Abstract
A public key cryptosystem based on free partially commutative monoids is constructed. The encryption of a message to create the cryptotext uses a Thue system which is formed from the free partially commutative monoid with the help of a trapdoor morphism. The decidability of the word problem for free partially commutative monoids can be used for decryption. Finding the trapdoor morphism of this system is shown to be NP-hard. But, a zero – knowledge protocol to convince a verifier that there is such a trapdoor morphism is provided. A related but different public key cryptosystem based on free partially commutative groups is also proposed.
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Abisha, P.J., Thomas, D.G., Subramanian, K.G. (2003). Public Key Cryptosystems Based on Free Partially Commutative Monoids and Groups. In: Johansson, T., Maitra, S. (eds) Progress in Cryptology - INDOCRYPT 2003. INDOCRYPT 2003. Lecture Notes in Computer Science, vol 2904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24582-7_16
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DOI: https://doi.org/10.1007/978-3-540-24582-7_16
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