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| Discrete Logarithms and the Diffie-Hellman Protocol |
This project is concerned with several computational complexity aspects
of the discrete logarithm problems and of cryptographic schemes based
on it. One of the main topics is the proof of the equivalence between
breaking the Diffie-Hellman protocol and computing discrete logarithms
in the underlying group. It is easy to construct groups for which the
equivalence holds, with essentially random parameters. Hence, from an
application viewpoint, the equivalence holds, while for an arbitrary group
the equivalence holds under a very plausible number-theoretic conjecture.
Contact: Ueli Maurer
Publications Concerning This Topic
Krzysztof Pietrzak
Composition Does Not Imply Adaptive Security
Advances in Cryptology - CRYPTO 2005, Lecture Notes in Computer Science, Springer-Verlag, vol. 3621, pp. 55-65, Aug 2005.
Available files:
[ Postscript ]
[ PDF ]
[ Abstract ]
[ BibTeX ]
Ueli Maurer and Stefan Wolf
The Diffie-Hellman Protocol
Designs, Codes and Cryptography, Special Issue Public Key Cryptography, Kluwer Academic Publishers, vol. 19, no. 3, pp. 147-171, Jan 2000.
Available files:
[ Postscript ]
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[ Abstract ]
[ BibTeX ]
Ueli Maurer and Stefan Wolf
The Relationship Between Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms
SIAM Journal on Computing, vol. 28, no. 5, pp. 1689-1721, Apr 1999.
Available files:
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[ Abstract ]
[ BibTeX ]
Ueli Maurer and Stefan Wolf
Lower Bounds on Generic Algorithms in Groups
Advances in Cryptology - EUROCRYPT '98, Lecture Notes in Computer Science, Springer-Verlag, vol. 1403, pp. 72-84, May 1998.
Available files:
[ Postscript ]
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Ueli Maurer and Stefan Wolf
Diffie-Hellman, Decision Diffie-Hellman, and Discrete Logarithms
IEEE International Symposium on Information Theory - ISIT '98, IEEE, pp. 327, Aug 1998.
Available files:
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Ueli Maurer and Stefan Wolf
On the Hardness of the Diffie-Hellman Decision Problem
1998, Manuscript.
Available files:
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Jan Camenisch
Group Signature Schemes and Payment Systems Based on the Discrete Logarithm Problem
PhD thesis, ETH Zurich, 1998.
Reprint as vol. 2 of ETH Series in Information Security and Cryptography, ISBN 3-89649-286-1, Hartung-Gorre Verlag, Konstanz, 1998.
Available files:
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[ Abstract ]
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Ueli Maurer and Stefan Wolf
The Generic Complexity of Index-Search Problems and Applications to Cryptography
1997, Manuscript.
Available files:
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Ueli Maurer and Stefan Wolf
On the Complexity of Breaking the Diffie-Hellman Protocol
Technical Report 244, Institute for Theoretical Computer Science, ETH Zurich, Apr 1996.
Available files:
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Ueli Maurer and Stefan Wolf
Diffie-Hellman Oracles
Advances in Cryptology - CRYPTO '96, Lecture Notes in Computer Science, Springer-Verlag, vol. 1109, pp. 268-282, Aug 1996.
Available files:
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Ueli Maurer
Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms
Advances in Cryptology - CRYPTO '94, Lecture Notes in Computer Science, Springer-Verlag, vol. 839, pp. 271-281, Aug 1994.
Available files:
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[ Abstract ]
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Jan Camenisch, Jean-Marc Piveteau, and Markus Stadler
Blind Signatures Based on the Discrete Logarithm Problem
Advances in Cryptology - EUROCRYPT '94, Lecture Notes in Computer Science, Springer-Verlag, vol. 950, pp. 428-432, May 1994.
Available files:
[ Postscript ]
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[ Abstract ]
[ BibTeX ]
Main Research Page
Number-Theoretic and Algebraic Cryptography
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