Related papers: Zero-Knowledge Proofs of the Conjugacy for Permuta…
We propose and develop a novel and effective perfect sampling methodology for simulating from posteriors corresponding to mixtures with either known (fixed) or unknown number of components. For the latter we consider the Dirichlet…
The conjugacy problem for a finitely generated group $G$ is the two-variable problem of deciding for an arbitrary pair $(u,v)$ of elements of $G$, whether or not $u$ is conjugate to $v$ in $G$. We construct examples of finitely generated,…
Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. Quantum zero-knowledge protocols have been proposed but, since their implementation…
We prove, under mild conditions on fixed points and two cycles, the asymptotic normality of vincular pattern counts for a permutation chosen uniformly at random in a conjugacy class.Additionally, we prove that the limiting variance is…
In this paper we consider the {\em conjugacy stability} property of subgroups and provide effective procedures to solve the problem in several classes of groups. In particular, we start with free groups, that is, we give an effective…
Let $G$ be a finite almost simple group of Lie type acting faithfully and primitively on a set $\Omega$. We prove an analogue of the Boston--Shalev conjecture for conjugacy classes: the proportion of conjugacy classes of $G$ consisting of…
A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of alternating groups.
This paper studies the complexity classes QZK and HVQZK of problems having a quantum computational zero-knowledge proof system and an honest-verifier quantum computational zero-knowledge proof system, respectively. The results proved in…
The study of rational relations is fundamental to the study of formal languages and automata theory. A rational relation is conjugate if each pair of words in the relation is conjugate (or cyclic shifts of each other). The notion of…
We prove that a finite group is rational if and only if it has a set of permutation characters which separate conjugacy classes. It follows from this that a finite group is rational if and only if it has a representation as a permutation…
Perez-Marco proved the existence of non-trivial totally invariant connected compacts called hedgehogs near the fixed point of a nonlinearizable germ of holomorphic diffeomorphism. We show that if two nonlinearisable holomorphic germs with a…
The zero divisor conjecture is sufficient to prove for certain class of finitely presented groups where the relations are given by a pairing of generators. We associate Mealy automata to such pairings, and prove that the zero divisor…
A semigroup conjugacy is an equivalence relation that equals group conjugacy when the semigroup is a group. In this note, we answer five open problems related to semigroup conjugacy. (Problem One) We say a conjugacy ~ is partition-covering…
We consider pairs of finitely presented, residually finite groups $P\hookrightarrow\G$ for which the induced map of profinite completions $\hat P\to \hat\G$ is an isomorphism. We prove that there is no algorithm that, given an arbitrary…
This paper proves that several interactive proof systems are zero-knowledge against quantum attacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class…
We say that two elements of a group or semigroup are $\Bbbk$-linear conjugates if their images under any linear representation over $\Bbbk$ are conjugate matrices. In this paper we characterize $\Bbbk$-linear conjugacy for finite semigroups…
The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} =…
Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical…
A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. We prove that limit…
We present a protocol for verification of ``no such entry'' replies from databases. We introduce a new cryptographic primitive as the underlying structure, the keyed hash tree, which is an extension of Merkle's hash tree. We compare our…