论文信息 - A representation of elements in F 2 m enabling unified field arithmetic for elliptic curve cryptography

A representation of elements in F 2 m enabling unified field arithmetic for elliptic curve cryptography

In this letter we propose a change of representation for elements in F 2 m. The proposed representation is useful for architectures that implement unified Montgomery multiplication in finite fields F 2 m and F p used for elliptic curve cryptography since it transforms a standard F 2 m multiplication into a Montgomery multiplication and comes at virtually no cost in terms of conversion operations.

N. Mazzocca | A. Cilardo | A. Mazzeo

[1] P. L. Montgomery. Modular multiplication without trial division , 1985 .

[2] H. Niederreiter,et al. Finite Fields: Encyclopedia of Mathematics and Its Applications. , 1997 .

[3] ÇETIN K. KOÇ,et al. Montgomery Multiplication in GF(2k) , 1998, Des. Codes Cryptogr..

[4] Ian F. Blake,et al. Elliptic curves in cryptography , 1999 .

[5] Erkay Savas,et al. A Scalable and Unified Multiplier Architecture for Finite Fields GF(p) and GF(2m) , 2000, CHES.

[6] C. D. Walter,et al. Improved linear systolic array for fast modular exponentiation , 2000 .

[7] 尚弘島影. National Institute of Standards and Technologyにおける超伝導研究及び生活 , 2001 .

[8] Johann Großschädl,et al. Low-Power Design of a Functional Unit for Arithmetic in Finite Fields GF(p) and GF(2m) , 2003, WISA.

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

[10] Berk Sunar,et al. Achieving NTRU with Montgomery Multiplication , 2003, IEEE Trans. Computers.

[11] Guy-Armand Kamendje,et al. Low-Power Design of a Functional Unit for Arithmetic in Finite Fields GF ( p ) and GF ( 2 m ) , 2003 .

[12] ÇETIN K. KOÇ,et al. A Design Framework for Scalable and Unified Multipliers in Gf(p) and Gf(2 M ) X.1. Introduction , 2004 .