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This paper examines the practical feasibility of solving the discrete logarithm problem in finite fields of characteristic two, which is a fundamental assumption underlying many cryptographic systems. The authors implement a massively parallel version of Coppersmith’s algorithm and introduce an improved method for smoothness testing to enhance performance. Through extensive computational experiments, they demonstrate that discrete logarithms can be computed in fields as large as GF(2⁵⁰³), significantly extending previously known limits. The study also identifies both strengths and weaknesses in earlier theoretical analyses of the algorithm. Overall, the paper highlights how advances in parallel computing can reduce the security margins of cryptographic systems based on discrete logarithms.

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245: $a: Massively Parallel Elliptic Curve Factoring
245: $b:
082: $a:
100: $a: B. Dixon & Arjen K. Lenstra
650: $a: Computer Science
250: $a:
440: $v:
250: $b: Springer Verlag
250: $c: 1998
020: $a:
300: $a: 11