Related papers: About set-theoretic properties of one-way function…
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.…
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…
The existence of one-way functions is arguably the most important problem in computer theory. The article discusses and refines a number of concepts relevant to this problem. For instance, it gives the first combinatorial complete owf,…
We prove that P != NP by proving the existence of a class of functions we call Tau, each of whose members satisfies the conditions of one-way functions. Each member of Tau is a function computable in polynomial time, with negligible…
We examine possibility to design an efficient solving algorithm for problems of the class \np. It is introduced a classification of \np problems by the property that a partial solution of size $k$ can be extended into a partial solution of…
We present the finite first-order theory (FFOT) machine, which provides an atemporal description of computation. We then develop a concept of complexity for the FFOT machine, and prove that the class of problems decidable by a FFOT machine…
We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
The polynomial hierarchy is a grading of problems by difficulty, including P, NP and coNP as the best known classes. The promise polynomial hierarchy is similar, but extended to include promise problems. It turns out that the promise…
A problem based on the Extended Euclidean Algorithm applied to a class of polynomials with many factors is presented and believed to be hard. If so, it is a one-way function well suited for applications in digital signicatures.
In this note, we study the easy certificate classes introduced by Hemaspaandra, Rothe, and Wechsung, with regard to the question of whether or not surjective one-way functions exist. This is an important open question in cryptology. We show…
We say that a function is rare-case hard against a given class of algorithms (the adversary) if all algorithms in the class can compute the function only on an $o(1)$-fraction of instances of size $n$ for large enough $n$. Starting from any…
Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
In this tutorial, selected topics of cryptology and of computational complexity theory are presented. We give a brief overview of the history and the foundations of classical cryptography, and then move on to modern public-key cryptography.…
One-way functions are fundamental to classical cryptography and their existence remains a longstanding problem in computational complexity theory. Recently, a provable quantum one-way function has been identified, which maintains its…
We prove that the equivalence of two fundamental problems in the theory of computing. For every polynomial $t(n)\geq (1+\varepsilon)n, \varepsilon>0$, the following are equivalent: - One-way functions exists (which in turn is equivalent to…