Low complexity multiplication in a finite field using ring representation

IEEE Transactions on Computers

Volumn 52, Issue 4, 2003, Pages 418-427

  Katti, Rajendra ^a   Brennan, Joseph ^a  

^a North Dakota State University   (United States)

Author keywords

Finite field multiplication; Ring representation; Systolic arrays

Indexed keywords

COMPUTATIONAL COMPLEXITY; CRYPTOGRAPHY; ENCODING (SYMBOLS); POLYNOMIALS; SYSTOLIC ARRAYS;

ERROR CONTROL CODING; FINITE FIELD MULTPLICATION; RING REPRESENTATION;

MULTIPLYING CIRCUITS;

EID: 0038639373     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/TC.2003.1190583     Document Type: Article

References (16)

1. D.R. Hankerson, D.G. Hoffman, D.A. Leonard, C.C. Lindner, K.T. Phelps, C.A. Rodger, and J.R. Wall, Coding Theory and Cryptography: The Essentials, second ed. Marcel Dekker, 2000.
2. E. Trichina, M. Bucci, and D. De Seta, and R. Luzzi, "Supplemental Cryptographic Hardware for Smart Cards," IEEE Micro, pp. 26-35, Nov./Dec. 2001.
3. J. Dhem and N. Feyt, "Hardware and Software Symbiosis Helps Smart Card Evolution," IEEE Micro, pp. 14-25, Nov./Dec. 2001.
4. M. Smith, "Smart Cards: Integrating for Portable Complexity," Computer, pp. 110-115, Aug. 1998.
5. P.W. Dowd and J.T. McHenry, "Network Security," Computer, pp. 24-28, Sept. 1998.
6. B. Schneier, Applied Cryptography. John Wiley & Sons, 1996.
7. N. Koblitz, A Course in Number Theory and Cryptography. Springer-Verlag, 1994.
8. C.K. Koc and B. Sunar, "Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields," IEEE Trans. Computers, vol. 47, no. 3, pp. 353-356, Mar. 1998.
9. A. Halbutogullari and C.K. Koc, "Mastrovito Multiplier for General Irreducible Polynomials," IEEE Trans. Computers, vol. 49, no. 5, pp. 503-518, May 2000.
10. m) Processor," IEEE Trans. Computers, vol. 49, no. 10, pp. 1064-1073, Oct. 2000.
11. m) Yielding Small Complexity Arithmetic Circuits," IEEE Trans. Computers, vol. 47, no. 9, pp. 938-946, Sept. 1998.
12. C. Paar, P. Fleischmann, and P. Soria-Rodriguez, "Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents," IEEE Trans. Computers, vol. 48, no. 10, pp. 1025-1034, Oct. 1999.
13. T.W. Hungerford, Algebra, eighth ed. Springer-Verlag, 1997.
14. W.V. Vasconcelos, Computational Methods in Commutative Algebra and Algebraic Geometry. Springer-Verlag, 1997.
15. m) Fields Defined by All-One and Equally Spaced Polynomials," IEEE Trans. Computers, vol. 50, no. 5, pp. 385-393, May 2001.
16. T. Zhong and K.K. Parhi, "Systematic Design of Original and Modified Mastrovito Multipliers for General Irreducible Polynomials," IEEE Trans. Computers, vol. 50, no. 7, pp. 734-749, July 2001.