On non-abelian homomorphic public-key cryptosystems

An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f:G --> H, where G, H are (publically known) groups and H is finite. A letter of a message to be encrypted is an element h element of H, while its encryption g element of G is such that f(g)=h. A homomorphic cryptosystem allows one to perform computations (operating in a group G) with encrypted information (without knowing the original message over H). In this paper certain homomorphic cryptosystems are constructed for the first time for non-abelian groups H (earlier, homomorphic cryptosystems were known only in the Abelian case). In fact, we present such a system for any solvable (fixed) group H.Comment: 15 pages, LaTe

Cryptanalysis of group-based key agreement protocols using subgroup distance functions

We introduce a new approach for cryptanalysis of key agreement protocols based on noncommutative groups. This approach uses functions that estimate the distance of a group element to a given subgroup. We test it against the Shpilrain-Ushakov protocol, which is based on Thompson's group F

A new key exchange protocol based on the decomposition problem

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 distinct), find elements $a \in A, b \in B$ such that $w_1 = a w b$. Here we introduce two new ideas that improve the security of key establishment protocols based on the decomposition problem. In particular, we conceal (i.e., do not publish explicitly) one of the subgroups $A, B$, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a given finitely generated subgroup.Comment: 7 page

Homomorphic public-key cryptosystems and encrypting boolean circuits

In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over an appropriate finitely generated group