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Keywords = twisted-skew group ring

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23 pages, 519 KiB  
Article
Public Key Protocols from Twisted-Skew Group Rings
by Javier de la Cruz, Edgar Martínez-Moro, Steven Muñoz-Ruiz and Ricardo Villanueva-Polanco
Cryptography 2024, 8(3), 29; https://doi.org/10.3390/cryptography8030029 - 5 Jul 2024
Viewed by 2172
Abstract
This article studies some algebraic structures known as twisted-skew group rings in the context of public key cryptography. We first present some background related to these structures to then specifically introduce particular twisted-skew group rings and show how to utilize them as the [...] Read more.
This article studies some algebraic structures known as twisted-skew group rings in the context of public key cryptography. We first present some background related to these structures to then specifically introduce particular twisted-skew group rings and show how to utilize them as the underlying algebraic structure to build cryptographic protocols. We closely follow an incremental-like methodology to construct these protocols by putting parts together. As as result, we first introduce a key-agreement protocol and then generalize it to a group key-agreement protocol. We then proceed to construct a probabilistic public key encryption from our two-party key agreement and, finally, introduce a key-encapsulation mechanism from a well-known generic construction applied to probabilistic public encryption. Furthermore, we provide an in-depth security analysis for each cryptographic construction under new related algebraic assumptions and supply a proof-of-concept implementation for various candidate chosen groups. Full article
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