Related papers: On One-way Functions and Kolmogorov Complexity
Alice and Bob are given two correlated n-bit strings x_1 and, respectively, x_2, which they want to losslessly compress and send to Zack. They can either collaborate by sharing their strings, or work separately. We show that there is no…
In this paper, the authors give the definitions of a coprime sequence and a lever function, and describe the five algorithms and six characteristics of a prototypal public key cryptosystem which is used for encryption and signature, and…
The main subject of the paper is everywhere complex sequences. An everywhere complex sequence is a sequence that does not contain substrings of Kolmogorov complexity less than $\alpha n-O(1)$ where $n$ is the length of substring and…
One-time programs are modelled after a black box that allows a single evaluation of a function, and then self-destructs. Because software can, in principle, be copied, general one-time programs exists only in the hardware token model: it…
A recent breakthrough [Hirahara and Nanashima, STOC'2024] established that if $\mathsf{NP} \not \subseteq \mathsf{ioP/poly}$, the existence of zero-knowledge with negligible errors for $\mathsf{NP}$ implies the existence of one-way…
We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem,…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
Sponge hashing is a widely used class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a…
The no-go theorem regarding unconditionally secure Quantum Bit Commitment protocols is a relevant result in quantum cryptography. Such result has been used to prove the impossibility of unconditional security for other protocols, such as…
We investigate quantum analogues of collision resistance and obtain separations between quantum ``one-way'' and ``collision-resistant'' primitives. 1. Our first result studies one-wayness versus collision-resistance defined over quantum…
We study the Isomorphism of Polynomial (IP2S) problem with m=2 homogeneous quadratic polynomials of n variables over a finite field of odd characteristic: given two quadratic polynomials (a, b) on n variables, we find two bijective linear…
The radical solution of polynomials with rational coefficients is a famous solved problem. This paper found that it is a $\mathbb{NP}$ problem. Furthermore, this paper found that arbitrary $ \mathscr{P} \in \mathbb{P}$ shall have a one-way…
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal…
We show that one-way functions exist if and only if there exists an efficient distribution relative to which almost-optimal compression is hard on average. The result is obtained by combining a theorem of Ilango, Ren, and Santhanam and one…
The paper revisits the robust $s$-$t$ path problem, one of the most fundamental problems in robust optimization. In the problem, we are given a directed graph with $n$ vertices and $k$ distinct cost functions (scenarios) defined over edges,…
For many algorithmic problems on graphs of treewidth $t$, a standard dynamic programming approach gives an algorithm with time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. It turns out that when one considers the more…
Given a sound first-order p-time theory $T$ capable of formalizing syntax of first-order logic we define a p-time function $g_T$ that stretches all inputs by one bit and we use its properties to show that $T$ must be incomplete. We leave it…
Circuit lower bounds are important since it is believed that a super-polynomial circuit lower bound for a problem in NP implies that P!=NP. Razborov has proved superpolynomial lower bounds for monotone circuits by using method of…
We give a public key encryption scheme with plausible quasi-exponential security based on the conjectured intractability of two constraint satisfaction problems (CSPs), both of which are instantiated with a corruption rate of $1 - o(1)$.…
In [3] a short proof is given that some strings have maximal plain Kolmogorov complexity but not maximal prefix-free complexity. The proof uses Levin's symmetry of information, Levin's formula relating plain and prefix complexity and Gacs'…