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 -