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Pitfalls in public key cryptosystems based on free partially commutative monoids and groups

María Isabel González Vasco, Rainer Steinwandt
2006 Applied Mathematics Letters  
At INDOCRYPT 2003 Abisha, Thomas, and Subramanian proposed two public key schemes based on word problems in free partially commutative monoids and groups.  ...  We show that both proposals are vulnerable to chosen ciphertext attacks, and thus in the present form must be considered as insecure.  ...  Acknowledgments This work has been partially supported by the German Academic Exchange Service DAAD and the Spanish M.E.C. as part of the BaSe CoAT project within the Acciones Integradas Hispano-Alemanas  ... 
doi:10.1016/j.aml.2005.11.014 fatcat:utp3easzmvdktortnssuwpnm6u

Gröbner Basis Cryptosystems

Peter Ackermann, Martin Kreuzer
2006 Applicable Algebra in Engineering, Communication and Computing  
Over monoids presented by a finitely generated convergent string rewriting system we generalize Madlener's Gröbner basis theory based on prefix reduction from right ideals to right modules.  ...  In the first sections we extend and generalize Gröbner basis theory to submodules of free right modules over monoid rings.  ...  Rosenberger, and Springer Verlag for enabling us to disseminate these results to a wide audience.  ... 
doi:10.1007/s00200-006-0002-0 fatcat:fxvsivuxa5a6rc3vbmvqmlujrm

Length-Based Attacks for Certain Group Based Encryption Rewriting Systems [article]

James Hughes, Allen Tannenbaum
2003 arXiv   pre-print
In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld  ...  The attack in this paper is based on having a canonical representative of each string relative to which a length function may be computed. Hence the term length attack.  ...  Background on Monoid and Group Based Rewriting Systems In this section, we review some of the relevant concepts from group theory for rewriting based encryption.  ... 
arXiv:cs/0306032v1 fatcat:x6j7ch3o7vcjte7dunngqf6iiq

Using non-commutative monoids to construct three-party key establishment

Song Han, Elizabeth Chang, Tharam S. Dillon
2008 2008 2nd IEEE International Conference on Digital Ecosystems and Technologies  
In this paper, a novel three-party key agreement protocol is proposed. The protocol is based on non-commutative monoids in mathematics.  ...  It is a generic construction and one-time protocol per key establishment.  ...  In [4] , Vasco et al. proposed two attacks on a public key cryptosystem based on free partially commutative monoids and groups.  ... 
doi:10.1109/dest.2008.4635201 fatcat:uwchir5i7bbdtatjtje4t7emva

Secure web services using two-way authentication and three-party key establishment for service delivery

Song Han, Tharam Dillon, Elizabeth Chang, Biming Tian
2009 Journal of systems architecture  
Traditional approaches which can enable such transactions are based on peer-to-peer architecture or hierarchical group architecture.  ...  The former method resides on two-party communications while the latter resides on hierarchical group communications.  ...  In [44] , Vasco et al. proposed two attacks on a public key cryptosystem based on free partially commutative monoids and groups.  ... 
doi:10.1016/j.sysarc.2009.01.004 fatcat:6xy4fe6lxncw7mottvqzou4lqu

Braid Group Cryptography [article]

David Garber
2008 arXiv   pre-print
based on the braid group, and some of the known attacks on these cryptosystems.  ...  In the last decade, a number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed.  ...  Acknowledgements First, I wish to thank the organizers of the PRIMA school and conference on Braids which took place at Singapore in June 2007, Jon Berrick and Fred  ... 
arXiv:0711.3941v2 fatcat:etc5sbsvyvemplcyme2jeqsije

An Algebraic Characterization of Security of Cryptographic Protocols [article]

Manas K Patra, Yan Zhang
2008 arXiv   pre-print
Formal models proposed by Dolev and Yao to study the (unconditional) security of public key protocols form a group.  ...  In this case, we propose a definition in terms of pseudo-free groups.  ...  We investigate algebraic structures associated with a class of protocols based on public key cryptosystems.  ... 
arXiv:0802.3328v1 fatcat:iqrzpxv475hmlnqyoxd4mbop4q

Semidirect Product Key Exchange: the State of Play [article]

Christopher Battarbee, Delaram Kahrobaei, Siamak F. Shahandashti
2022 arXiv   pre-print
In this report we survey the various proposals of the key exchange protocol known as semidirect product key exchange (SDPKE).  ...  We discuss the various platforms proposed and give an overview of the main cryptanalytic ideas relevant to each scheme.  ...  Acknowledgement We wish to thank Vladimir Shpilrain for reading this manuscript and provided helpful comments.  ... 
arXiv:2202.05178v1 fatcat:h476ibsfjfaklktvchq46ctfee

