On the embedding degree of reductions of an elliptic curve

Alina Carmen Cojocaru, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)652-654
Number of pages3
JournalInformation Processing Letters
Volume109
Issue number13
DOIs
Publication statusPublished - 15 Jun 2009

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