NIST started the standardization of additional post-quantum signatures in 2022. Among 40 candidates, a few of them showed their stronger security than existential unforgeability, strong existential unforgeability and BUFF (beyond unforgeability features) securities. Recently, Aulbach, Düzlü, Meyer, Struck, and Weishäupl (PQCrypto 2024) examined the BUFF securities of 17 out of 40 candidates. Unfortunately, on the so-called MPC-in-the-Head (MPCitH) signature schemes, we have no knowledge of...

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...

This work presents the first hardware realisation of the Syndrome-Decoding-in-the-Head (SDitH) signature scheme, which is a candidate in the NIST PQC process for standardising post-quantum secure digital signature schemes. SDitH's hardness is based on conservative code-based assumptions, and it uses the Multi-Party-Computation-in-the-Head (MPCitH) construction. This is the first hardware design of a code-based signature scheme based on traditional decoding problems and only the second for...

We show that here standard decoding algorithms for generic linear codes over a finite field can speeded up by a factor which is essentially the size of the finite field by reducing it to a low weight codeword problem and working in the relevant projective space. We apply this technique to SDitH and show that the parameters of both the original submission and the updated version fall short of meeting the security requirements asked by the NIST.

The MPC in the Head (MPCitH) paradigm has recently led to significant improvements for signatures in the code-based setting. In this paper we consider some modifications to a recent twist of MPCitH, called Hypercube-MPCitH, that in the code-based setting provides the currently best known signature sizes. By compressing the Hypercube-MPCitH five-round code-based identification scheme into three-rounds we obtain two main benefits. On the one hand, it allows us to further develop recent...

This paper presents a code-based signature scheme based on the well-known syndrome decoding (SD) problem. The scheme builds upon a recent line of research which uses the Multi-Party-Computation-in-the-Head (MPCitH) approach to construct efficient zero-knowledge proofs, such as Syndrome Decoding in the Head (SDitH), and builds signature schemes from them using the Fiat-Shamir transform. At the heart of our proposal is a new approach, Hypercube-MPCitH, to amplify the soundness of any MPC...

The MPC-in-the-Head paradigm is a popular framework to build zero-knowledge proof systems using techniques from secure multi-party computation (MPC). While this paradigm is not restricted to a particular secret sharing scheme, all the efficient instantiations for small circuits proposed so far rely on additive secret sharing. In this work, we show how applying a threshold linear secret sharing scheme (threshold LSSS) can be beneficial to the MPC-in-the-Head paradigm. For a general...