Practical Validation of Several Fault Attacks against the Miller Algorithm

Pairing based cryptography (PBC) is touted as an efficient approach to address usability and privacy issues in the cyberspace. Like most cryptographic algorithms, PBC must be robust not only against theoretical cryptanalysis but also against practical physical attacks such as fault injections. The computation of the Tate pairing can be divided into two parts, the Miller Algorithm and the Final Exponentiation. In this paper, we describe practical implementations of fault attacks against the Miller Algorithm validating common fault models used against pairings. In the light of the implemented fault attacks, we show that some blinding techniques proposed to protect the algorithm against Side-Channels Analyses cannot be used as countermeasures against the implemented fault attacks.