Related papers: Linear decomposition attack on public key exchange…
We show that a linear decomposition attack based on the decomposition method introduced by the first author in monography "Algebraic cryptography" and in a series of papers works by finding the exchanging key in the Abdrecut's protocol.
We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…
In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This…
In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our…
In a recent paper [arXiv:2009.00716], Rahman and Shpilrain proposed a new key-exchange protocol MAKE based on external semidirect product of groups. The purpose of this paper is to show that the key exchange protocol is insecure. We were…
We show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme of such type. In most cases, such schemes are built on…
We show that the attacks based on the linear decomposition method introduced by the author and the span-method introduced by Tsaban allow one to find the transmitted message in the cryptosystem and the exchanged key in the protocol which…
A generalization of the original Diffie-Hellman key exchange in $(\Z/p\Z)^*$ found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further…
We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z_p. One of the (semi)groups is additive, the other one multiplicative. This allows us to take advantage of both operations on…
All instances of the semidirect key exchange protocol, a generalisation of the famous Diffie-Hellman key exchange protocol, satisfy the so-called "telescoping equality"; in some cases, this equality has been used to construct an attack. In…
We propose new provable practical deterministic polynomial time algorithm for the braid Wang, Xu, Li, Lin and Wang Double shielded public key cryptosystems. We show that a linear decomposition attack based on the decomposition method…
The security of neural cryptography is investigated. A key-exchange protocol over a public channel is studied where the parties exchanging secret messages use multilayer neural networks which are trained by their mutual output bits and…
We present a cryptanalysis of a key exchange protocol based on the digital semiring. For this purpose, we find the maximal solution of a linear system over such semiring, and use the properties of circulant matrix to demonstrate that the…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
In this paper we use the nonrepresentable ring E_p(m)to introduce public key cryptosystems in noncommutative settings and based on the Semigrouop Action Problem and the Decomposition Problem respectively.
In this work, we introduce an active attack on a Group Key Exchange protocol by Burmester and Desmedt. The attacker obtains a copy of the shared key, which is created in a collaborative manner with the legal users in a communication group.
Recently, several cryptosystems have been proposed based semidirect products of various algebraic structures. Efficient attacks against several of them have already been given, along with a very general attack. The purpose of this note is…
It was recently demonstrated that the Matrix Action Key Exchange (MAKE) algorithm, a new type of key exchange protocol using the semidirect product of matrix groups, is vulnerable to a linear algebraic attack if the matrices are over a…
In this paper we present a new key establishment protocol based on the decomposition problem in non-commutative groups which is: given two elements $w, w_1$ of the platform group $G$ and two subgroups $A, B \subseteq G$ (not necessarily…
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…