A public key cryptosystem based on the word problem
Proceedings of CRYPTO 84 on Advances in cryptology
Rewriting systems and word problems in a free partially commutative monoid
Information Processing Letters
A D0L-T0L public key cryptosystem
Information Processing Letters
A public-key cryptosystem based on language theory
Computers and Security
The word problem for free partially commutative groups
Journal of Symbolic Computation
A cryptanalytic observation concerning systems based on language theory
Discrete Applied Mathematics
A public key cryptosystem based on Lyndon words
Information Processing Letters
Confluent and Other Types of Thue Systems
Journal of the ACM (JACM)
On Public-Key Cryptosystem Based on Church-Rosser String-Rewriting Systems (Extended Abstract)
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
A Reaction Attack on a Public Key Cryptosystem Based on the Word Problem
Applicable Algebra in Engineering, Communication and Computing
On the wagner–magyarik cryptosystem
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
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At indocrypt 2003, Abisha, Thomas and Subramanian have proposed a public key encryption scheme and a zero-knowledge authentication protocol based on the word problem on monoids, as well as a group variant of these systems. We here present a total break attack on each of the two encryption schemes. The complexity bounds of our algorithms show that these schemes are insecure for practical parameter sizes. In the monoid setting, we go one step further by proposing an algorithm that breaks the NP-hard problem underlying both the encryption scheme and the zero-knowledge protocol, as well as an upper bound on its complexity.