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.