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 · 2015
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.