Cryptosystems based on RS and BCH codes over finite noncommutative algebras

Abstract

The purpose of this paper is to introduce new cryptosystems based on linear Reed-Solomon (RC) and Bose-Chaudhuri-Hocquenghem (BCH) codes over finite Cayley-Dickson and finite Clifford algebras with fast code and encode procedures based on fast Fourier- Clifford-Galois transforms. © 2018 Institute of Physics Publishing. All rights reserved.Springer) p 88 [21] Pall G 1940 On the arithmetic of quaternions Tran. Amer. Math. Soc. 47 487-500 [22] Chernov V M 2015 Quasiparallel algorithm for error-free convolution computation using reduced Mersenne–Lucas codes Computer Optics 39 241-248 [23] Conway J H and Sloane N J A 1993 Sphere Packings, Lattices and Groups (Berlin: Verlag-Springer) p 573 [24] Hurwitz A 1896 Uber die Zahlentheorie der Quaternione Math.-Phys. Klasse (Gottingen: Nachr. Ges. Wiss.) 303-330, 313-340 Acknowledgments This work was supported by grants the RFBR № 17-07-00886 and by Ural State Forest Engineering’s Center of Excellence in ”Quantum and Classical Information Technologies for Remote Sensing Systems”