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Pitfalls in public key cryptosystems based on free partially commutative monoids and groups
2006
Applied Mathematics Letters
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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
2006
Applicable Algebra in Engineering, Communication and Computing
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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]
2003
arXiv
pre-print
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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
2008
2008 2nd IEEE International Conference on Digital Ecosystems and Technologies
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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
2009
Journal of systems architecture
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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]
2008
arXiv
pre-print
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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]
2008
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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
2011
Journal of symbolic computation
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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]
2003
Lecture Notes in Computer Science
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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
2018
Symmetry
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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
2007
Zenodo
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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]
2010
arXiv
pre-print
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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]
2005
Lecture Notes in Computer Science
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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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