Abstract
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.
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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: Kim, K. (eds) Information Security and Cryptology — ICISC 2001. ICISC 2001. Lecture Notes in Computer Science, vol 2288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45861-1_32
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DOI: https://doi.org/10.1007/3-540-45861-1_32
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