Strongly Secure Authenticated Key Exchange from Factoring, Codes, and Lattices

Establishing secure channels is one of the most important areas of cryptographic research. Secure channels provide secrecy and authenticity for both communication parties. When parties can share secret information via a public communication channel, secure channels would be constructed on (symmetric key) encryptions and message authentication codes with the shared secret information called session keys. Public-key cryptography can provide various solutions: one approach uses a Key Encapsulation Mechanism (KEM) and another uses Authenticated Key Exchange (AKE). An unresolved problem in research on Authenticated Key Exchange (AKE) is to construct a secure protocol against advanced attacks such as key compromise impersonation and maximal exposure attacks without relying on random oracles.