### 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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Pages (from-to) | 173-186 |

Number of pages | 14 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2947 |

Publication status | Published - 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

**Short exponent diffie-hellman problems.** / Koshiba, Takeshi; Kurosawa, Kaoru.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 2947, pp. 173-186.

}

TY - JOUR

T1 - Short exponent diffie-hellman problems

AU - Koshiba, Takeshi

AU - Kurosawa, Kaoru

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=35048903103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35048903103&partnerID=8YFLogxK

M3 - Article

VL - 2947

SP - 173

EP - 186

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -