## Abstract

To examine the computational complexity of cryptographic primitives such as the discrete logarithm problem, the factoring problem and the Diffle-Hellman problem, we define a new problem called square-root exponent, which is a problem to compute a value whose discrete logarithm is a square root of the discrete logarithm of a given value. We analyze reduction between the discrete logarithm problem modulo a prime and the factoring problem through the square-root exponent. We also examine reductions among the computational version and the decisional version of the square-root exponent and the Diffie-Hellman problem and show that the gap between the computational square-root exponent and the decisional square-root exponent partially overlaps with the gap between the computational Diffie-Hellman and the decisional Diffie-Hellman under some condition.

Original language | English |
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Pages (from-to) | 1083-1091 |

Number of pages | 9 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E87-A |

Issue number | 5 |

Publication status | Published - 2004 May |

## Keywords

- Computing problem
- Decision problem
- Diffie-Hellman problem
- Discrete logarithm problem
- Factoring problem
- Square-root exponent

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics