Digit-Serial Systolic Karatsuba Multiplier for Special Classes over GF(2^m)

Che Wun Chiou ； Chiou-Yng Lee ； Jim-Min Lin ； Yun-Chi Yeh ； Hung Wei Chang ； Liuh-Chii Lin

《電腦學刊》 26卷1期 (2015/04) Pp. 40-57

並列摘要

Finite field multiplication over GF (2^m) is one of the most important arithmetic operations for Elliptic Curve Cryptosystem (ECC). Polynomial basis multipliers over GF (2^m) are widely applied in ECC due to its regular, modular, easily expansible benefits and the high suitability for VLSI implementation. This study will present a novel digit-serial polynomial basis multiplier using Karatsuba algorithm representation. To achieve efficient architectures, our proposed digit-serial architecture is different from existing digit-serial polynomial basis multipliers that use cut-set algorithm. The proposed digit-serial polynomial basis multiplier saves 90% space complexity as compared to existing similar studies. Existing digit-serial polynomial basis multipliers employ one dimensional array of digit cells, but our proposed digit-serial polynomial basis multiplier uses only one digit cell.

並列關鍵字

Karatsuba algorithm ； elliptic curve cryptosystem ； finite field multiplication ； digit-serial multiplier ； systolic