Fault Attack against Miller's algorithm

Nadia El Mrabet (1)

1 LIASD - Laboratoire d'Informatique Avancée de Saint-Denis

We complete the study of [23] and [27] about Miller's algorithm. Miller's algorithm is a central step to compute the Weil, Tate and Ate pairings. The aim of this article is to analyze the weakness of Miller's algorithm when it undergoes a fault attack. We prove that Miller's algorithm is vulnerable to a fault attack which is valid in all coordinate systems, through the resolution of a nonlinear system. We highlight the fact that putting the secret as the rst argument of the pairing is not a countermeasure. This article is an extensed version of the article [15].

Mots clés: Pairing Based Cryptography; Side Channel Attacks; Fault attacks

Domaines: Cryptographie et sécurité [cs.CR]; Systèmes embarqués

Nadia El Mrabet. Fault Attack against Miller's algorithm. 2010. ⟨hal-00655465⟩