**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30135

##### Efficient Semi-Systolic Finite Field Multiplier Using Redundant Basis

**Authors:**
Hyun-Ho Lee,
Kee-Won Kim

**Abstract:**

**Keywords:**
Finite field,
Montgomery multiplication,
systolic array,
cryptography.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1126730

**References:**

[1] A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography, Boca Raton, FL, CRC Press, 1996.

[2] R. E. Blahut, Theory and Practice of Error Control Codes, Reading, MA, Addison-Wesley, 1983.

[3] N. Kobliz, “Elliptic Curve Cryptography,” Math. Computation, vol. 48, no. 177, pp. 203-209, Jan. 1987.

[4] P. Montgomery, “Modular multiplication without trial division,” Math. Comput., vol. 44, no. 170, pp. 519-521, Apr. 1985.

[5] C. Koc, and T. Acar, “Montgomery multiplication in GF(2k),” Des. Codes Cryptogr., vol. 14, no. 1, pp. 57-69, Apr. 1998.

[6] C. Y. Lee, J. S. Horng, and I. C. Jou, “Low-complexity bit-parallel systolic Montgomery multipliers for special classes of GF(2m),” IEEE Trans. Comput., vol. 54, no. 9, pp. 1061-1070, Sep. 2005.

[7] A. Hariri and A. Reyhani-Masoleh, “Bit-serial and bit-parallel Montgomery multiplication and squaring over GF(2m),” IEEE Trans. Comput., vol. 58, no. 10, pp. 1332-45, Oct. 2009.

[8] A. Hariri and A. Reyhani-Masoleh, “Concurrent error detection in Montgomery multiplication over binary extension fields,” IEEE Trans. Comput., vol. 60, no. 9, pp. 1341-53, Sep. 2011.

[9] K. W. Kim and W. J. Lee, “Efficient cellular automata based Montgomery AB2 multipliers over GF(2m),” IETE Technical Review, vol. 31, no. 1, pp. 92-102, May 2014.

[10] K. W. Kim and J. C. Jeon, “Polynomial basis multiplier using cellular systolic architecture,” IETE Journal of Research, vol. 60, no. 2, pp. 194-199, Jun. 2014.

[11] S. H. Choi and K. J. Lee, “Low complexity semisystolic multiplication architecture over GF(2m),” IEICE Electron. Express, vol. 11, no. 20, pp. 20140713, Oct. 2014.

[12] K. W. Kim and J. C. Jeon, “A semi-systolic Montgomery multiplier over GF(2m),” IEICE Electonics Express, vol. 12, no. 21, pp. 20150769, Nov. 2015.

[13] C. W. Chiou, C. Y. Lee, A. W. Deng, and J. M. Lin, “Concurrent error detection in Montgomery multiplication over GF(2m),” IEICE Trans. Fund. Electron. Commun. Comput. Sci., vol. E89-A, no. 2, pp. 566-574, Feb. 2006.

[14] W.T. Huang, C.H. Chang, C.W. Chiou and F.H. Chou, “Concurrent error detection and correction in a polynomial basis multiplier over GF(2m),” IET Inf. Secur., vol. 4, no. 3, p. 111-124, Sep. 2010.

[15] K. W. Kim and S. H. Kim, “A low latency semi-systolic multiplier over GF(2m),” IEICE Electron. Express, vol. 10, no. 13, pp. 20130354, July 2013.

[16] C. Y. Lee, C. W. Chiou and J. M. Lin, “Concurrent error detection in a polynomial basis multiplier over GF(2m),” J. Electron. Test., vol. 22, no. 2, pp. 143-150, Apr. 2006.

[17] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications. Cambridge Univ. Press, 1986.

[18] H. Wu, M.A. Hasan, I.F. Blake and S. Gao, “Finite field multiplier using redundant representation,” IEEE Trans. Comput. Vol.51, No.11, pp.1306-1316, 2002.

[19] A. H. Namin, H. Wu and M. Ahmadi, “A New Finite Field Multiplier Using Redundant Representation”, IEEE Trans. Computers, Vol.57, No.5, pp. 716-720, May 2008.