论文信息 - A New Method for Speeding Up Arithmetic on Elliptic Curves over Binary Fields

A New Method for Speeding Up Arithmetic on Elliptic Curves over Binary Fields

Now, It is believed that the best costs of a point doubling and addition on elliptic curves over binary fields are S M 5 4 + (namely, four finite field multiplications and five field squarings) and , respectively. In this paper we reduce the costs to less than S M 5 8 + S M 3 3 + and , respectively, by using a new projective coordinates we call PL-coordinates and rewriting the point doubling formula. Combining some programming skills, the method can speed up a elliptic curve scalar multiplication by about 15~20 percent in practice. S M 1 8 +

Kwang Ho Kim | So In Kim

[1] G. Seroussi,et al. Elliptic Curves in Cryptography: Hyperelliptic Cryptosystems , 1999 .

[2] Çetin Kaya Koç,et al. High-speed implementation of an ECC-based wireless authentication protocol on an ARM microprocessor , 2001 .

[3] Ricardo Dahab,et al. Improved Algorithms for Elliptic Curve Arithmetic in GF(2n) , 1998, Selected Areas in Cryptography.

[4] Naofumi Takagi,et al. A fast addition algorithm for elliptic curve arithmetic in GF(2n) using projective coordinates , 2000, Inf. Process. Lett..

[5] Ramlan Mahmod,et al. A New Addition Formula for Elliptic Curves over GF(2n) , 2002, IEEE Trans. Computers.

[6] Akashi Satoh,et al. A Scalable Dual-Field Elliptic Curve Cryptographic Processor , 2003, IEEE Trans. Computers.