High performance elliptic curve scalar multiplication with resistance against power analysis attacks

This study presents a high performance scalar multiplication method with resistance against simple and differential power attacks. The scalar multiplier k is divided into a number of partitions that are independently processed in some random order. Each key partition is associated with a precomputed point to keep its significance. Portions of random lengths of randomly selected key partitions are processed depending on a random number that specifies the number of bits to be processed from the randomly picked partition. After processing these randomly selected bits, another portion of another key partition is randomly selected to be processed and so on until all key bits are processed. The curve points resulting from processing the key partitions are assimilated at the end to produce the target scalar product kP. The proposed randomization causes the relation between any leaked information and tile actual private key k to be fully confused. The comparison results show that the proposed method outperforms other recent countermeasures in terms of reducing the number of point additions without losing immunity against Simple Power Analysis (SPA),. doubling, Refined Power Analysis (RPA) and Zero Value Point(RVP) attacks.