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