## Abstract

Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u ∈ GF(q) is that integer k, 1 ≤ k ≤ q−1, for which u = g ^{k}. The well-known problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its applicability in cryptography. Several cryptographic systems would become insecure if an efficient discrete logarithm algorithm were discovered. This paper surveys and analyzes known algorithms in this area, with special attention devoted to algorithms for the fields GF(2^{n}). It appears that in order to be safe from attacks using these algorithms, the value of n for which GF(2^{n}) is used in a cryptosystem has to be very large and carefully chosen. Due in large part to recent discoveries, discrete logarithms in fields GF(2^{n}) are much easier to compute than in fields GF(p) with p prime. Hence the fields GF(2^{n}) ought to be avoided in all cryptographic applications. On the other hand, the fields GF(p) with p prime appear to offer relatively high levels of security.

Original language | English (US) |
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Title of host publication | Advances in Cryptology |

Subtitle of host publication | Proceedings of EUROCRYPT 1984 - A Workshop on the Theory and Application of Cryptographic Techniques |

Editors | Ingemar Ingemarsson, Norbert Cot, Thomas Beth |

Publisher | Springer Verlag |

Pages | 224-314 |

Number of pages | 91 |

ISBN (Print) | 9783540160762 |

DOIs | |

State | Published - 1985 |

Event | Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1984 - Paris, France Duration: Apr 9 1984 → Apr 11 1984 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 209 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1984 |
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Country/Territory | France |

City | Paris |

Period | 4/9/84 → 4/11/84 |

### Bibliographical note

Publisher Copyright:© 1985, Springer-Verlag Berlin Heidelberg.