### Abstract

In this paper, we study short exponent Diffie-Hellman problems, where significantly many lower bits are zeros in the exponent. We first prove that the decisional version of this problem is as hard as two well known hard problems, the standard decisional Diffie-Hellman problem (DDH) and the short exponent discrete logarithm problem. It implies that we can improve the efficiency of ElGamal scheme and Cramer-Shoup scheme under the two widely accepted assumptions. We next derive a similar result for the computational version of this problem.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Feng Bao, Robert Deng, Jianying Zhou |

Publisher | Springer Verlag |

Pages | 173-186 |

Number of pages | 14 |

ISBN (Print) | 3540210180, 9783540210184 |

DOIs | |

Publication status | Published - 2004 Jan 1 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2947 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Koshiba, T., & Kurosawa, K. (2004). Short exponent diffie-hellman problems. In F. Bao, R. Deng, & J. Zhou (Eds.),

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 173-186). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2947). Springer Verlag. https://doi.org/10.1007/978-3-540-24632-9_13