Generating quasigroups for cryptographic applications

• Autorzy: Kościelny Cz.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

quasigroups; latin squares; stream ciphers; cryptography

PL

kwadrat łaciński; szyfr strumieniowy; kryptografia

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: Vol. 12, no 4
• Strony: 559--569
• Opis fizyczny: Bibliogr. 10 poz., tab.

Twórcy

autor

Kościelny Cz.

• University of Zielona Gora, Institute of Control and Computation Engineering ul. Podgorna 50, 65-246 Zielona Gora, Poland,

Bibliografia

• [1] Dénes J. and Keedwell A.D. (1974): Latin Squares and Their Applications. - Budapest: Akadémiai Kiadó.
• [2] Dénes J. and Keedwell A.D. (1999): Some applications of non-associative algebraic systems in cryptology. - Techn. Rep. 99/03, Dept. Math. Stat., University of Surrey.
• [3] Jacobson M.T. and Matthews P. (1996): Generating uniformly distributed random latin squares. - J. Combinat. Desig., Vol. 4, No. 6, pp. 405-437.
• [4] Kościelny C. (1995): Spurious Galois fields. - Appl. Math. Comp. Sci., Vol. 5, No. 1, pp. 169-188.
• [5] Kościelny C. (1996): A method of constructing quasigroup-based stream-ciphers. - Appl. Math. Comp. Sci., Vol. 6, No. 1, pp. 109-121.
• [6] Kościelny C. (1997): NLPN sequences over GF(q). - Quasigr. Related Syst., No. 4, pp. 89-102.
• [7] 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.
• [8] Laywine C.F. and Mullen G.L. (1998): Discrete Mathematics Using Latin Squares. - New York: Wiley.
• [9] McKay B. and Rogoyski E. (1995): Latin Squares od Order 10. - Electr. J. Combinat., Vol. 2, No. 3.
• [10] Ritter T. (1998): Latin squares: A literature survey - Research comments from ciphers by Ritter. - Available at http://www.io.com/~ritter/RES/LATSQR.HTM.