# Information Security and Cryptography Research Group

## Diffie-Hellman, Decision Diffie-Hellman, and Discrete Logarithms

### Ueli Maurer and Stefan Wolf

IEEE International Symposium on Information Theory — ISIT '98, IEEE, pp. 327, Aug 1998.

Let $G$ be a cyclic group of order $n$. With respect to polynomial-time non-uniform generic reductions, the Diffie-Hellman problem and the discrete logarithm problem are equivalent in $G$ if and only if $n$ contains no multiple large prime factors. The Diffie-Hellman decision problem is equivalent to the Diffie-Hellman problem in $G$ if and only if all prime factors of $n$ are small.

## BibTeX Citation

@inproceedings{MauWol98c,
author       = {Ueli Maurer and Stefan Wolf},
title        = {{D}iffie-{H}ellman, {D}ecision {D}iffie-{H}ellman, and Discrete Logarithms},
booktitle    = {IEEE International Symposium on Information Theory --- ISIT~'98},
pages        = 327,
year         = 1998,
month        = 8,
publisher    = {IEEE},
}