An acceleration of quasigroup operations by residue arithmetic. (28th July 2017)

• Record Type: Journal Article
• Authors: Krömer, Pavel; Platoš, Jan; Nowaková, Jana; Snášel, Václav
• Other Names: Ogiela Marek R. guestEditor.; Ko Hoon guestEditor.
• Is Part Of: Concurrency and computation. Volume 30:Number 2(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-07-28
• Subjects: acceleration -- quasigroup operations -- residue arithmetic -- residue number systems -- security; Parallel processing (Electronic computers) -- Periodicals; Parallel computers -- Periodicals; 004.35
• DOI: 10.1002/cpe.4239
• Languages: English
• ISSNs: 1532-0626

Abstract

Summary: Quasigroup operations are essential for a wide range of cryptographic procedures that includes cryptographic hash functions, electronic signatures, pseudorandom number generators, and stream and block ciphers. Quasigroup cryptography achieves high levels of security at low memory and computational costs by an iterative application of quasigroup operations to streams and blocks of data. The use of large quasigroups can further improve the strength of cryptographic operations. However, the order of used quasigroups is the main factor affecting the memory requirements of quasigroup cryptographic schemes. Alternative quasigroup representations that do not store their multiplication tables in computer memory yield increased computational costs. In any case, an efficient implementation of quasigroup operations is critical for practical applications of quasigroup cryptography. Residue number systems allow a fast, concurrent realization of addition and multiplication. In this work, residue arithmetic is used to accelerate quasigroup operations, and an efficient computational approach to their implementation, designed with respect to the extended instruction sets of modern processors, is proposed.