Protections against differential analysis for elliptic curve cryptography: An algebraic approach

Abstract

We propose several new methods to protect the scalar multiplication on an elliptic curve against Differential Analysis. The basic idea consists in transforming the curve through various random morphisms to provide a non-deterministic execution of the algorithm. The solutions we suggest complement and improve the state-of-the-art, but also provide a practical toolbox of efficient countermeasures. These should suit most of the needs for protecting implementations of cryptoalgorithms based on elliptic curves.