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

  • Authors:
  • S. Pohlig;M. Hellman

  • Affiliations:
  • -;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

A cryptographic system is described which is secure if and only if computing logarithms overGF(p)is infeasible. Previously published algorithms for computing this function requireO(p^{1/2})complexity in both time and space. An improved algorithm is derived which requiresO =(log^{2} p)complexity ifp - 1has only small prime factors. Such values ofpmust be avoided in the cryptosystem. Constructive uses for the new algorithm are also described.