On the Distribution of the Diffie-Hellman Pairs

  • Authors:
  • Igor E. Shparlinski

  • Affiliations:
  • Department of Computing, Macquarie University, Sydney, NSW 2109, Australiaf1igor@comp.mq.edu.auf1

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2002

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Abstract

Let F"p be a prime field of p elements and let g be an element of F"p of multiplicative order t modulo p. We show that for any @e0 and t=p^1^/^3^+^@e the distribution of the Diffie-Hellman pairs (x, g^x) is close to uniform in the Cartesian product Z"txF"p, where x runs through*the residue ring Z modulo (that is, as in the classical Diffie-Hellman scheme); *The all -sums =+...+, 1@?