• DocumentCode
    927841
  • Title

    An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.)

  • Author

    Pohlig, Stephen C. ; Hellman, Martin E.

  • Volume
    24
  • Issue
    1
  • fYear
    1978
  • fDate
    1/1/1978 12:00:00 AM
  • Firstpage
    106
  • Lastpage
    110
  • Abstract
    A cryptographic system is described which is secure if and only if computing logarithms over GF(p) is infeasible. Previously published algorithms for computing this function require O(p^{1/2}) complexity in both time and space. An improved algorithm is derived which requires O =(\\log ^{2} p) complexity if p - 1 has only small prime factors. Such values of p must be avoided in the cryptosystem. Constructive uses for the new algorithm are also described.
  • Keywords
    Cryptography; Galois fields; Logarithms; Acoustics; Convolution; Convolutional codes; Cryptography; Decoding; Error correction codes; Notice of Violation; Reed-Solomon codes; Speech; Systems engineering and theory;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.1978.1055817
  • Filename
    1055817
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=927841