Title :
Scalable and systolic Montgomery multiplier over GF(2m) generated by trinomials
Author :
Lee, C.-Y. ; Chiou, C.W. ; Lin, J.-M. ; Chang, C.-C.
Author_Institution :
Dept. of Comput. Inf. & Network Eng., Lunghwa Univ. of Sci. & Technol., Taoyuan
fDate :
12/1/2007 12:00:00 AM
Abstract :
A Montgomery´s algorithm in GF(2m) based on the Hankel matrix-vector representation is proposed. The hardware architecture obtained from this algorithm indicates low-complexity bit-parallel systolic multipliers with irreducible trinomials. The results reveal that the proposed multiplier saves approximately 36% of space complexity as compared to an existing systolic Montgomery multiplier for trinomials. A scalable and systolic Montgomery multiplier is also developed by applying the block-Hankel matrix-vector representation. The proposed scalable systolic architecture is demonstrated to have significantly less time-area product complexity than existing digit-serial systolic architectures. Furthermore, the proposed architectures have regularity, modularity and local interconnectability, making the.m highly appropriate for VLSI implementation.
Keywords :
Galois fields; Hankel matrices; VLSI; computational complexity; multiplying circuits; systolic arrays; VLSI implementation; block-Hankel matrix-vector representation; digit-serial systolic architectures; hardware architecture; low-complexity bit-parallel systolic multipliers; systolic Montgomery multiplier; trinomials;
Journal_Title :
Circuits, Devices & Systems, IET
DOI :
10.1049/iet-cds:20060314