Abstract

Given a finite field F q of order q, and g a primitive element of F q , the discrete logarithm base g of an arbitrary, non-zero y 2 F q is that integer x, 0 x q \Gamma 2, such that g x = y in F q . The security of many real-world cryptographic schemes depends on the difficulty of computing discrete logarithms in large finite fields. This thesis is a survey of the discrete logarithm problem in finite fields, including: some cryptographic applications (password authentication, the Diffie-Hellman key exchange, and the ElGamal public-key cryptosystem and digital signature scheme); Niederreiter's proof of explicit formulas for the discrete logarithm; and algorithms for computing discrete logarithms (especially Shank's algorithm, Pollard's ae-method, the Pohlig-Hellman algorithm, Coppersmith's algorithm in fields of order 2 n , and the Gaussian integers method for fields of prime order). This abstract accurately represents the content of the candidate's thesis. I recommend its publicat...

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