An efficient montgomery exponentiation algorithm for cryptographic applications

Informatica

Volumn 16, Issue 3, 2005, Pages 449-468

  Wu, Chia Long ^a   Lou, Der Chyuan ^b   Chang, Te Jen ^b  

^a AIR FORCE INSTITUTE OF TECHNOLOGY   (Taiwan)

^b NATIONAL DEFENSE UNIVERSITY   (Taiwan)

Author keywords

Common multiplicand multiplication; Modular exponentiation; Montgomery reduction algorithm; Public key cryptosystems; Signed digit recoding

Indexed keywords

EID: 24944483330     PISSN: 08684952     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. Arno, S., and F.S. Wheeler (1993). Signed digit representations of minimal hamming weight. IEEE Transactions an Computers, 42(8), 1007-1010.
2. Avizienis, A. (1961). Signed digit number representation for fast parallel arithmetic. IRE Transactions on Electronic Computers, EC-10(3), 389-400.
3. Chang, C.-C., Y.-T. Kuo and C.-H. Lin (2003). Fast algorithms for common-multiplicand multiplication and exponentiation by performing complements. In Proceedings of the 17th IEEE Symposium on Advanced Information Networking and Applications, pp. 807-811.
4. DeBrunner, L.S., V.E. DeBrunner and D. Bhogaraju (2002). Defining canonical-signed-digit number systems as arithmetic codes. In Proceedings of the 36th Asilomar Conference on Signals, Systems and Computers, vol. 2. pp. 1593-1597.
5. Diffie, W., and E. Hellmen (1976). New directions in cryptography. IEEE Transactions on Information Theory, 22(6), 644-654.
6. Dusse, S.R., and B.S. Kaliski (1990). A cryptographic library for the Motorola DSP 56000. In Proceedings of EUROCRYPT Workshop on Theory and Application of Cryptographic Techniques, Advances in Cryptology, LNCS 473. Springer-Verlag, pp. 230-244.
7. ElGamal, T. (1985). A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 31(4), 469-472.
8. Joye, M., and S.-M. Yen (2000). Optimal left-to-right binary signed-digit recoding. IEEE Transactions on Computers, 49(7), 740-748.
9. Ha, J.-C., and S.-J. Moon (1998). A common-multiplicand method to the Montgomery algorithm for speeding up exponentiation. Information Processing Letters, 66(2), 105-107.
10. Gordon, D.M. (1998). A survey of fast exponentiation methods. Journal of Algorithms, 27(1), 129-146.
11. Knuth, D.E. (1997). The. Art of Computer Programming, Vol. II: Seminumerical Algorithms, 3rd edition. MA: Addison-Wesley.
12. Koren, I. (2002). Computer Arithmetic Algorithms, 2nd edition. A.K. Peters, Natick, MA.
13. Kunihiro, N., and H. Yamamoto (2000). New methods for generating short addition chains. IEICE Transactions on Fundamentals, E83-A(1), 60-67.
14. Lee, S.-Y., Y.-J. Jeong and O.-J. Kwon (2002). A faster modular multiplication based on key size partitioning for RSA public-key cryptosystem. IEICE Transactions on Information and Systems, E85-D(4), 789-791.
15. Lou, D.-C., and C.-C. Chang (1996). Fast exponentiation method obtained by folding the exponent in half. Electronics Letters, 32(11), 984-985.
16. Montgomery, P.L. (1985). Modular multiplication without trial division. Mathematics of Computation, 44(170), 519-521.
17. Nedjah, N., and L.M. Mourelle (2002). Efficient parallel modular exponentiation algorithm. In Proceedings of the 2nd Advances in Information Systems (ADVIS) International Conference, pp. 405-414.
18. Nozaki, H., A. Shimbo and S. Kawamura (2003). RNS Montgomery multiplication algorithm for duplicate processing of base transformations. IEICE Transactions Fundamentals, E86-A(1), 89-97.
19. Premkumar, A.B. (2002). A formal framework for conversion from binary to residue numbers. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 49(2), 135-144.
20. Rivest, R.L., A. Shamir and L. Adleman (1978). A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM, 21(2), 120-126.
21. Su, C.-Y., S.-A. Hwang, P.-S. Chen and C.-W. Wu (1999). An improved Montgomery's algorithm's for high-speed RSA public-key cryptosystem. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 7(2), 280-284.
22. Syuto, M., E. Satake, K. Tanno and O. Ishizuka (2002). A high-speed binary to residue converter using a signed-digit number representation. IEICE Transactions on Information and Systems, E85-D(5), 903-905.
23. n) using normal basis. IEEE Transactions on Computers, 50(5), 394-398.
24. Tenca, A.F., and C.K. Koc (2003). A scalable architecture for modular multiplication based on Montgomery's algorithm. IEEE Transactions on Computers, 52(9), 1215-1221.
25. m) based on extended binary GCD algorithm. IEICE Transactions on Fundamentals, E85-A(5), 994-999.
26. Wei, S., S. Chen and K. Shimizu (2002). Fast modular multiplication using booth recoding based on signed-digit number arithmetic. In Proceedings of the 2nd IEEE Asia-Pacific Conference on Circuits and Systems. pp. 31-36.
27. Wu, T.-C., and Y.-S. Chang (1995). Improved generalization common-multiplicand multiplications algorithm of Yen and Laih. Electronics Letters, 31(20), 1738-1739.
28. Yen, S.-M. (1997). Improved common-multiplicand multiplication and fast exponentiation by exponent decomposition. IEICE Transactions on Fundamentals, E80-A(6), 1160-1163.
29. Yen, S.-M., and C.-S. Laih (1993a). Common-multiplicand multiplication and its applications to public key cryptography. IEE Electronics Letters, 29(17), 1583-1584.
30. Yen, S.-M., and C.-S. Laih (1993b). Common-multiplicand multiplication and its applications to public key cryptography. Electronics Letters, 29(17), 1583-1584.