Heuristics on pairing-friendly elliptic curves

John Boxall (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We present a heuristic asymptotic formula as x tends to infinity for the number of isogeny classes of pairing-friendly elliptic curves over prime fields with fixed embedding degree k 3, with fixed discriminant, with rho-value bounded by a fixed rho0 such that 1 < rho0 < 2, and with prime subgroup order at most x.

Mots clés: Elliptic curves; finite fields; pairing-based cryptography

Domaines: Théorie des nombres [math.NT]

John Boxall. Heuristics on pairing-friendly elliptic curves. Journal of Mathematical Cryptology, 2012, 6 (2), pp.14 - 52. ⟨10.1515/jmc-2011-0004⟩. ⟨hal-02153424⟩