Research For Algorithms And Applications Of Elliptic Curve Cryptography

Elliptic Curve Cryptography (ECC) provides the highest strength-per-key-bit of any cryptography known. Compared with other public-key cryptographies, ECC not only has the higher security but also has less computation overheads, shorter key size and narrower bandwidth. Therefore, the experts believe that ECC will become the next generation popular public-key cryptography.This paper mainly researches algorithms and applications of elliptic curve cryptography. Firstly, based on the signed factorial expansions, .the fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are presented. Secondly, the fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are designed based on integer splitting and precomputation technique. Thirdly, the paper also proposes the algorithms for scalar multiplication and multi-scalar multiplication for an arbitrary point on Weierstrass elliptic curves over fields of characteristic Three. Fourthly, the new idea that key isrepresented by a vector is presented. The theory analysis and experiment results show that the presented algorithms are faster than the other existing algorithms and easily parallelized. Finally, a new hierarchical and two-level group key management scheme and two group signature schemes for large dynamic multicast groups based on the elliptic curve cryptography are presented. The theory analysis shows that our schemes are secure and efficient, and fit the applications in large dynamic multicast groups.