Dutta, Abhraneel (2014) *Introduction of Discrete Logarithm Problem and Mathematical Aspects of Modern Number Field Sieve Method of Solving Discrete Logarithm in Finite Field.* Masters thesis, Indian Institute of Science Education and Research Kolkata.

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## Abstract

There are numerous cryptosystems whose security is based on the di�culty of solving the discrete logarithm problem. . Several algorithms using number �eld sieve have been given to factor a number n in heuristic expected time Ln[1=3; c]. In my thesis I will introduce some general attacks on discrete logarithm problem including the modern method of number �eld sieve and the mathematical aspects behind it. I have concentrated her the basic foundations of algebraic number theory which are the building blocks of the number �eld sieve algorithm. And also I have studied the notions of a virtual logarithm of a prime �eld in a number ring and schirokauer's maps which Joux and Lercier recently have used to compute the logarithms in a prime �eld of a 120 decimal digits.

Item Type: | Thesis (Masters) |
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Additional Information: | Supervisor: Dr. Subhamoy Maitra and Dr. Satyaki Mazudmer |

Uncontrolled Keywords: | Discrete Logarithm; Finite Field; Modern Number Field; Sieve Method |

Subjects: | Q Science > QA Mathematics |

Divisions: | Department of Mathematics and Statistics |

Depositing User: | IISER Kolkata Librarian |

Date Deposited: | 19 Jan 2015 15:11 |

Last Modified: | 19 Jan 2015 15:12 |

URI: | http://eprints.iiserkol.ac.in/id/eprint/241 |

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