Abstract
We show how to use ideal arithmetic in the divisor class group of an affine normal subring of K[X, Y] generated by monomials, where K is a field, to design new public-key cryptosystems, whose security is based on the difficulty of the discrete logarithm problem in the divisor class group of that integral domain.
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Adams, W., Loustaunau, P.: An introduction to Gröbner bases, Graduate Studies in Mathematics vol. 3, Amer. Math. Soc., Providence, 1994.
Anderson, D. F.: Subrings of k[X, Y] generated by monomials. Canad. J. Math. 30 (1978) 215–224.
Buchmann, J., Düllmann, S.: On the computation of discrete logarithm in class groups, in Advances in Cryptology-CRYPTO’ 90, LNCS 537, Springer-Velag, Berlin, 1991, pp. 134–139.
Buchmann, J., Willams, H. C.: A key-exchange system based on imaginary quadratic fields. J. Cryptology 1 (1988) 107–118.
Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer-Velag, New York, 1997.
Denning, D. E.: Cryptography and Data Security, Addison-Wesley, Reading, Massachusetts, 1982.
Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inform. Theory 22 (1976) 472–492.
Gilmer, R.: Multiplicative Ideal Theory, Queen’s Papers in Pure and Applied Mathematics, vol 90, Queen’s University, Kingston, Ontario, 1992.
Grayson, D., Stillman, M.: Macaulay 2, 1996. Available via anonymous ftp from http://www.math.uiuc.edu.
Hafner, J. L., McCurley, K. S.: A rigorous subexponential algorithm for computation of class group. J. Amer. Math. Soc. 2 (1989) 837–850.
Jacobson Jr., M. J.: Computing discrete logarithms in quadratic orders. J. Cryptology 13 (2000) 473–492.
Koblitz, N.: Elliptic curve cryptosystems. Math. Comp. 48 (1987) 203–209.
Koblitz, N.: Hyperelliptic cryptosystems. J. Cryptology 1 (1989) 139–150.
McCurley, K. S.: Cryptographic key distribution and computation in class groups, in R. A. Mollin, editor, Number Theory and Applications, Kluwer Academic Publishers, 1989, pp. 459–479.
Odlyzko, A. M.: Discrete logarithms in finite fields and their cryptographic significance, Advances in Cryptology-EUROCRYPT’ 84, LNCS 209, Springer-Velag, Berlin, 1985, pp. 224–314.
Paulus, S., Takaki, T.: A new public-key cryptosystem over a quadratic order with quadratic decryption time. J. Cryptology 13 (2000) 263–272.
Rivest, R. L., Shamir, A., Adelman, L.: A method for abtaining digital signatures and public key cryptosystems. Communications of the ACM 21 (1978) 120–126.
Vasconcelos, W. V.: Computational Methods in Commutative Algebra and Algebraic Geometry, Algorithms and Computation in Mathematics, vol. 2, Springer-Velag, Berlin, 1998.
Winkler, F.: On the complexity of the Gröbner-bases algorithm over K[x, y, z]. EUROSAM’ 84, LNCS 174, Springer, Berlin, 1984, pp. 184–194.
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Kim, H., Moon, S. (2001). New Public-Key Cryptosystem Using Divisor Class Groups. In: Varadharajan, V., Mu, Y. (eds) Information Security and Privacy. ACISP 2001. Lecture Notes in Computer Science, vol 2119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47719-5_8
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DOI: https://doi.org/10.1007/3-540-47719-5_8
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