Secure and Efficient RNS Approach for Elliptic Curve Cryptography

摘要: Scalar multiplication, the main operation in elliptic curve cryptographic protocols, is vulnerable to side-channel (SCA) and fault injection (FA) attacks. An efficient countermeasure for scalar multiplication can be provided by using alternative number systems like Residue Number System (RNS). In RNS, a number represented as a set of smaller numbers, where each one result modular reduction with given moduli basis. Under certain requirements, uniquely transformed from integers RNS domain (and vice versa) all arithmetic operations performed RNS. This representation provides an inherent SCA FA resistance to many attacks further enhanced arithmetic manipulation or more traditional algorithmic countermeasures. In this paper, extending our previous work, we explore the potentials countermeasure provide an description based resistance means. We propose secure Montgomery Power Ladder based scalar algorithm on discuss its SCAFA resistance. The proposed implemented an ARM Cortex A7 processor SCA-FA evaluated by collecting preliminary leakage trace results that validate our initial assumptions.