A problem that has more than two possible yes/no outputs.
Complexity: NP-intermediate as of 2020:
- expected not to be NP-complete because it would imply NP != Co-NP: cstheory.stackexchange.com/questions/167/what-are-the-consequences-of-factoring-being-np-complete#comment104849_169
- expected not to be in P because "could we be that dumb that we haven't found a solution after having tried for that long?
This is natural question because both integer factorization and discrete logarithm are the basis for the most popular public-key cryptography systems as of 2020 (RSA and Diffie-Hellman key exchange respectively), and both are NP-intermediate. Why not use something more provenly hard?
- cs.stackexchange.com/questions/356/why-hasnt-there-been-an-encryption-algorithm-that-is-based-on-the-known-np-hard "Why hasn't there been an encryption algorithm that is based on the known NP-Hard problems?"
An important case is the discrete logarithm of the cyclic group in which the group is a cyclic group.
In this case, the problem becomes equivalent to reversing modular exponentiation.
This computational problem forms the basis for Diffie-Hellman key exchange, because modular exponentiation can be efficiently computed, but no known way exists to efficiently compute the reverse function.
Simple interview problem!
Note that the subsequences do not need to be contiguous.
Implementations:
Sample implementation:
