Masked Prime Number Generation

Abstract. We here consider the protection of prime number generation against Side-Channel Attacks. Indeed, there is a need now to perform this procedure on-chip, in insecure environments. Our work uses techniques published by Boneh and Franklin on the generation of shared RSA keys in 1997. Their procedure allows the distribution of the computations among dierent participants such that, at the end, each of them owns a part of the secret keys { including prime numbers {, but none of them knows anything about their actual value. We use this shared generation of primes to design a procedure where prime numbers are generated in a masked way. Thus doing we turn a distributed protocol into a secure implementation of prime generation, suitable for smart-cards. The eectiveness of the masking is analyzed based on works by Howgrave-Graham