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Issue No.08 - August (2010 vol.59)
pp: 1145-1151
Ming-Der Shieh , National Cheng Kung University, Tainan
Wen-Ching Lin , National Cheng Kung University, Tainan
Modular multiplication is a crucial operation in public key cryptosystems like RSA and elliptic curve cryptography (ECC). This paper presents a new word-based Montgomery modular multiplication algorithm which can be used to achieve a low-latency scalable architecture for efficient hardware implementations. We show how to relax the data dependency in conventional word-based algorithms so that a latency of exactly one cycle can be obtained regardless of the chosen word size w (w > 1). With the presented operand reduction scheme, the proposed scalable architecture can operate at high speeds and suitable data paths can be chosen for specific applications. Complexity analysis shows that the proposed architecture has the lowest latency and area complexity compared to related scalable architectures. Experimental results demonstrate that our design has area, speed, and flexibility advantages over related schemes.
Algorithms implemented in hardware, computations in finite fields, computer arithmetic, high-speed arithmetic, VLSI.
Ming-Der Shieh, Wen-Ching Lin, "Word-Based Montgomery Modular Multiplication Algorithm for Low-Latency Scalable Architectures", IEEE Transactions on Computers, vol.59, no. 8, pp. 1145-1151, August 2010, doi:10.1109/TC.2010.72
[1] R. Rivest, A. Shamir, and L. Adleman, "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems," Comm. ACM, vol. 21, pp. 120-126, Feb. 1978.
[2] N. Koblitz, "Elliptic Curve Cryptosystems," Math. Computation, vol. 48, pp. 203-209, 1987.
[3] V.S. Miller, "Use of Elliptic Curve in Cryptography," Proc. Adv. Cryptology (Crypto), pp. 417-426, 1986.
[4] P.L. Montgomery, "Modular Multiplication without Trial Division," Math. Computation, vol. 44, pp. 519-521, Apr. 1985.
[5] C. McIvor, M. McLoone, and J.V. McCanny, "Modified Montgomery Modular Multiplication and RSA Exponentiation Techniques," IEE Proc.—Computer and Digital Techniques, vol. 151, no. 6, pp. 402-408. Nov. 2004.
[6] M.D. Shieh, J.H. Chen, H.S. Wu, and W.C. Lin, "A New Modular Exponentiation Architecture for Efficient Design of RSA Cryptosystem," IEEE Trans. Very Large Scale Integration Systems, vol. 16, no. 9, pp. 1151-1161, Sept. 2008.
[7] M. Huang, K. Gaj, S. Kwon, and T. El-Ghazawi, "An Optimized Hardware Architecture for Montgomery Multiplication Algorithm," Proc. Public Key Cryptography (PKC '08), pp. 214-228, 2008.
[8] F. Tenca and C.K. Koc, "A Scalable Architecture for Modular Multiplication Based on Montgomery's Algorithm," IEEE Trans. Computers, vol. 52, no. 9, pp. 1215-1221, Sept. 2003.
[9] D. Harris, R. Krishnamurthy, S. Mathew, and S. Hsu, "An Improved Unified Scalable Radix-2 Montgomery Multiplier," Proc. IEEE Symp. Computer Arithmetic, pp. 1196-1200, 2005.
[10] C.D. Walter, "Montgomery Exponentiation Needs No Final Subtractions," Electronics Letters, vol. 32, no. 21, pp. 1831-1832, Oct. 1999.
[11] N. Jiang and D. Harris, "Parallelized Radix-2 Scalable Montgomery Multiplier," Proc. IFIP Int'l Conf. Very Large Scale Integration, pp. 146-150, 2007.
[12] H. Orup, "Simplifying Quotient Determination in High-Radix Modular Multiplication," Proc. 12th IEEE Symp. Computer Arithmetic, pp. 193-199, 1995.
[13] P. Kornerip, "High-Radix Modular Multiplication for Cryptosystems," Proc. 11th IEEE Symp. Computer Arithmetic, pp. 277-283, 1993.
[14] F. Tenca, G. Todorov, and K. Koc, "High-Radix Design of a Scalable Modular Multiplier," Proc. Cryptographic Hardware and Embedded Systems (CHES '01), pp. 189-205, 2001.
[15] N. Pinckney and D. Harris, "Parallelized Radix-4 Scalable Montgomery Multiplier," Proc. 20th Ann. Conf. Integrated Circuits and Systems Design, pp. 306-331, 2007.
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