Related papers: Assessing security of some group based cryptosyste…
Conjugacy is not the only possible primitive for designing braid-based protocols. To illustrate this principle, we describe a Fiat--Shamir-style authentication protocol that be can be implemented using any binary operation that satisfies…
We present an algorithm for solving the conjugacy search problem in the four strand braid group. The computational complexity is cubic with respect to the braid length.
Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability.…
In this paper we discuss generic properties of "random subgroups" of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they "sit" inside G in a very…
We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover's long-term private key. The latter would follow from solving the conjugacy search problem in the platform (noncommutative)…
Artin's braid groups have been recently suggested as a new source for public-key cryptography. In this paper we propose the first undeniable signature schemes using the conjugacy problem and the decomposition problem in the braid groups…
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new…
Analyzing the security of cryptosystems under attacks based on the malicious modification of memory registers is a research topic of high importance. This type of attacks may affect the randomness of the secret parameters by forcing a…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…
A paper presented at the ICICS 2019 conference describes what is claimed to be a `provably secure group authentication [protocol] in the asynchronous communication model'. We show here that this is far from being the case, as the protocol…
There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…
There are recent cryptographic protocols that are based on Multiple Simultaneous Conjugacy Problems in braid groups. We improve an algorithm, due to Sang Jin Lee and Eonkyung Lee, to solve these problems, by applying a method developed by…
We discuss the time complexity of the word and conjugacy search problems for free products $G = A \star_C B$ of groups $A$ and $B$ with amalgamation over a subgroup $C$. We stratify the set of elements of $G$ with respect to the complexity…
In 1991 the first public key protocol involving automaton groups has been proposed. In this paper we give a survey about algorithmic problems around automaton groups which may have potential applications in cryptography. We then present a…
Given a cryptographic group action, we show that the Group Action Inverse Problem (GAIP) and other related problems cannot be NP-hard unless the Polynomial Hierarchy collapses. We show this via random self-reductions and the design of…
Group ring NTRU (GR-NTRU) provides a general structure to design different variants of NTRU-like schemes by employing different groups. Although, most of the schemes in literature are built over cyclic groups, nonabelian groups can also be…
An improved design of a cryptosystem based on small Ree groups is proposed. We have changed the encryption algorithm and propose to use a logarithmic signature for the entire Ree group. This approach improves security against sequential key…
Software-based approaches for search over encrypted data are still either challenged by lack of proper, low-leakage encryption or slow performance. Existing hardware-based approaches do not scale well due to hardware limitations and…
Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in…