Inferring a sequence generated by a linear congruence

  • Authors:
  • Joan B. Plumstead

  • Affiliations:
  • -

  • Venue:
  • SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
  • Year:
  • 1982

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Abstract

Suppose it is known that {X0, X1,...,Xn} is produced by a pseudo-random number generator of the form Xi+1 = aXi + b mod m, but a, b, and m are unknown. Can one efficiently predict the remainder of the sequence with knowledge of only a few elements from that sequence? This question is answered in the affirmative and an algorithm is given.