Short-exponent RSA

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E92-A, Issue 3, 2009, Pages 912-918

  Sun, Hung Min ^a   Yang, Cheng Ta ^b   Wu, Mu En ^a  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

^b NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

Digital signature; Encryption; Public key cryptosystem; RSA

Indexed keywords

ECONOMIC AND SOCIAL EFFECTS; ELECTRONIC DOCUMENT IDENTIFICATION SYSTEMS; POLYNOMIALS; PUBLIC KEY CRYPTOGRAPHY;

COMPUTATIONAL COSTS; FEASIBILITY ANALYSIS; MODULAR POLYNOMIAL; PRIME FACTORS; PUBLIC KEY CRYPTOSYSTEMS; RSA PUBLIC-KEY CRYPTOSYSTEM; SECURITY ANALYSIS; SIGNING PROCESS;

CRYPTOGRAPHY;

EID: 77956073401     PISSN: 09168508     EISSN: 17451337     Source Type: Journal    
DOI: 10.1587/transfun.E92.A.912     Document Type: Article

References (27)

1. 0.292," Proc. Eurocrypt'99, LNCS 1592, pp.1-11, 1999.
2. 0.292," IEEE Trans. Inf. Theory, vol.46, no.4, pp.1339- 1349, July 2000.
3. S. Cavallar, B. Dodson, A.K. Lenstra, W. Lioen, P.L. Montgomery, B. Murphy, H. te Riele, K. Aardal, J. Gilchrist, G. Guillerm, P. Leyland, J. Marchand, F. Morain, A. Muffett, C. Putnam, C. Putnam, and P. Zimmermann, "Factorization of 512-bit RSA key using the number field sieve," Proc. Eurocrypt'00, LNCS 1807, pp.1-18, 2000.
4. D. Coppersmith, "Finding a small root of a bivariate integer equation; Factoring with high bits known," Proc. Eurocrypt'96, LNCS 1070, pp.178-189, 1996.
5. C. Crépeau and A. Slakmon, "Simple backdoors for RSA key generation," Topics in Cryptology-CT-RSA 2003, LNCS 2612, pp.403- 416, Springer-Verlag, 2003.
6. G. Durfee and P. Nguyen, "Cryptanalysis of the RSA schemes with short secret exponent from Asiacrypt'99," Proc. Asiacrypt'00, LNCS 1976, pp.14-29, 2000.
7. I.N. Herstein, Topics in Algebra, Xerox Corporation, 1975.
8. Y. Frankel, "A practical protocol for large group oriented networks," Proc. Eurocrypt'89, LNCS 0434, pp.56-61, 1989.
9. H.S. Hong, H.K. Lee, H.S. Lee, and H.J. Lee, "The better bound of private key in RSA with unbalanced primes," Appl. Math. Comput., vol.139, pp.351-362, 2003.
10. S.D. Galbraith, C. Heneghan, and J.F. McKee, "Tunable balancing of RSA. Information security and privacy," 10th Australasian Conference- ACISP 2005, LNCS 3574, pp.280-292, 2005.
11. D. Alpern. (2003, Oct.). Available: http://www.alpertron.com.ar/ECM.HTM
12. M. Joye, J.J. Quisquater, S.M. Yen, and M. Yung, "Security paradoxes: How improving a cryptosystem may weaken it," Proc. Ninth National Conference on Information Security, pp.27-32, 1999.
13. A. Lenstra, H. Lenstra, and L. Lovasz, "Factoring polynomial with rational coefficients," Mathematiche Annalen, vol.261, pp.515-534, 1982.
14. H.W. Lenstra, Jr., "Factoring integers with elliptic curves," Annuals of Mathematics, vol.126, pp.649-673, 1987.
15. A.J. Menezes, P.C. van Oorschot, and S.A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997.
16. R. Pinch, "Extending the Wiener attack to RSA-type cryptosystems," Electron. Lett., vol.31, pp.1736-1738, 1995.
17. J. Pollard, "Theorems of factorization and primality testing," Proc. Cambridge Philos. Soc., pp.76:521-528, 1974.
18. R.L. Rivest, A. Shamir, and L.M. Adleman, "A method for obtaining digital signatures and public-key cryptosystems," Commun. ACM, vol.21, pp.120-126, 1987.
19. R. Rivest and R.D. Silverman, "Are strong primes needed for RSA?," 1997 RSA Laboratories Seminar Series, Seminar Proceedings, 1997.
20. R. Sakai, M. Morii, and M. Kasahara, "New key generation algorithm for RSA cryptosystem," IEICE Trans. Fundamentals, vol.E77- A, no.1, pp.89-97, Jan. 1994.
21. H.M. Sun, W.C. Yang, and C.S. Laih, "On the design of RSA with short secret exponent," Proc. Asiacrypt'99, LNCS 1716, pp.150- 164, 1999.
22. H.M. Sun and M.E. Wu, "Design of rebalanced RSA-CRT for fast encryption," Information Security Conference 2005, pp.16-27, 2005.
23. H.M. Sun, M.J. Hinek, and M.E. Wu, "On the design of rebalanced RSA-CRT," Technical Report CACR 2005-35, 2005.
24. E. Verheul and H. van Tilborg, "Cryptanalysis of less short RSA secret exponents," Applicable Algebra in Engineering, Communication and Computing, vol.8, pp.425-435, 1997.
25. B. de Weger, "Cryptanalysis of RSA with small prime difference," Applicable Algebra in Engineering, Communication and Computing, vol.13, pp.17-28, 2002.
26. M. Wiener, "Cryptanalysis of short RSA secret exponents," IEEE Trans. Inf. Theory, vol.36, no.3, pp.553-558, 1990.
27. A. Young and M. Yung, "The dark side of "black-box" cryptography, or: Should we trust capstone?," Advances in Cryptology- CRYPTO'96, LNCS 1109, pp.89-103, 1996.