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The Conjugacy Search Problem in Public Key Cryptography: Unnecessary and Insufficient

The Conjugacy Search Problem in Public Key Cryptography: Unnecessary and Insufficient 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 et 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Applicable Algebra in Engineering, Communication and Computing" Springer Journals

The Conjugacy Search Problem in Public Key Cryptography: Unnecessary and Insufficient

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer-Verlag
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Symbolic and Algebraic Manipulation ; Theory of Computation ; Computer Hardware
ISSN
0938-1279
eISSN
1432-0622
DOI
10.1007/s00200-006-0009-6
Publisher site
See Article on Publisher Site

Abstract

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 et 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.

Journal

"Applicable Algebra in Engineering, Communication and Computing"Springer Journals

Published: Aug 1, 2006

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