An observation concerning the complexity of problems with few solutions and its application to cryptography

  • Shimon Even
  • Yacov Yacobi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 100)


In this paper we state a hypothesis which is an extension of NP ≠ CoNP. We show that this new hypothesis implies the following statement: If a decision problem A is solvable by a Nondeterministic Turing Machine (NDTM) — M in polynomial time, and there is at most one computational path of M which leads to a ‘yes’ answer — then A is not NP-hard. We apply this result to Cryptography, and show that if our new hypothesis is true then a well designed cryptosystem, whose cracking problem is NP-hard, contains a large subproblem which is not NP-hard.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Shimon Even
    • 1
  • Yacov Yacobi
    • 2
  1. 1.Computer Science Department, TechnionHaifaISRAEL
  2. 2.Electrical Engineering Department, TechnionHaifaISRAEL

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