The multi-dimension RSA and its low exponent security

Zhenfu Cao1
1Department of Mathematics, Harbin Institute of Technology, Harbin, China

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Tài liệu tham khảo

Rivest, R. L., Shamir, A., Adleman, L., A method for obtaining digital signatures and public key cryptosystems, Comm. ACM, 1978, 21: 120.

Salomaa, A., Public-Key Cryptography, New York: Springer-Verlag, 1990.

Cao Zhenfu, Public Key Cryptology (in Chinese), Harbin: Heilongjiang Education Press, 1993.

Sun, Qi, A kind of trap-door one-way functions over algebraic integer ring, Journal of Sichuan University (in Chinese), 1986, (2): 22.

Cao Zhenfu, Two new types of cryptosystems over Eisenstein’s ring ℤ[ω], J. Electronics, 1992, 14(3): 286.

Buchmann, J., Williams, H. C., Quadratic fields and cryptography, Number Theory and Cryptography (ed. Loxton, J. H.), Cambridge: Cambridge University Press, 1990, 9–25.

Sun, Q., A kind of Trap-Door one-way functions, Journal of Sichuan University (in Chinese), 1985, (4): 33.

Williams, H. C., Some public-key crypto-functions as intractable as factorization, Cryptologia, 1985, 9: 233.

Cao Zhenfu, On the security of the RSA based on a polynomial over finite fieldsZ p and a new analog of the RSA, J. of China Institute of Communications (in Chinese), 1999, 20(6): 15.

Boneh, D., Twenty years of attacks on the RSA cryptosystem, Notices of the AMS, 1999, 46(2): 203.

Wiener, M., Cryptanalysis of short RSA secret exponents, IEEE Trans. Inform. Theory, 1990, 36: 553.

Boneh, D., Durfee, G., New results on cryptanalysis of low private exponent RSA, Preprint, 1998.

Coppersmith, D., Small solutions to polynomial equations, and low exponent RSA vulnerabilities, J. Cryptology, 1997, 10: 233.

Hastad, J., Solving simultaneous modular equations of low degree, SIAM J. Comput., 1988, 17: 336.