Abstract
We generalize and improve the schemes of [4]. We introduce analogues of exponentiation and discrete logarithms in the principle cycle of real quadratic orders. This enables us to implement many cryptographic protocols based on discrete logarithms, e.g. a variant of the signature scheme of ElGamal [8].
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References
Bernstein, D.J., Lenstra, A.K.: A general number field sieve implementation. In: A. K. Lenstra, H. W. Lenstra, Jr. (Eds.) The Development of the Number Field Sieve (LNM 1554) (1993), Springer-Verlag, pp. 103–126
Buchmann, J., Thiel, C., Williams, H.C.: Short representation of quadratic integers. To appear in Proc. of CANT 1992
Buchmann, J.: Number Theoretic Algorithms and Cryptology. Proc. of FCT’91 (LNCS 529) (1991), Springer-Verlag, pp. 16–21
Buchmann, J., Williams, H.C.: A Key Exchange System Based on Real-quadratic Fields. Proc. of CRYPTO’89 (LNCS 435) (1989), Springer-Verlag, pp. 335–343
Buchmann, J., Loho, J., Zayer, J.: An Implementation of the General Number Field Sieve. Proc. of CRYPTO’93 (LNCS 773) (1993), Springer-Verlag, pp. 159–165
Biehl, I., Buchmann, J.: Algorithms for quadratic orders. To appear in Proc. of Symposia in Applied Mathematics (1993)
Diffie, W., Hellman, M.: New directions in Cryptography. IEEE Trans. Inform. Theory 22 (1976), pp. 472–492
ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inform. Theory 31 (1985), pp. 469–472
Gordon, D.: Discrete Logarithms in GF(p) Using the Number Field Sieve. Siam Jour. on Discrete Math. 6 (1993), pp. 124–138
Koblitz, N.: Elliptic curve cryptosystems. Math. Comp. 48 (1987), pp. 203–209
Miller, V.: Use of Elliptic Curves in Cryptography. Proc. of CRYPTO’85 (LNCS 218) (1986), Springer-Verlag, pp. 417–426
National Institute of Standards and Technology. The Digital Signature Standard, proposal and discussion. Comm. of the ACM, 35(7), Juli 1992, pp. 36–54
Scheidler, R., Buchmann, J., Williams, H.C.: Implementation of a Key Exchange Protocol Using Real Quadratic Fields. Proc. of EUROCRYPT’90 (LNCS 473) (1990), Springer-Verlag, pp. 98–109
Shanks, D.: The infrastructure of a real quadratic field and its applications. Proc. of the 1972 Number Theory Conference, Boulder (1972), pp. 217–224
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© 1994 Springer-Verlag Berlin Heidelberg
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Biehl, I., Buchmann, J., Thiel, C. (1994). Cryptographic Protocols Based on Discrete Logarithms in Real-quadratic Orders. In: Desmedt, Y.G. (eds) Advances in Cryptology — CRYPTO ’94. CRYPTO 1994. Lecture Notes in Computer Science, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48658-5_7
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DOI: https://doi.org/10.1007/3-540-48658-5_7
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