TY - JOUR

T1 - On the embedding degree of reductions of an elliptic curve

AU - Cojocaru, Alina Carmen

AU - Shparlinski, Igor E.

PY - 2009/6/15

Y1 - 2009/6/15

N2 - Given an elliptic curve E over Q we estimate the number of primes p ≤ T for which the number of points on reduction of E modulo p has a large prime factor ℓ and also a small embedding degree with respect to ℓ. Such curves are important for a number of cryptographic applications. However our result shows that they are very rare. On the other hand, it also shows that the so-called MOV attack is not likely to affect the reduction of a given elliptic curve over Q modulo a random prime.

AB - Given an elliptic curve E over Q we estimate the number of primes p ≤ T for which the number of points on reduction of E modulo p has a large prime factor ℓ and also a small embedding degree with respect to ℓ. Such curves are important for a number of cryptographic applications. However our result shows that they are very rare. On the other hand, it also shows that the so-called MOV attack is not likely to affect the reduction of a given elliptic curve over Q modulo a random prime.

UR - http://www.scopus.com/inward/record.url?scp=67349112425&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2009.02.018

DO - 10.1016/j.ipl.2009.02.018

M3 - Article

AN - SCOPUS:67349112425

VL - 109

SP - 652

EP - 654

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 13

ER -