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Computing discrete logarithms with the general number field sieve

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Algorithmic Number Theory (ANTS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1122))

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Abstract

The difficulty in solving the discrete logarithm problem is of extreme cryptographic importance since it is widely used in signature schemes, message encryption, key exchange, authentication and so on ([15], [17], [21], [29] etc.). The General Number Field Sieve (GNFS) is the asymptotically fastest known method to compute discrete logs mod p [18]. With the first implementation of the GNFS for discrete logs by using Schirokauer's improvement [27] we were able to show its practicability [31].

In this report we write about a new record in computing discrete logarithms mod p and some experimental data collected while finishing the precomputation step for breaking K. McCurley's 129-digit challenge [10].

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  1. FB Informatik, Universität des Saarlandes, Postfach 151150, 66041, Saarbrücken, Germany

    Damian Weber

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  1. Damian Weber
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Henri Cohen

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© 1996 Springer-Verlag Berlin Heidelberg

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Weber, D. (1996). Computing discrete logarithms with the general number field sieve. In: Cohen, H. (eds) Algorithmic Number Theory. ANTS 1996. Lecture Notes in Computer Science, vol 1122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61581-4_70

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  • DOI: https://doi.org/10.1007/3-540-61581-4_70

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61581-1

  • Online ISBN: 978-3-540-70632-8

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