Abstract
Using a well-known result of polynomial over the finite field p , we show that the Euler-Fermat theorem holds inN [x]. We present a multi-dimension RSA cryptosystem and point out that low exponent algorithm of attacking RSA is not suitable for the multi-dimension RSA. Therefore, it is believed that the security of the new cryptosystem is mainly based on the factorization of large integers.
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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.
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Cao, Z. The multi-dimension RSA and its low exponent security. Sci. China Ser. E-Technol. Sci. 43, 349–354 (2000). https://doi.org/10.1007/BF02916982
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DOI: https://doi.org/10.1007/BF02916982