Long modular multiplication for cryptographic applications

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3156, Issue , 2004, Pages 45-61

  Hars, Laszlo ^a  

^a SEAGATE RESEARCH   (United States)

Author keywords

Computer arithmetic; Cryptography; Modular multiplication; Modular reduction; Montgomery multiplication; Multiply accumulate architecture; Optimization; Quisquater multiplication; Reciprocal

Indexed keywords

EMBEDDED SYSTEMS; OPTIMIZATION;

COMPUTER ARITHMETIC; MODULAR MULTIPLICATION; MODULAR REDUCTION; MONTGOMERY MULTIPLICATION; MULTIPLY ACCUMULATE; QUISQUATER MULTIPLICATION; RECIPROCAL;

CRYPTOGRAPHY;

EID: 27244441300     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-28632-5_4     Document Type: Article

References (17)

1. ALTERA Literature: Stratix II Devices http://www.altera.com/literature/ lit-stx2.jsp
2. P.D.Barrett, Implementing the Rivest Shamir Adleman public key encryption algorithm on standard digital signal processor, In Advances in Cryptology-Crypto'86, Springer, 1987, pp.311-323.
3. Bosselaers, R. Govaerts and J. Vandewalle, Comparison of three modular reduction functions, In Advances in Cryptology-Crypto'93, LNCS 773, Springer-Verlag, 1994, pp. 175-186.
4. E. F. Brickell. A Survey of Hardware Implementations of RSA. Proceedings of Crypto'89, Lecture Notes in Computer Science, Springer-Verlag, 1990.
5. J.-F. Dhem, J.-J. Quisquater, Recent results on modular multiplications for smart cards, Proceedings of CARDIS 1998, Volume 1820 of Lecture Notes in Computer Security, pp 350-366, Springer-Verlag, 2000
6. GNU Multiple Precision Arithmetic Library http://www.swox.com/gmp/gmp- man4.1.2.pdf
7. K. Hensel, Theorie der algebraische Zahlen. Leipzig, 1908
8. J. Jedwab and C. J. Mitchell. Minimum weight modified signed-digit representations and fast exponentiation. Electronics Letters, 25(17):1171-1172, 17. August 1989.
9. D. E. Knuth. The Art of Computer Programming. Volume 2. Seminumerical Algorithms. Addison-Wesley, 1981. Algorithm 4.3.3R
10. W. Krandick, J. R. Johnson, Efficient Multiprecision Floating Point Multiplication with Exact Rounding, Tech. Rep. 93-76, RISC-Linz, Johannes Kepler University, Linz, Austria, 1993.
11. A.Menezes, P.van Oorschot, S.Vanstone, Handbook of Applied Cryptography, CRC Press, 1996.
12. P.L. Montgomery, Modular Multiplication without Trial Division, Mathematics of Computation, Vol. 44, No. 170, 1985, pp. 519-521.
13. J.-J. Quisquater, Presentation at the rump session of Eurocrypt'90.
14. R. L. Rivest; A. Shamir, and L. Adleman. 1978. A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM 21(2): 120-126
15. SNIA OSD Technical Work Group http://www.snia.org/tech activities/workgroups/osd/
16. C. D. Walter, Faster modular multiplication by operand scaling, Advances in Cryptology, Proc. Crypto'91, LNCS 576, J. Feigenbaum, Ed., Springer-Verlag, 1992, pp. 313-323
17. L. Hars, manuscript, 2003.