Introduction of Discrete Logarithm Problem and Mathematical Aspects of Modern Number Field Sieve Method of Solving Discrete Logarithm in Finite Field

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.

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