International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Alexander Ushakov

Affiliation: Stevens Institue of Technology

Publications

Year
Venue
Title
2015
EPRINT
2015
EPRINT
2007
PKC
2006
PKC
2005
CRYPTO
2005
EPRINT
A new key exchange protocol based on the decomposition problem
Vladimir Shpilrain Alexander Ushakov
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 of 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 In particular, we conceal (i.e., do not publish explicitly) one of the subgroups A, B, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a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.
2004
EPRINT
The conjugacy search problem in public key cryptography: unnecessary and insufficient
Vladimir Shpilrain Alexander Ushakov
The conjugacy search problem in a group $G$ is the problem of recovering an $x \in G$ from given $g \in G$ and $h=x^{-1}gx$. This problem is in the core of several recently suggested public key exchange protocols, most notably the one due to Anshel, Anshel, and Goldfeld, and the one due to Ko, Lee at al. In this note, we make two observations that seem to have eluded most people's attention. The first observation is that solving the conjugacy search problem is not necessary for an adversary to get the common secret key in the Ko-Lee protocol. It is sufficient to solve an apparently easier problem of finding $x, y \in G$ such that $h=ygx$ for given $g, h \in G$. Another observation is that solving the conjugacy search problem is not sufficient for an adversary to get the common secret key in the Anshel-Anshel-Goldfeld protocol.