On the structure of the class NP

TL;DR

This paper introduces a new class UF within NP, proves P≠NP based on this class, and explores properties of one-way functions relevant to cryptology.

Contribution

It defines the class UF, establishes its implications for P vs NP, and analyzes properties of cryptographic one-way functions.

Findings

Proves P ≠ NP using the class UF

Defines the class UF as a subset of NP

Analyzes properties of one-way functions in cryptology

Abstract

A new class UF of problems is introduced, strictly included in the class NP, which arises in the analysis of the time verifying the intermediate results of computations. The implications of the introduction of this class are considered. First of all, we prove that $P\not= NP$ and establish that it needs to consider the problem "P vs UF" instead the problem "P vs NP". Also, we determine the set-theoretical of properties of a one-way functions that used in cryptology.