Journal of Mathematical Cryptology (Jun 2011)

Compact elliptic curve representations

  • Ciet Mathieu,
  • Quisquater Jean-Jacques,
  • Sica Francesco

DOI
https://doi.org/10.1515/jmc.2011.007
Journal volume & issue
Vol. 5, no. 1
pp. 89 – 100

Abstract

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Let y2 = x3 + ax + b be an elliptic curve over 𝔽p, p being a prime number greater than 3, and consider a, b ∈ [1, p]. In this paper, we study elliptic curve isomorphisms, with a view towards reduction in the size of elliptic curves coefficients. We first consider reducing the ratio a/b. We then apply these considerations to determine the number of elliptic curve isomorphism classes. Later we work on both coefficients. We introduce the number M(p) as the lower bound of all M ∈ ℕ such that each isomorphism class has a representative with max(a, b) 0.

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