A Tale of Three Signatures: practical attack of ECDSA with wNAF

Gabrielle de Micheli (1) , Rémi E. Piau (2) , Cécile Pierrot (1)

1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
2 ENS Rennes - École normale supérieure - Rennes

Attacking ECDSA with wNAF implementation for the scalar multiplication first requires some side channel analysis to collect information, then lattice based methods to recover the secret key. In this paper, we reinvestigate the construction of the lattice used in one of these methods, the Extended Hidden Number Problem (EHNP). We find the secret key with only 3 signatures, thus reaching a known theoretical bound, whereas best previous methods required at least 4 signatures in practice. Given a specifoc leakage model, our attack is more efficient than previous attacks, and for most cases, has better probability of success. To obtain such results, we perform a detailed analysis of the parameters used in the attack and introduce a preprocessing method which reduces by a factor up to 7 the total time to recover the secret key for some parameters. We perform an error resilience analysis which has never been done before in the setup of EHNP. Our construction find the secret key with a small amount of erroneous traces, up to 2% of false digits, and 4% with a specific type of error.

Mots clés: Public key cryptography; ECDSA; Side channel attack; windowed Non-Adjacent Form; Lattice techniques

Domaines: Informatique [cs]; Cryptographie et sécurité [cs.CR]

Gabrielle de Micheli, Rémi E. Piau, Cécile Pierrot. A Tale of Three Signatures: practical attack of ECDSA with wNAF. AFRICACRYPT 2020, Jul 2020, Cairo, Egypt. pp.361-381, ⟨10.1007/978-3-030-51938-4_18⟩. ⟨hal-02393302v2⟩