Testing Quasigroup Identities using Product of Sequence
作者： Eliska Ochodkova , Jiri Dvorský , Václav Snásel , Ajith Abraham , None
DOI:
关键词: Discrete mathematics 、 Associative property 、 Algebraic properties 、 Cryptography 、 Sequence 、 Mathematics 、 Combinatorial design 、 Product (mathematics) 、 Quasigroup
摘要: Non-associative quasigroups are well known combinatorial designs with many dierent applications. Many cryptographic algorithms based on primitives have been published. There several classifications of their algebraic properties. In this paper we propose a new classification upon strings (product elements) obtained by product sequence. It is shown in that the more various results elements, less associative quasigroup.
参考文章(11)
Kristen Ann Meyer, A new message authentication code based on the non-associativity of quasigroups Iowa State University. ,(2006) , 10.31274/RTD-180813-58
Danilo Gligoroski, Smile Markovski, Svein Johan Knapskog, The Stream Cipher Edon80 Lecture Notes in Computer Science. pp. 152- 169 ,(2008) , 10.1007/978-3-540-68351-3_12
Otakar Borůvka, Foundations of the theory of groupoids and groups ,(1976)
Smile Markovski, Danilo Gligoroski, Ljupco Kocarev, Unbiased random sequences from quasigroup string transformations fast software encryption. pp. 163- 180 ,(2005) , 10.1007/11502760_11
R. P. Burn, J. Denes, A. D. Keedwell, Latin Squares and Their Applications The Mathematical Gazette. ,vol. 59, pp. 116- ,(1975) , 10.2307/3616653
Smile Markovski, Danilo Gligoroski, Jasen Markovski, CLASSIFICATION OF QUASIGROUPS BY RANDOM WALK ON TORUS Journal of Applied Mathematics and Computing. ,vol. 19, pp. 57- 75 ,(2005) , 10.1007/BF02935788
Peter Hilton, Jean Pedersen, Catalan Numbers, Their Generalization, and Their Uses The Mathematical Intelligencer. ,vol. 13, pp. 64- 75 ,(1991) , 10.1007/BF03024089
Brendan D. McKay, Ian M. Wanless, On the number of Latin squares Annals of Combinatorics. ,vol. 9, pp. 335- 344 ,(2005) , 10.1007/S00026-005-0261-7
Kôshichi Toyoda, On axioms of linear functions Proceedings of the Imperial Academy. ,vol. 17, pp. 221- 227 ,(1941) , 10.3792/PIA/1195578751
Danilo Gligoroski, Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations IACR Cryptology ePrint Archive. ,vol. 2005, pp. 352- ,(2005)