EDSM:secure and efficient scalar multiplication algorithm on Edwards curves

Abstract

Investigate the secure and efficient algorithm for scalar multiplication on Edwards curves.First,several new addition and doubling formulas were proposed.Analysis shows that our new formulas are more efficient than existed formulas.Then a new scalar multiplication algorithm was forwarded,called EDSM algorithm.Finally,our EDSM algo-rithm with the improved Montgomery method and other existed secure and efficient algorithms were compared.Experi-mental results show that our EDSM（scalar multiplication on Edwards curve） algorithm make great improvements in as-pects of efficiency and security.

Keywords

• elliptic curve;Edwards curve;scalar multiplication;side-channel attacks;Montgomery method