Power attacks in the presence of exponent blinding

Exponent blinding has been known as an effective countermeasure against side-channel attacks on RSA. However, if single power traces reveal some exponent bits with certainty, an attack by Fouque et al. (Power attack on small RSA public exponent. Springer, Berlin, pp 339–353, 2006) applies that recovers the exponent. Since this attack becomes infeasible if some of these assumed exponent bits are incorrect it has not been assumed to be a realistic threat in the context of side-channel attacks. In this paper we present three generic attack variants (basic attack, enhanced attack, alternate attack), which work in the presence of considerable error rates at each bit position, disproving the hypothesis that mere exponent blinding is always sufficient to protect SPA-resistant implementations against any type of power attacks. Simulation experiments confirm that for small blinding factors the basic attack permits error rates of more than $$25~\%$$25%. The enhanced attack allows smaller error rates but requires much less power traces and computations. Unlike the basic attack and the enhanced attack the alternate attack (against ECC and RSA without CRT) cannot effectively be prevented by simply enlarging the blinding factor. This paper extends (Schindler and Itoh, Exponent blinding does not always lift (Partial) SPA resistance to higher-level security. Springer, Berlin, pp 73–90, 2011) by many new results.