On the embedding degree of reductions of an elliptic curve

Alina Carmen Cojocaru; Igor E. Shparlinski

doi:10.1016/j.ipl.2009.02.018

On the embedding degree of reductions of an elliptic curve

Alina Carmen Cojocaru, Igor E. Shparlinski^*

^*Corresponding author for this work

Department of Computing

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	652-654
Number of pages	3
Journal	Information Processing Letters
Volume	109
Issue number	13
DOIs	https://doi.org/10.1016/j.ipl.2009.02.018
Publication status	Published - 15 Jun 2009

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abstract = "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.",

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