Cryptology ePrint Archive: Report 2018/1205

Cryptanalysis of a code-based one-time signature

Jean-Christophe Deneuville and Philippe Gaborit

Abstract: In 2012, Lyubashevsky introduced a new framework for building lattice-based signature schemes without resorting to any trapdoor (such as GPV [6] or NTRU [7]). The idea is to sample a set of short lattice elements and construct the public key as a Short Integer Solution (SIS for short) instance. Signatures are obtained using a small subset sum of the secret key, hidden by a (large) Gaussian mask. (Information leakage is dealt with using rejection sampling.) Recently, Persichetti proposed an efficient adaptation of this framework to coding theory [12]. In this paper, we show that this adaptation cannot be secure, even for one-time signatures (OTS), due to an inherent difference between bounds in Hamming and Euclidean metrics. The attack consists in rewriting a signature as a noisy syndrome decoding problem, which can be handled efficiently using the extended bit flipping decoding algorithm. We illustrate our results by breaking Persichetti’s OTS scheme built upon this approach [12]: using a single signature, we recover the secret (signing) key in about the same amount of time as required for a couple of signature verifications.

Category / Keywords: public-key cryptography / Post-Quantum Cryptography, Coding Theory, Digital Signature, One-time, Cryptanalysis

Original Publication (in the same form): WCC 2019: The Eleventh International Workshop on Coding and Cryptography

Date: received 9 Dec 2018, last revised 20 Mar 2019

Contact author: jean-christophe deneuville at insa-cvl fr

Available format(s): PDF | BibTeX Citation

Version: 20190320:075049 (All versions of this report)

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