Practical Key Recovery for Discrete-Logarithm Based Authentication Schemes from Random Nonce Bits.

Aurélie Bauer (1) , Damien Vergnaud (2)

1 LCR - Laboratoire de cryptographie de l'ANSSI
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities

We propose statistical cryptanalysis of discrete-logarithm based authentication schemes such as Schnorr identification scheme or Girault-Poupard-Stern identification and signature schemes. We consider two scenarios where an adversary is given some information on the nonces used during the signature generation process or during some identification sessions. In the first scenario, we assume that some bits of the nonces are known exactly by the adversary, while no information is provided about the other bits. We show, for instance, that the GPS scheme with 128-bit security can be broken using only 710 signatures assuming that the adversary knows (on average) one bit per nonce. In the second scenario, we assume that all bits of the nonces are obtained from the correct ones by independent bit flipping with some small probability. A detailed heuristic analysis is provided, supported by extensive experiments.

Mots clés: Schnorr identification; Girault-Poupard-Stern identification; Girault-Poupard-Stern signatures; statistical cryptanalysis

Domaines: Cryptographie et sécurité [cs.CR]

Aurélie Bauer, Damien Vergnaud. Practical Key Recovery for Discrete-Logarithm Based Authentication Schemes from Random Nonce Bits.. Cryptographic Hardware and Embedded Systems - CHES 2015, Sep 2015, Saint-Malo, France. pp.287-306, ⟨10.1007/978-3-662-48324-4_15⟩. ⟨hal-01214701⟩