Algorithmic problems in right-angled Artin groups: complexity and applications [article]

Ramón Flores, Delaram Kahrobaei, Thomas Koberda
2018 arXiv   pre-print
In this paper we consider several classical and novel algorithmic problems for right-angled Artin groups, some of which are closely related to graph theoretic problems, and study their computational complexity  ...  Kim and A. Sale for helpful comments and corrections.  ...  The authors are indebted to an anonymous referee who read the manuscript very carefully and provided a large number of helpful comments and corrections which greatly improved the paper.  ... 
arXiv:1802.04870v3 fatcat:6ccx3f4gwfh6zfox6esvnzb6iq

Lattice Polly Cracker cryptosystems

Massimo Caboara, Fabrizio Caruso, Carlo Traverso
2011 Journal of symbolic computation  
Using Gröbner bases for the construction of public key cryptosystems has been often attempted, but has always failed.  ...  We show how to build a cryptosystem based on lattice ideals and their Gröbner bases, and, after breaking a simple variant, we construct a more elaborate one.  ...  While LPC has shown that Gröbner bases can be used in the construction of public key cryptosystems, that apparently cannot be broken trivially, and perform quite reasonably compared with other lattice  ... 
doi:10.1016/j.jsc.2010.10.004 fatcat:cb7pm2rmifcslk6tb3tzi7yfsy

A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem [chapter]

Jung Hee Cheon, Byungheup Jun
2003 Lecture Notes in Computer Science  
We propose the first polynomial time algorithm for the braid Diffie-Hellman conjugacy problem (DHCP) on which the braid key exchange scheme and the braid encryption scheme are based [10] .  ...  We show the proposed method solves the DHCP for the image of braids under the Lawrence-Krammer representation and the solutions play the equivalent role of the original key for the DHCP of braids.  ...  Lee, and J. C. Cha for initial discussions on this problem. We also thank to D. Krammer for the comment on the inverting algorithm of the representation and S. Shin for helpful discussions.  ... 
doi:10.1007/978-3-540-45146-4_13 fatcat:wtksckbx3fegtlf5ffxm4qg4b4

Enhanced Matrix Power Function for Cryptographic Primitive Construction

Eligijus Sakalauskas
2018 Symmetry  
According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right.  ...  An example of the application of the proposed MPF for the Key Agreement Protocol (KAP) is presented.  ...  The author also gives thanks to his colleagues Aleksejus Mihalkovich and Inga Timofejeva for their contribution in the professional editing of this manuscript, testing example preparation, and other aid  ... 
doi:10.3390/sym10020043 fatcat:nph5nqzlcjfa5g3yfpcc633hv4

A Computer Proven Application Of The Discrete Logarithm Problem

Sebastian Kusch, Markus Kaiser
2007 Zenodo  
If an attacker succeeds in changing the public key data, faked signatures might be mistaken for legitimate ones since a correct verification requires the correct public key.  ...  Digital Signatures based on Asymmetric Cryptography For an asymmetric cryptosystem, let e be an arbitrary encryption key, d the corresponding decryption key, and E e as well as D d the associated encryption  ... 
doi:10.5281/zenodo.1332057 fatcat:rvvqxigyqbhwloskuq64aptvse

Mean-Set Attack: Cryptanalysis of Sibert et al. Authentication Protocol [article]

Natalia Mosina, Alexander Ushakov
2010 arXiv   pre-print
We analyze the Sibert et al. group-based (Feige-Fiat-Shamir type) authentication protocol and show that the protocol is not computationally zero-knowledge.  ...  In addition, we provide experimental evidence that our approach is practical and can succeed even for groups with no efficiently computable length function such as braid groups.  ...  Since then a number of new cryptographic protocols, including public-key authentication protocols, based on infinite groups were invented and analyzed.  ... 
arXiv:1006.4850v1 fatcat:qv3qkil2zzcndj4rjqwvozthpe

A Unification Algorithm for Analysis of Protocols with Blinded Signatures [chapter]

Deepak Kapur, Paliath Narendran, Lida Wang
2005 Lecture Notes in Computer Science  
In this theory, multiplication forms an Abelian group; exponentiation function distributes over multiplication, and exponents can commute.  ...  the commuting homomorphisms serving as indeterminates, is generalized to give a unification algorithm over the theory of Abelian groups with commuting homomorphism with a linear constraint.  ...  For instance, most public key based cryptosystems use multiplication, exponentiation, and modulus operations on numbers. Relations are specified by terminating rewrite rules.  ... 
doi:10.1007/978-3-540-32254-2_25 fatcat:a5tcdldv2bdohd4u3xlnexsrpq
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