Evaluating Large Degree Isogenies and Applications to Pairing Based Cryptography

Authors:
Reinier Bröker;Denis Charles;Kristin Lauter
Affiliations:
Microsoft Research, One Microsoft Way, Redmond, USA WA 98052;Microsoft Research, One Microsoft Way, Redmond, USA WA 98052;Microsoft Research, One Microsoft Way, Redmond, USA WA 98052
Venue:
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Year:
2008

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Abstract

We present a new method to evaluate large degree isogenies between elliptic curves over finite fields. Previous approaches all have exponentialrunning time in the logarithm of the degree. If the endomorphism ring of the elliptic curve is `small' we can do much better, and we present an algorithm with a running time that is polynomialin the logarithm of the degree. We give several applications of our techniques to pairing based cryptography.