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On the Use of Complexity In Cryptography

A computational complexity gap, captured in the definition of one-way functions, is a necessary and sufficient condition for much of modern cryptography. Loosely speaking, one-way functions are functions that are easy to compute but hard to invert (in an average-case sense). The existence of one-way functions implies that P is different than NP , which means that such a complexity gap is only wide conjectured to exist (rather than known for a fact). We demonstrate the use of this gap in the case of two basic cryptographic tasks: The tasks of providing secret and authenticated communication, which in turn are reduced to the construction of encryption and signature schemes.