Comparing the MOV and FR Reductions in Elliptic Curve Cryptography

Abstract. This paper addresses the discrete logarithm problem in elliptic curve cryptography. In particular, we generalize the Menezes, Okamoto, and Vanstone (MOV) reduction so that it can be applied to some non-supersingular elliptic curves (ECs); decrypt Frey and R¨uck (FR)’s idea to describe the detail of the FR reduction and to implement it for actual elliptic curves with finite fields on a practical scale; and based on them compare the (extended) MOV and FR reductions from an algorithmic point of view. (This paper has primarily an expository role.)

• Type: Conference
• Year: 1999
• Where: EUROCRYPT
• Authors: Ryuichi Harasawa, Junji Shikata, Joe Suzuki, Hideki Imai
• Keywords: Cryptology, Elliptic Curve Cryptography, Elliptic Curves, EUROCRYPT 1999, Fr Reductions