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The quadratic nonresidue problem has both an NP and a co-NP algorithm, and so lies in the intersection of NP and co-NP. This was also true of several other problems for which zero-knowledge proofs were subsequently discovered, such as an unpublished proof system by Oded Goldreich verifying that a two-prime modulus is not a Blum integer .
Diffie–Hellman (DH) key exchange [nb 1] is a mathematical method of securely generating a symmetric cryptographic key over a public channel and was one of the first public-key protocols as conceived by Ralph Merkle and named after Whitfield Diffie and Martin Hellman.
Quadratic programming (NP-hard in some cases, P if convex) Subset sum problem [3]: SP13 Variations on the Traveling salesman problem. The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric.
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Digital signatures, in which a message is signed with the sender's private key and can be verified by anyone who has access to the sender's public key. [9] This verification proves that the sender had access to the private key, and therefore is very likely to be the person associated with the public key.
The Subgraph Isomorphism problem is NP-complete. The graph isomorphism problem is suspected to be neither in P nor NP-complete, though it is in NP. This is an example of a problem that is thought to be hard, but is not thought to be NP-complete. This class is called NP-Intermediate problems and exists if and only if P≠NP.
In particular, it has been shown there exist languages A and B such that P A =NP A and P B ≠NP B. [4] The fact the P = NP question relativizes both ways is taken as evidence that answering this question is difficult, because a proof technique that relativizes (i.e., unaffected by the addition of an oracle) will not answer the P = NP question. [5]
A network service access point address (NSAP address), defined in ISO/IEC 8348, is an identifying label for a service access point (SAP) used in OSI networking.. These are roughly comparable to IP addresses used in the Internet Protocol; they can specify a piece of equipment connected to an Asynchronous Transfer Mode (ATM) network.