with the local-view paradigm of MPC-in-the-Head. Utilizing this value-to-calculation technique, we introduce the RSD relation into a ZKBoo-style (2, 3)-secret-sharing MPC-in-the-Head framework and obtain an RSD-based zero-knowledge proof scheme via mixed-field secret sharing. The resulting scheme reduces the proof size relative to generic formulations while preserving completeness, soundness, and zero-knowledge for the interactive protocol. The Fiat–Shamir non-interactive extension is analyzed only in the classical random oracle model; we do not claim QROM security for this variant.
The rise of quantum computing threatens to break many of the cryptographic systems that secure today’s digital world. In response, researchers are developing new tools designed to remain secure in a post-quantum future. Most of the promising candidates for post-quantum digital signatures rely on security assumptions based on lattices or properties of hash functions. Another promising approach transforms secure multi-party computation protocols into zero-knowledge proofs, which are then turned into digital signatures. This technique, known as multi-party computation in-the-head (MPCitH), offers strong security properties and flexibility for distributed applications. This thesis investigates whether MPCitH digital signatures can be efficiently adapted for use by two cooperating parties to jointly produce a signature. Here we show how to construct two-party signatures based on syndrome decoding in-the-head (SDitH) signatures. We propose a provably secure scheme that achieves the smallest known communication overhead among two-party MPCitH signatures, while resulting in a signature size approximately double that of a single-prover variant. This result provides a new data point in the design space of multi-party MPCitH signatures and post-quantum digital signatures in general.
Since 2016’s NIST call for standardization of post-quantum cryptographic primitives, developing efficient post-quantum secure digital signature schemes has become a highly active area of research. The difficulty in constructing such schemes is evidenced by NIST reopening the call in 2022 for digital signature schemes, because of missing diversity in existing proposals. In this work, we introduce the new postquantum digital signature scheme MiRitH. As direct successor of a scheme recently developed by Adj, Rivera-Zamarripa and Verbel (Africacrypt ’23), it is based on the hardness of the MinRank problem and follows the MPC-in-the-Head paradigm. We revisit the initial proposal, incorporate design-level improvements and provide more efficient parameter sets. We also provide the missing justification for the quantum security of all parameter sets following NIST metrics. In this context we design a novel Grover-amplified quantum search algorithm for solving the MinRank problem that outperforms a naive quantum brute-force search for the solution.MiRitH obtains signatures of size 5.7 kB for NIST category I security and therefore competes for the smallest signatures among any post-quantum signature following the MPCitH paradigm.At the same time MiRitH offers competitive signing and verification timings compared to the state of the art. To substantiate those claims we provide extensive implementations. This includes a reference implementation as well as optimized constant-time implementations for Intel processors (AVX2), and for the ARM (NEON) architecture. The speedup of our optimized AVX2 implementation relies mostly on a redesign of the finite field arithmetic, improving over existing implementations as well as an improved memory management.
Picnic is a digital signature algorithm designed to provide security against attacks by quantum computers. The design uses only symmetric-key primitives, and is an efficient instantiation of the MPC-in-the-head paradigm. In this work, we explore the Picnic design in great detail. We investigate and benchmark different parameter choices and show that there exist better parameter choices than those in the current specification. We also present improvements to the MPC protocol that shorten signatures and reduce signing time. The proposed MPC changes tailor the protocol to the circuit of interest in Picnic, but may also be of independent interest. Taken together, these changes give a new instantiation of Picnic that signs messages 7.9 to 13.9 times faster, and verifies signatures 4.5 to 5.5 times faster than the existing “Picnic2” design, while having nearly the same signature sizes.
The MPC-in-the-Head framework has been proposed 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 repeated MPC evaluations, resulting in a NIZKAoK protocol for any NP relation that we call Diet. The proof size and time of Diet are asymptotically only polylogarithmic with respect to the size of the circuit C of the NP relation, but are independent of the security parameter λ. Hence, both the proof size and time can be significantly reduced.Moreover, Diet offers promising concrete efficiency for proving Learning With Errors (LWE) problems and its variants. Our solution provides significant advantages over other schemes in terms of both proof size and proof time, when considering both factors together. Specifically, Diet is a promising method for proving knowledge of secret keys for lattice-based key encapsulation mechanisms (KEMs) such as Frodo and Kyber, offering a practical solution to future post-quantum certificate management. For Kyber 512, our implementation achieves an online proof size of 83.65 kilobytes (KB) with a preprocessing overhead of 152.02KB. The implementation is highly efficient, with an online proof time of only 0.68 seconds and a preprocessing time of 0.81 seconds. Notably, our approach provides the first reported implementation of proving knowledge of secret keys for Kyber 512 using post-quantum primitives-based zero-knowledge proofs.
Recently, NIST released the quantum cryptography standard, which includes three new encryption algorithms capable of effectively resisting attacks from quantum computers. Experts predict that quantum computers with the ability to break current encryption methods may emerge within the next decade. In particular, the advent of Shor’s algorithm [1] has rendered public-key encryption systems based on factoring and discrete logarithm problems vulnerable. Therefore, the release of the PQC (Post-Quantum Cryptography) standard is especially timely and significant. NIST encourages system administrators to begin integrating these standards into their systems immediately to ensure future security.Among these three new encryption algorithms, SLH-DSA (derived from SPHINCS+ [2]) is a stateless hash-based digital signature scheme. This innovative scheme is designed to provide robust security while maintaining efficiency. In the SLH-DSA signature scheme, the One-Time Signature (OTS) serves as its fundamental building block. This means that improving the OTS directly enhances the overall performance of the SLH-DSA scheme.Hash-based signature schemes are generally constructed using OTS schemes. The underlying OTS scheme plays a crucial role in determining the key size and signature size of hash-based signature schemes. We propose a novel signature scheme that allows partial key reuse while maintaining a minimum quantum security level of 128 bits. Compared to the popular Winternitz OTS scheme [3] [4] [5], our proposed signature scheme demonstrates superior performance in terms of key and signature sizes for the same number of signatures, while still preserving post-quantum security.