Related papers: Zero-Knowledge Proofs of the Conjugacy for Permuta…
We show that the Double Coset Membership problem for permutation groups possesses perfect zero-knowledge proofs.
Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other…
Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…
We study conjugacy classes of solutions to systems of equations and inequations over torsion-free hyperbolic groups, and describe an algorithm to recognize whether or not there are finitely many conjugacy classes of solutions to such a…
We show that on an infinite set, there exist no other precomplete clones closed under conjugation except those which contain all permutations. Since on base sets of some infinite cardinalities, in particular on countably infinite ones, the…
We show that the perfect commutation graph is the sufficient tight condition for admitting the noncontextual description of each observable set satisfying it in the yes-no question scenario. With this condition, we propose a method for…
Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. An intrinsic characteristic of a zero-knowledge systems is the assumption that is…
We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a null…
The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a…
Conjugation spaces are equipped with an involution such that the fixed points have the same mod 2 cohomology (as a graded vector space, a ring, and even an unstable algebra) but with all degrees divided by 2, generalizing the classical…
Recursive permutations whose cycles are the classes of a decidable equivalence relation are studied; the set of these permutations is called $\mathrm{Perm}$, the group of all recursive permutations $\mathcal{G}$. Multiple equivalent…
Although the conjugacy classes of the general linear group are known, it is not obvious (from the canonic form of matrices) that two permutation matrices are similar if and only if they are conjugate as permutations in the symmetric group,…
Conjugacy separability of any group of the class of one-relator groups given by the presentation $<a, b; [a^m,b^n]=1>$ ($m,n>1$) is proven.
We prove the Complete nontrivial cycle-intersection theorem for systems of permutations.
We study the notion of zero-knowledge secure against quantum polynomial-time verifiers (referred to as quantum zero-knowledge) in the concurrent composition setting. Despite being extensively studied in the classical setting, concurrent…
The phase conjugation of an unknown Gaussian state cannot be realized perfectly by any physical process. A semi-classical argument is used to derive a tight lower bound on the noise that must be introduced by an approximate phase…
Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a…
Using the concept of algebraically closed groups, we prove that there is a countable torsion free group with exactly two conjugacy classes.
Foundational results in theoretical computer science have established that everything provable, is provable in zero knowledge. However, this assertion fundamentally assumes a classical interpretation of computation and many interesting…
In this short note we present a simple combinatorial trick which can be effectively applied to show the non--existence of sharply transitive sets of permutations in certain finite permutation groups.