Generating quasigroups for cryptographic applications

Czesław Kościelny

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 4, page 559-569
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Kościelny, Czesław. "Generating quasigroups for cryptographic applications." International Journal of Applied Mathematics and Computer Science 12.4 (2002): 559-569. <http://eudml.org/doc/207612>.

@article{Kościelny2002,
abstract = {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.},
author = {Kościelny, Czesław},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {quasigroups; stream-ciphers; latin squares; cryptography; Latin squares},
language = {eng},
number = {4},
pages = {559-569},
title = {Generating quasigroups for cryptographic applications},
url = {http://eudml.org/doc/207612},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Kościelny, Czesław
TI - Generating quasigroups for cryptographic applications
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 4
SP - 559
EP - 569
AB - 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.
LA - eng
KW - quasigroups; stream-ciphers; latin squares; cryptography; Latin squares
UR - http://eudml.org/doc/207612
ER -

References

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  1. Dénes J. and Keedwell A.D. (1974): Latin Squares and Their Applications. - Budapest: Akademiai Kiado. Zbl0283.05014
  2. Dénes J. and Keedwell A.D. (1999): Some applications of non-associative algebraic systems incryptology. - Techn. Rep. 9903, 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. Zbl0913.05027
  4. Kościelny C. (1995): Spurious Galois fields. - Appl. Math. Comp. Sci., Vol. 5, No. 1, pp. 169-188. Zbl0826.11059
  5. Kościelny C. (1996): A method of constructing quasigroup-based stream-ciphers. - Appl. Math. Comp. Sci., Vol. 6, No. 1, pp. 109-121. Zbl0845.94014
  6. Kościelny C. (1997): NLPN sequences over GF(q).- Quasigr. Related Syst., No. 4, pp. 89-102. Zbl0956.94006
  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. Zbl0954.94014
  8. Laywine C.F. and Mullen G.L. (1998): Discrete Mathematics Using Latin Squares.- New York: Wiley. Zbl0957.05002
  9. McKay B. and Rogoyski E. (1995): Latin Squares od Order 10. - Electr. J. Combinat., Vol. 2, No. 3. Zbl0824.05010
  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 

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