ON SOME KNOWN POSSIBLE APPLICATIONS OF QUASIGROUPS IN CRYPTOLOGY

It is surveyed known (published) possible application of binary and n-ary quasigroups in cryptology. Mathematics Subject Classification: 20N05, 94A60.

[1]  Wolfgang Tittel,et al.  Practical Aspects of Quantum Cryptographic Key Distribution , 2000, Journal of Cryptology.

[2]  Ales Drápal.  How far apart can the group multiplication tables be? , 1992, Eur. J. Comb..

[3]  G. Mullen,et al.  Discrete Mathematics Using Latin Squares , 1998, The Mathematical Gazette.

[4]  Diane Donovan.  Critical sets for families of Latin squares , 1998 .

[5]  Gary L. Mullen,et al.  A Quasigroup-Based Public-Key Cryptosystem , 1999 .

[6]  J. Dénes,et al.  Latin squares and their applications , 1974 .

[7]  Hu Chuan-Gan,et al.  On The Shift Register Sequences , 2004 .

[8]  J. Dénes.  On Latin squares and a digital encrypting communication system , 2000 .

[9]  Gustavus J. Simmons,et al.  Contemporary Cryptology: The Science of Information Integrity , 1994 .

[10]  Ales Drápal.  Hamming distances of groups and quasi-groups , 2001, Discret. Math..

[11]  J. Seberry,et al.  Secret sharing schemes arising from latin squares , 1994 .

[12]  A. D. Keedwell,et al.  Latin Squares: New Developments in the Theory and Applications , 1991 .

[13]  Anne Penfold Street,et al.  Steiner Trades That Give Rise To Completely Decomposable Latin Interchanges , 2002, Int. J. Comput. Math..

[14]  Czesław Kościelny.  Generating quasigroups for cryptographic applications , 2002 .

[15]  Antonio Maturo,et al.  A New Authentication System Based on the Generalized Affine Planes , 1992 .

[16]  Aleš Drápal.  Non-isomorphic 2-groups Coincide at Most in Three Quarters of their Multiplication Tables , 2000, Eur. J. Comb..

[17]  Nonlinear shift registers that produce all vectors of weight , 1992 .

[18]  L. Mittenthal.  A Source of Cryptographically Strong Permutations for Use in Block Ciphers , 1993, Proceedings. IEEE International Symposium on Information Theory.

[19]  H. O. Pflugfelder.  Quasigroups and loops : introduction , 1990 .

[20]  L. Mittenthal,et al.  Block Substitutions Using Orthomorphic Mappings , 1995 .

[21]  Diane Donovan.  Critical sets in Latin squares of order less than 11 , 1999 .

[22]  Douglas R. Stinson,et al.  New Approaches to Designing Public Key Cryptosystems Using One-Way Functions and Trapdoors in Finite Groups , 2001, Journal of Cryptology.

[23]  Jonas Gloeckner,et al.  Groups St Andrews 1997 In Bath , 1997 .

[24]  D. Frank Hsu,et al.  Cyclic Neofields and Combinatorial Designs , 1980 .

[25]  Yu. M. Movsisyan.  Hyperidentities in algebras and varieties , 1998 .

[26]  A. Donald Keedwell,et al.  Crossed-inverse quasigroups with long inverse cycles and applications to cryptography , 1999, Australas. J Comb..

[27]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[28]  S. A. Huggett,et al.  The geometric universe : science, geometry, and the work of Roger Penrose , 1998 .

[29]  D. Kahn.  The codebreakers : the story of secret writing , 1968 .

[30]  Diane Donovan,et al.  Towards the spectrum of critical sets , 2000, Australas. J Comb..

[31]  Ales Drápal.  On Groups that Differ in One of Four Squares , 2002, Eur. J. Comb..

[32]  Natalia Zhukavets,et al.  ON MULTIPLICATION TABLES OF GROUPS THAT AGREE ON HALF OF THE COLUMNS AND HALF OF THE ROWS , 2003, Glasgow Mathematical Journal.

[33]  Henry Beker,et al.  Cipher Systems: The Protection of Communications , 1982 .

[34]  A. D. Keedwell,et al.  Some applications of non-associative algebraic systems in cryptology , 2001 .

[35]  Spectrum of partial admissibility of finite quasigroups (latin squares) , 1982 .

[36]  A Drápal.  Groups St Andrews 1997 in Bath, I: On distances of multiplication tables of groups , 1999 .

[37]  Antonio Maturo,et al.  Rédei blocking sets with two Rédei lines and quasigroups , 2002 .

[38]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[39]  Jennifer Seberry,et al.  Encryption methods based on combinatorial designs , 1986 .