A practical Differential Power Analysis attack against the Miller algorithm

Pairings permit several protocol simplifications and original scheme creation, for example Identity Based Cryptography protocols. Initially, the use of pairings did not involve any secret entry, consequently, side channel attacks were not a threat for pairing based cryptography. On the contrary, in an Identity Based Cryptographic protocol, one of the two entries to the pairing is secret. Side Channel Attacks can be therefore applied to find this secret. We realize a Differential Power Analysis(DPA) against the Miller algorithm, the central step to compute the Weil, Tate and Ate pairing. We show that the countermeasure which consist in setting the secret during a pairing computation at the first parameter is not sufficient to prevent a DPA attack.