Cryptanalysis of a One-Time Code-Based Digital Signature Scheme

We consider a one-time digital signature scheme recently proposed by Persichetti and show that a successful key recovery attack can be mounted with limited complexity. The attack we propose exploits a single signature intercepted by the attacker, and relies on a statistical analysis performed over such a signature, followed by information set decoding. We assess the attack complexity and show that a full recovery of the secret key can be performed with a work factor that is far below the claimed security level. The efficiency of the attack is motivated by the sparsity of the signature, which leads to a significant information leakage about the secret key.Comment: 5 pages, 1 figur

Another code-based adaptation of Lyubashevsky’s signature cryptanalysed

In 2012, Lyubashevsky introduced a framework for obtaining efficient digital signatures relying on lattice assumptions. Several works attempted to make this approach compliant with the coding theory setting, unsuccessfully. Recently, Song et al. proposed another adaptation of this framework, using denser and permuted secret keys, claiming immunity against existing attacks. This paper describes an efficient attack against Song et al. signature scheme. We show that it is possible to fully recover the secret key from a very limited number of signatures. As an example, it requires 32 signatures and 2 hours to recover the secret key of the parameter set targeting 80 bits of security. The attack affects both proposed parameter sets, and discourages patching such an approach

Code-based signatures without trapdoors through restricted vectors

The Schnorr-Lyubashevsky approach has been shown able to produce secure and efficient signature schemes without trapdoors in the lattice-based setting, exploiting small vectors in the Euclidean metric and rejection sampling in the signature generation. Translating such an approach to the code-based setting has revealed to be challenging, especially for codes in the Hamming metric. In this paper, we propose a novel adaptation of the Schnorr-Lyubashevsky framework to the code-based setting, by relying on random non-binary linear codes and vectors with restricted entries to produce signatures. We provide some preliminary arguments to assess the security of the new scheme and to compute its parameters. We show that it achieves compact and competitive key and signature sizes, even without resorting to structured random codes

Zero Knowledge Protocols and Signatures from the Restricted Syndrome Decoding Problem

The Restricted Syndrome Decoding Problem (R-SDP) cor- responds to the Syndrome Decoding Problem (SDP) with the additional constraint that entries of the solution vector must live in a desired sub- set of a finite field. In this paper we study how this problem can be applied to the construction of signatures derived from Zero-Knowledge (ZK) proofs. First, we show that R-SDP appears to be well suited for this type of applications: almost all ZK protocols relying on SDP can be modified to use R-SDP, with important reductions in the communication cost. Then, we describe how R-SDP can be further specialized, so that solutions can be represented with a number of bits that is slightly larger than the security parameter (which clearly provides an ultimate lower bound), thus enabling the design of ZK protocols with tighter and rather competitive parameters. Finally, we show that existing ZK protocols can greatly benefit from the use of R-SDP, achieving signature sizes in the order of 7 kB, which are smaller than those of several other schemes ob- tained from ZK protocols. For instance, this beats all schemes based on the Permuted Kernel Problem (PKP), almost all schemes based on SDP and several schemes based on rank metric problems

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or transit. Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems, based on modular arithmetic to the contemporary cryptosystems based on quantum computing. The emergence of quantum computing poses a major threat to the modern cryptosystems based on modular arithmetic, whereby even the computationally hard problems which constitute the strength of the modular arithmetic ciphers could be solved in polynomial time. This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks. This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have been explored. Some potential research directions that are yet to be explored in code-based cryptography research from the perspective of codes is a key contribution of this paper

Cryptanalysis of a One-Time Code-Based Digital Signature Scheme

We consider a one-time digital signature scheme recently proposed by Persichetti and show that a successful key recovery attack can be mounted with limited complexity. The attack we propose exploits a single signature intercepted by the attacker, and relies on a statistical analysis performed over such a signature, followed by information set decoding. We assess the attack complexity and show that a full recovery of the secret key can be performed with a work factor that is far below the claimed security level. The efficiency of the attack is motivated by the sparsity of the signature, which leads to a significant information leakage about the secret key