Randomized Signed-Scalar Multiplication of ECC to Resist Power Attacks
نویسندگان
چکیده
Recently it has been shown that smart cards as cryptographic devices are vulnerable to power attacks if they have no defence against them. Randomization on ECC scalar multiplication is one of the fundamental concepts in methods of defence against side-channel attacks. In this paper by using the randomization concept together with the NAF recoding algorithm, we propose an efficient countermeasure for ECCs against power attacks. The countermeasure provides a randomized signed-scalar representation at every scalar multiplication to resist DPA. To protect against SPA it additionally employs a simple SPA-immune addition-subtraction multiplication algorithm. Our analysis shows that it needs no additional computation load compared to the ordinary binary scalar multiplication, where the average number of doublings plus additions for a bit length n is 1.5n+O(1).
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