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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]. (Update)
Context of citations to this paper: More
.... [11] and Research supported by NSF grant DMS 9631647 implemented in [33] A signature scheme using the same set was briefly mentioned in [8]. These ideas were subsequently adapted to real quadratic function fields over finite fields, where the set of reduced principal ideals...
...at least as difficult as factoring, and quite possibly harder. Real quadratic orders have also been proposed for use in these contexts [29, 2]. Breaking theses systems also appears to be at least as difficult as factoring, and they have the distinction of being the first...
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A Survey of Public-Key Cryptosystems - Koblitz, Menezes (Correct)
Computing Discrete Logarithms In Quadratic Orders - Jacobson, Jr. (2000) (Correct)
Cryptography in Quadratic Function Fields - Scheidler (1999) (Correct)
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1.0: Cryptographic Protocols Based on Discrete Logarithms in.. - Biehl, Buchmann, Thiel (1994) (Correct)
0.4: Number Theoretic Algorithms and Cryptology - Buchmann (1993) (Correct)
0.3: Discrete Logarithms: the Effectiveness of the Index.. - Schirokauer, Weber, Denny (1996) (Correct)
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0.6: Tools for Proving Zero Knowledge - Biehl, Buchmann, Meyer, Thiel, Thiel (1992) (Correct)
0.5: Algorithms for Quadratic Orders - Biehl, Buchmann (1993) (Correct)
0.3: Cryptographic Protocols Based on the Intractability of .. - Biehl, Buchmann.. (1999) (Correct)
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3: A Course in Computational Algebraic Number Theory (context) - Cohen - 1991
3: A key exchange system based on imaginary quadratic fields (context) - Buchmann, Williams - 1988
3: A subexponential algorithm for discrete logarithms over the rational subgroup of.. (context) - Adleman, DeMarrais et al. - 1994
BibTeX entry: (Update)
I. Biehl, J. A. Buchmann & C. Thiel, Cryptographic protocols based on discrete logarithms in real-quadratic orders. Proceedings of CRYPTO '94, Lecture Notes in Computer Science 839. Springer, New York 1994, 56--60. http://citeseer.ist.psu.edu/biehl94cryptographic.html More
@article{ biehl94cryptographic,
author = "Ingrid Biehl and Johannes A. Buchmann and Christoph Thiel",
title = "Cryptographic Protocols Based on Discrete Logarithms in Real-Quadratic Orders",
journal = "Lecture Notes in Computer Science",
volume = "839",
pages = "56--60",
year = "1994",
url = "citeseer.ist.psu.edu/biehl94cryptographic.html" }
Citations (may not include all citations):635 New directions in Cryptography - Diffie, Hellman - 1976
601 A public key cryptosystem and a signature scheme based on di.. (context) - ElGamal - 1985
257 Elliptic curve cryptosystems (context) - Koblitz - 1987
228 Use of Elliptic Curves in Cryptography (context) - Miller - 1986
143 The Digital Signature Standard (context) - of, Technology - 1992
34 Using the Number Field Sieve (context) - Gordon, Discrete - 1993
26 The infrastructure of a real quadratic field and its applica.. (context) - Shanks
18 An Implementation of the General Number Field Sieve - Buchmann, Loho et al. - 1993
13 A general number field sieve implementation (context) - Bernstein, Lenstra - 1993
11 A Key Exchange System Based on Real-quadratic Fields (context) - Buchmann, Williams - 1989
11 Short representation of quadratic integers - Buchmann, Thiel et al. - 1992
9 Algorithms for quadratic orders - Biehl, Buchmann - 1993
4 Number Theoretic Algorithms and Cryptology - Buchmann - 1991
3 Implementation of a Key Exchange Protocol Using Real Quadrat.. (context) - Scheidler, Buchmann et al. - 1990
Documents on the same site (http://www.informatik.tu-darmstadt.de/TI/Veroeffentlichung/reports/README.year.author.html): More
On the Security of a Modified Paillier Public-Key Primitive - Sakurai, Takagi (2002) (Correct)
On Some Computational Problems in Finite Abelian Groups - Buchmann, Jacobson, Jr.. (Correct)
Efficient Undeniable Signature Schemes Based on Ideal.. - Biehl, Paulus, Takagi (1999) (Correct)
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