New Elliptic Curve Multi-scalar Multiplication Algorithm for a Pair of Integers to Resist SPA

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The Simple Power Analysis (SPA) attack against an elliptic curve cryptosystem distinguishes between point doubling and point addition in a single execution of scalar multiplication. Although many SPA-resistant scalar multiplication algorithms have been proposed, few countermeasures for multi-scalar multiplications are known. In this paper, we propose a new SPA-resistant multi-scalar multiplication for a pair of integers combing the Joint Sparse Form (JSF) representation technique for pair of integers, point randomization, and uniform operation sequence. The new method requires about 8.5% less multiplications in the field compared to the known countermeasures.