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We complete the study of [16] and [20] about the Miller's algorithm. The Miller's algorithm is a central step to compute the Weil, Tate and Ate pairings. The aim of this article is to analyse the weakness of the Miller's algorithm when it undergoes a fault attack. We prove that the Miller's algorithm is vulnerable to a fault attack which is valid in all coordinate systems, through the resolution of a nonlinear system. We show that the final exponentiation is no longer a counter measure to this attack for the Tate and Ate pairings.

What about Vulnerability to a Fault Attack of the Miller’s Algorithm During an Identity Based Protocol?