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Communication Dans Un Congrès Année : 2008

Cryptanalysis of the TRMS Cryptosystem of PKC'05

Résumé

In this paper, we investigate the security of the Tractable Rationale Maps Signature (TRMS) signature scheme [9] proposed at PKC’05. To do so, we present a hybrid approach for solving the algebraic systems naturally arising when mounting a signature-forgery attack. The basic idea is to compute Gröbner bases of several modified systems rather than a Gröbner basis of the initial system. We have been able to provide a precise bound on the (worst-case) complexity of this approach. For that, we have however assumed a technical condition on the systems arising in our attack; namely the systems are semi-regular [3,5]. This claim is supported by experimental evidences. Finally, it turns out that our approach is efficient. We have obtained a complexity bounded from above by $2^{57}$ to forge a signature on the parameters proposed by the designers of TRMS [9]. This bound can be improved; assuming an access to $2^{16}$ processors (which is very reasonable), one can actually forge a signature in approximately 51 hours.

Dates et versions

hal-01305646 , version 1 (21-04-2016)

Identifiants

Citer

Luk Bettale, Jean-Charles Faugère, Ludovic Perret. Cryptanalysis of the TRMS Cryptosystem of PKC'05. AfricaCrypt 2008, Jun 2008, Casablanca, Morocco. pp.143-155, ⟨10.1007/978-3-540-68164-9_10⟩. ⟨hal-01305646⟩
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