Research On The Algorithm Of Elliptic Curve Scalar Multiplication

Elliptic Curve Cryptosystem is widely used due to its higher security,less low-cost computing work and smaller private keys, since its being putting forward. Scalar multiplication is difficult and key for its playing an important role in all sorts of elliptic curve cryptographic protocols. Simple power analysis poses threat to elliptic curve cryptographic scalar mutiplication and even regain private keys. This thesis for master's degree comes up with a side-channel atomic resisting against simple side-channel analysis with improvement of security. The work of this paper is:1.Firstly we make summary of basic theory related with Elliptic Curve Cryptosystem;2.Studying scalar multiplication based on an average Abelian group, we extend scalar mutiplication to elliptic curve group defined in a Galois field and modify the algorithm of k-band scalar multiplication, after analyzing several traditional ones ,with good implementation and high efficiency;3.Regarding security of scalar multiplication,we sum up the method of side-channel attack and implement protected scalar multiplication defined in F p by programming Montgomery Ladder algorithm;4.We bring forward a SPA-resisting side-channel atomicity, the frequency of point doubling and point addition being decreased and time being saved. By exploiting Crypto++ Library we implement our scalar multiplication algorithm for elliptic curve based in 160-bit prime field given by NIST and find a fact that our algorithm is about 37.6% faster than Montgomery Ladder algorithm.