Cryptographic Hardware and Embedded Systems — CHES 2001

Volume 2162 of the series Lecture Notes in Computer Science pp 118-125


The Hessian Form of an Elliptic Curve

  • N. P. SmartAffiliated withDept. Computer Science, University of Bristol


In this paper we use the Hessian form of an elliptic curve and show that it offers some performance advantages over the standard representation. In particular when a processor allows the evaluation of a number of field multiplications in parallel (either via separate ALU’s, a SIMD type operation or a pipelined multiplication unit) one can obtain a performance advantage of around forty percent.