Low Complexity Systolic Montgomery Multiplication over Finite Fields GF(2m)
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Galois field arithmetic is important in error correcting codes and public-key cryptography schemes. Hardware realization of these schemes requires an efficient implementation of Galois field arithmetic operations. Multiplication is the main finite field operation and designing efficient multiplier can clearly affect the performance of compute-intensive applications. Diverse algorithms and hardware architectures are presented in the literature for hardware realization of Galois field multiplication to acquire a reduction in time and area. This paper presents a low complexity semi-systolic multiplier to facilitate parallel processing by partitioning Montgomery modular multiplication (MMM) into two independent and identical units and two-level systolic computation scheme. Analytical results indicate that the proposed multiplier achieves lower area-time (AT) complexity compared to related multipliers. Moreover, the proposed method has regularity, concurrency, and modularity, and thus is well suited for VLSI implementation. It can be applied as a core circuit for multiplication and division/exponentiation.
Abstract
Galois field arithmetic is important in error correcting codes and public-key cryptography schemes. Hardware realization of these schemes requires an efficient implementation of Galois field arithmetic operations. Multiplication is the main finite field operation and designing efficient multiplier can clearly affect the performance of compute-intensive applications. Diverse algorithms and hardware architectures are presented in the literature for hardware realization of Galois field multiplication to acquire a reduction in time and area. This paper presents a low complexity semi-systolic multiplier to facilitate parallel processing by partitioning Montgomery modular multiplication (MMM) into two independent and identical units and two-level systolic computation scheme. Analytical results indicate that the proposed multiplier achieves lower area-time (AT) complexity compared to related multipliers. Moreover, the proposed method has regularity, concurrency, and modularity, and thus is well suited for VLSI implementation. It can be applied as a core circuit for multiplication and division/exponentiation.
참고문헌 (14)
- Diffie, W, "New directions in cryptography", IEEE Transaction Information Theory, 22(6), pp.644~654 (1976)
- Kobliz, N, "Elliptic curve cryptography", Mathematics of Computation, 48(177), pp.203~209 (1987)
- Lee, C. Y, "Concurrent error detection in a polynomial basis multiplier over GF(2m )", Journal of Electronic Testing, 22(2), pp.143~150 (2006)
- Chiou, C. W, "Concurrent error detection in Montgomery multiplication over GF(2m )", IEICE Transactions on Fundamentals of Electronics, E89-A(2), pp.566~574 (2006)
- Huang, W. T, "Concurrent error detection and correction in a polynomial basis multiplier oveGF(2m )", IET Information Security, 4(3), pp.111~124 (2010)
- Choi, S. H, "New systolic modular multiplication architecture for efficient Montgomery multiplication", IEICE Electronics Express, 12(2), pp.20141051~ (2015)
- Choi, S. H, "Efficient systolic modular multiplier", squarer for fast exponentiation over GF(2m ),, 2015, pp.12(11), 20150222~
- Chiou, C. W, "High-throughput Dickson basis multiplier with a trinomial for lightweight cryptosystems", IET Computers & Digital Techniques, 12(5), pp.187~191 (2018)
- 이건직, "Resource and Delay Efficient Polynomial Multiplier over Finite Fields GF (2m)", (사)디지털산업정보학회 논문지, 16(2), pp.1~9 (2020), (사)디지털산업정보학회
- Sudha Ellison Mathe, "Design and Implementation of a Sequential Polynomial Basis Multiplier over GF(2m)", KSII Transactions on Internet and Information Systems, 11(5), pp.2680~2700 (2017), 한국인터넷정보학회[DOI]
- Ibrahim, A, "Efficient parallel and serial systolic structures for multiplication and squaring over GF(2m)", Canadian Journal of Electrical and Computer Engineering, 42(2), pp.114~120 (2019)
- Pillutla, S. R, "Low-latency area-efficient systolic bit-parallel GF(2m)multiplier for a narrow class of trinomials", Microelectronics Journal, 117, pp.105275~ (2021)
- Montgomery, P. L, "Modular multiplication without trial division", Mathematics of Computation, 44(170), pp.519~521 (1985)
- Koc, C. K, "Montgomery multiplication in GF(2k)", Designs Codes and Cryptography, 14(1), pp.57~69 (1998)