In this paper, we propose a scalar multiplication method that does not incur a higher computational cost for randomized projective coordinates of the Montgomery form of elliptic curves. A randomized projective coordinates method is a countermeasure against side channel attacks on an elliptic curve cryptosystem in which an attacker cannot predict the appearance of a specific value because the coordinates have been randomized. However, because of this randomization, we cannot assume the Z-coordinate to be 1. Thus, the computational cost increases by multiplications of Z-coordinates, 10%. Our results clarify the advantages of cryptographic usage of Montgomery-form elliptic curves in constrained environments such as mobile devices and smart cards.
CITATION STYLE
Okeya, K., Miyazaki, K., & Sakurai, K. (2002). A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2288, pp. 428–439). Springer Verlag. https://doi.org/10.1007/3-540-45861-1_32
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