A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups are of order 256, suitable for a fast software encryption of messages written down in the universal ASCII code. That is exactly what this paper provides: fast and easy ways of generating quasigroups of order up to 256 and a little more.
@article{bwmeta1.element.bwnjournal-article-amcv12i4p559bwm,
author = {Ko\'scielny, Czes\l aw},
title = {Generating quasigroups for cryptographic applications},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {12},
year = {2002},
pages = {559-569},
zbl = {1026.94011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv12i4p559bwm}
}
Kościelny, Czesław. Generating quasigroups for cryptographic applications. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) pp. 559-569. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv12i4p559bwm/
[000] Dénes J. and Keedwell A.D. (1974): Latin Squares and Their Applications. - Budapest: Akademiai Kiado. | Zbl 0283.05014
[001] Dénes J. and Keedwell A.D. (1999): Some applications of non-associative algebraic systems incryptology. - Techn. Rep. 9903, Dept. Math. Stat., University of Surrey.
[002] Jacobson M.T. and Matthews P. (1996): Generating uniformly distributed random latin squares. - J. Combinat.Desig., Vol. 4, No. 6, pp. 405-437. | Zbl 0913.05027
[003] Kościelny C. (1995): Spurious Galois fields. - Appl. Math. Comp. Sci., Vol. 5, No. 1, pp. 169-188. | Zbl 0826.11059
[004] Kościelny C. (1996): A method of constructing quasigroup-based stream-ciphers. - Appl. Math. Comp. Sci., Vol. 6, No. 1, pp. 109-121. | Zbl 0845.94014
[005] Kościelny C. (1997): NLPN sequences over GF(q).- Quasigr. Related Syst., No. 4, pp. 89-102. | Zbl 0956.94006
[006] Kościelny C. and Mullen G.L. (1999): A quasigroup-based public-key cryptosystem. - Int. J. Appl. Math. Comp. Sci., Vol. 9, No. 4, pp. 955-963. | Zbl 0954.94014
[007] Laywine C.F. and Mullen G.L. (1998): Discrete Mathematics Using Latin Squares.- New York: Wiley. | Zbl 0957.05002
[008] McKay B. and Rogoyski E. (1995): Latin Squares od Order 10. - Electr. J. Combinat., Vol. 2, No. 3. | Zbl 0824.05010
[009] Ritter T. (1998): Latin squares: A literature survey-Research comments from ciphers by Ritter. -Available at http://www.io.com/~ritter/RES/LATSQR.HTM