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.

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Bibtex

@inproceedings{WCC:DenGab19,
  title={Cryptanalysis of a code-based one-time signature},
  author={Deneuville, {Jean-Christophe} and Gaborit, Philippe},
  booktitle={WCC 2019: The Eleventh International Workshop on Coding and Cryptography},
  year={2019},
}