Parallel computation of modular exponentiation for fast cryptography

International Journal of High Performance Systems Architecture

Volumn 1, Issue 1, 2007, Pages 44-49

  Nedjah, Nadia ^a   Mourelle, Luiza de Macedo ^a  

^a STATE UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

cryptography; modular exponentiation; modular multiplication

Indexed keywords

EID: 65349181644     PISSN: 17516528     EISSN: 17516536     Source Type: Journal    
DOI: 10.1504/IJHPSA.2007.013290     Document Type: Article

References (13)

1. Bos, J. and Coster, M. (1989) ‘Addition chain heuristics’, Proceedings of CRYPTO’89, Lecture Notes in Computer Science, Vol. 435, Springer-Verlag, pp.400–407.
2. Downey, P., Leony, B. and Sethi, R. (1981) ‘Computing sequences with addition chains’, SIAM Journal on Computing, Vol. 3, pp.638–696.
3. Kaliski Jr., B.S. (1993) ‘The Z80180 and big-number arithmetic’, Dr. Dobb’s Journal, Vol. 50, p.58.
4. Knuth, D.E. (1981) The Art of Programming: Seminumerical Algorithms, 2nd edition, Vol. 2, Reading, MA: Addison-Wesley.
5. Koç, Ç.K. (1991) ‘High-radix and bit recoding techniques for modular exponentiation’, International Journal of Computer Mathematics, Vol. 40, Nos. 3–4, pp.139–156.
6. Koç, Ç.K. (1994) High Speed RSA Implementation, Research Report, RSA Laboratories, Version 2, California, USA.
7. Koç, Ç.K. (1995) ‘Analysis of sliding window techniques for exponentiation’, Computers and Mathematics with Applications, Vol. 30, No. 10, pp.17–24.
8. Koç, Ç.K. and Hung, C.Y. (1992) ‘Adaptive m-ary segmentation and canonical recoding algorithms for multiplication of large binary numbers’, Computers and Mathematics with Applications, Vol. 24, No. 3, pp.3–12.
9. Kunihiro, N. and Yamamoto, H. (1998) ‘Window and extended window methods for addition chain and addition-subtraction chain’, IEICE Transactions, Vol. E81-A, No. 1, pp.72–81.
10. Kunihiro, N. and Yamamoto, H. (2000) ‘New methods for generating short addition chain’, IEICE Transactions, Vol. E83-A, No. 1, pp.60–67.
11. Menezes, A., van Oorschot, P. and Vanstone, S. (1996) Handbook of Applied Cryptography, CRC Press.
12. National Institute of Standards and Technology (1991) ‘Digital signature standard – DSS’, Federal Register, Vol. 56, p.169.
13. Rivest, R.L., Shamir, A. and Adleman, L. (1978) ‘A method for obtaining digital signatures and public-key cryptosystems’, Communications of the ACM, Vol. 21, No. 2, pp.120–126.