Information Security and Cryptology — ICISC 2001

Volume 2288 of the series Lecture Notes in Computer Science pp 428-439


A Fast Scalar Multiplication Method with Randomized Projective Coordinates on a Montgomery-Form Elliptic Curve Secure against Side Channel Attacks

  • Katsuyuki OkeyaAffiliated withSystems Development Laboratory, Hitachi, Ltd.
  • , Kunihiko MiyazakiAffiliated withSystems Development Laboratory, Hitachi, Ltd.
  • , Kouichi SakuraiAffiliated withGraduate School of Information Science and Electrical Engineering, Kyushu University

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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.


Elliptic Curve Cryptosystem Montgomery Form Side Channel Attacks Randomized Projective Coordinates