Elliptic Curve Cryptosystems And Its Application On Smart Card

One primary problem in ECC is the selection of secure elliptic curves. If the selectedcurve is insecure, any scheme based on this curve is insecure too. Under the samesecurity level, ECC has smaller key,so it has especial use in smart card,whosememory \ computation and power are restricted.In this paPer, we primarily introduce some kind of common used public-keycryPtosystems, especially ECC and its use on smed card. The work we have done is:write a program to find secure elliptic curves over big prime field and imPlement ECDSAover GF(2"' -- 2" -- 1). We also put forward tWo kind of smed card authenticationschemes based on ECC: zero-knowledge authentication scheme based on ECC andSchnorr authentication scheme based on ECC.