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Cryptanalysis of the Anshel-Anshel-Goldfeld-Lemieux Key Agreement Protocol

Cryptanalysis of the Anshel-Anshel-Goldfeld-Lemieux Key Agreement Protocol The Anshel-Anshel-Goldfeld-Lemieux (abbreviated AAGL) key agreement protocol Contemp. Math. 418: 1–34, 2006 is proposed to be used on low-cost platforms which constraint the use of computational resources. The core of the protocol is the concept of an Algebraic Eraser TM (abbreviated AE) which is claimed to be a suitable primitive for use within lightweight cryptography. The AE primitive is based on a new and ingenious idea of using an action of a semidirect product on a (semi)group to obscure involved algebraic structures. The underlying motivation for AAGL protocol is the need to secure networks which deploy Radio Frequency Identification (RFID) tags used for identification, authentication, tracing and point-of-sale applications. In this paper we revisit the computational problem on which AE relies and heuristically analyze its hardness. We show that for proposed parameter values it is impossible to instantiate a secure protocol. To be more precise, in 100% of randomly generated instances of the protocol we were able to find a secret conjugator z generated by the TTP algorithm (part of AAGL protocol). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

Cryptanalysis of the Anshel-Anshel-Goldfeld-Lemieux Key Agreement Protocol

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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/GCC.2009.63
Publisher site
See Article on Publisher Site

Abstract

The Anshel-Anshel-Goldfeld-Lemieux (abbreviated AAGL) key agreement protocol Contemp. Math. 418: 1–34, 2006 is proposed to be used on low-cost platforms which constraint the use of computational resources. The core of the protocol is the concept of an Algebraic Eraser TM (abbreviated AE) which is claimed to be a suitable primitive for use within lightweight cryptography. The AE primitive is based on a new and ingenious idea of using an action of a semidirect product on a (semi)group to obscure involved algebraic structures. The underlying motivation for AAGL protocol is the need to secure networks which deploy Radio Frequency Identification (RFID) tags used for identification, authentication, tracing and point-of-sale applications. In this paper we revisit the computational problem on which AE relies and heuristically analyze its hardness. We show that for proposed parameter values it is impossible to instantiate a secure protocol. To be more precise, in 100% of randomly generated instances of the protocol we were able to find a secret conjugator z generated by the TTP algorithm (part of AAGL protocol).

Journal

Groups - Complexity - Cryptologyde Gruyter

Published: Apr 1, 2009

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