tailieunhanh - Efficient VLSI Implementation for Montgomery Multiplication in GF(2m)

The Montgomery multiplication algorithm without division operations is popular both in prime field GF(p) and Finite field GF(2m). However, the Montgomery multiplication algorithm has the time-dependent problem. | Tamkang Journal of Science and Engineering Vol. 9 No 4 pp. 365-372 2006 365 Efficient VLSI Implementation for Montgomery Multiplication in GF 2m Che-Wun Chiou1 Chiou-Yng Lee2 An-Wen Deng3 and Jim-Min Lin4 department of Computer Science and Information Engineering Ching Yun University Chung-Li Taiwan 320 . department of Computer Information and Network Engineering LungHwa University of Science Technology Taoyuan Taiwan 333 . department of Information Management Ching Yun University Chung-Li Taiwan 320 . department of Information Engineering and Computer Science Feng Chia University Taichung City Taiwan 407 . Abstract The Montgomery multiplication algorithm without division operations is popular both in prime field GF p and Finite field GF 2m . However the Montgomery multiplication algorithm has the time-dependent problem. We will present a time-independent Montgomery multiplication algorithm. The results show that our proposed time-independent Montgomery multiplication algorithm not only saves about 50 time complexity but also saves about 11 space complexity as compared to the traditional Montgomery multiplication algorithm. Our proposed systolic array Montgomery multiplier has simplicity regularity modularity and concurrency and is very suitable for VLSI implementation. Key Words Finite Field Cryptography ECC Montgomery Multiplication Parallel Processing 1. Introduction Recently finite field arithmetic operations in GF 2m were frequently desired in coding theory 1 cryptography 2 digital signal processing 3 4 switching theory 5 and pseudorandom number generation 6 . There are three popular types of bases over finite fields polynomial basis PB 7-15 normal basis NB 16 17 and dual basis DB 18 19 . Among the finite field arithmetic operations multiplication is the most important complex and time consuming. In general other complex operations such as exponentiation inversion and division can be used with Fermat s theorem to perform the iterative .

• An ninh - Bảo mật
• Efficient VLSI Implementation
• The Montgomery Multiplication
• Montgomery Multiplication Algorithm
• The Efficient VLSI
• Science and Engineering
• The Montgomery Multiplication
• The digital signature algorithm
• An efficient implementation
• The Roposed architecture
• Hash Function Architecture
• RSA Algorithm Architecture
• VLSI implementation results
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• Fundamentals of Extension Fields
• Addition and Subtraction
• Binary extension field
• Ternary extension field
• Efficient Unified Arithmetic