Block Cipher Based on Randomly Generated Quasigroups
Quasigroups are algebraic structures closely related to
Latin squares which have many different applications. The
construction of block cipher is based on quasigroup string
transformation. This article describes a block cipher based
Quasigroup of order 256, suitable for fast software encryption of
messages written down in universal ASCII code. The novelty of this
cipher lies on the fact that every time the cipher is invoked a new set
of two randomly generated quasigroups are used which in turn is
used to create a pair of quasigroup of dual operations. The
cryptographic strength of the block cipher is examined by calculation
of the xor-distribution tables. In this approach some algebraic
operations allows quasigroups of huge order to be used without any
requisite to be stored.
[1] A. J. Menezes, P.C. Van Oorschot, S.A. Vanstone, Handbook of Applied
Cryptography, CRC Press 1997
[2] J. Dénes and A. D. Keedwell, Latin Squares. New Developments in the
Theory and Applications, North-Holland Publishing Co., Amsterdam,
1981.
[3] J. Dénes and A. D. Keedwell: A New Authentication Scheme based on
Latin Squares, Discrete Mathematics, no. 106/107, (1992), pp. 157-162.
[4] Hall, M.: Combinatorial theory, Blaisdell Publishing Company, 1967.
[5] Bakhtiari, S., Safavi-Naini, R., Pieprzyk, J., "A Message Authentication
Code Based on Latin Squares, Proc. Australasian Conference on
Information Security and Privacy", pp. 194-203, 1997.
[6] S. Markovski, D. Gligoroski, S. Andova, Using quasigroups for one-one
secure encoding, Proc. VIII Conf. Logic and Computer Science "LIRA
-97", Novi Sad, pp. 157-162, 1997.
[7] S. Markovski, D. Gligoroski, B. Stoj─ìevska, Secure two-way on-line
communication by using quasigroup enciphering with almost public key,
Novi Sad Journal of Mathematics, vol. 30, 2000.
[8] S.I. Marnas, L. Angelis and G.L. Bleris, All-Or-Nothing Transform
Using Quasigroups, Proc. 1st Balkan Conference in Informatics, pp.
183-191, 2003.
[9] V. A. Shcherbacov, On linear and inverse quasigroups and its
applications in code theory, 2003,
www.karlin.mff.cuni.cz/drapal/speccurs.pdf
[10] D. Gligoroski, S. Markovski, L. Kocarev, EdonR, An Infinite Family of
Cryptographic Hash functions, International Journal of Network
Security, Vol. 8(3), pp. 293-300, 2009
[11] D. Gligoroski, Edon - library of reconfigurable cryptographic primitives
suitable for embedded systems, Workshop on cryptographic hardware
and embedded systems, 2003.
[12] S. Markovski, D. Gligoroski, V. Bakeva: Quasigroup String Processing:
Part 1, Maced. Acad. of Sci. and Arts, Sc. Math. Tech. Scien. XX 1-2,
pp. 13-28, 1999.
[13] S. Markovski, V. Kusakatov: Quasigroup String Processing: Part 2,
Contributions, Sec. math. Tech.Sci., MANU, XXI, vol. 1-2, pp. 15-32
2000.
[14] D. Gligoroski, Stream Cipher based on Quasigroup string
transformations in ZZP
*, arXiv:cs.CR/0403043, Macedonian Academy of
Science and Arts, annual Proceedings in Mathematical and Technical
Sciences, 2004.
[15] Kościelny, C.: Generating Quasigroups for cryptographic applications,
Int. J. Appl. Math. Sci., Vol. 12, No.4, pp. 559-569, 2002.
[16] Kościelny, C.: A method of constructing quasigroup-based streamciphers.
Appl. Math. and Comp. Sci. vol 6,pp. 109-121, 1996.
[17] Roman Barták, On generators of Random Quasigroup Problems, In proc.
Of ERCIM 05 workshop, pp. 264-278, 2006.
[18] M Hassinen, S Markoviski, Differential Cryptanalysis of the
quasigroup cipher, Proceedings of the Finnish Data Processing Week,
Petrozavodsk, Russia. Petrozavodsk State University, (2004).
[19] D. Gligoroski, S. Markovski, Cryptographic potentials of quasigroup
transformations, Talk at EIDMA Cryptography Working Group, Utrecht,
2003.
[20] McKay, B.D., Rogoyski, E.:Latin squares of order 10, Electronic J.
Comb.2,1995, http://ejc.math.gatech.edu:8080/Journal/journalhome.html
[1] A. J. Menezes, P.C. Van Oorschot, S.A. Vanstone, Handbook of Applied
Cryptography, CRC Press 1997
[2] J. Dénes and A. D. Keedwell, Latin Squares. New Developments in the
Theory and Applications, North-Holland Publishing Co., Amsterdam,
1981.
[3] J. Dénes and A. D. Keedwell: A New Authentication Scheme based on
Latin Squares, Discrete Mathematics, no. 106/107, (1992), pp. 157-162.
[4] Hall, M.: Combinatorial theory, Blaisdell Publishing Company, 1967.
[5] Bakhtiari, S., Safavi-Naini, R., Pieprzyk, J., "A Message Authentication
Code Based on Latin Squares, Proc. Australasian Conference on
Information Security and Privacy", pp. 194-203, 1997.
[6] S. Markovski, D. Gligoroski, S. Andova, Using quasigroups for one-one
secure encoding, Proc. VIII Conf. Logic and Computer Science "LIRA
-97", Novi Sad, pp. 157-162, 1997.
[7] S. Markovski, D. Gligoroski, B. Stoj─ìevska, Secure two-way on-line
communication by using quasigroup enciphering with almost public key,
Novi Sad Journal of Mathematics, vol. 30, 2000.
[8] S.I. Marnas, L. Angelis and G.L. Bleris, All-Or-Nothing Transform
Using Quasigroups, Proc. 1st Balkan Conference in Informatics, pp.
183-191, 2003.
[9] V. A. Shcherbacov, On linear and inverse quasigroups and its
applications in code theory, 2003,
www.karlin.mff.cuni.cz/drapal/speccurs.pdf
[10] D. Gligoroski, S. Markovski, L. Kocarev, EdonR, An Infinite Family of
Cryptographic Hash functions, International Journal of Network
Security, Vol. 8(3), pp. 293-300, 2009
[11] D. Gligoroski, Edon - library of reconfigurable cryptographic primitives
suitable for embedded systems, Workshop on cryptographic hardware
and embedded systems, 2003.
[12] S. Markovski, D. Gligoroski, V. Bakeva: Quasigroup String Processing:
Part 1, Maced. Acad. of Sci. and Arts, Sc. Math. Tech. Scien. XX 1-2,
pp. 13-28, 1999.
[13] S. Markovski, V. Kusakatov: Quasigroup String Processing: Part 2,
Contributions, Sec. math. Tech.Sci., MANU, XXI, vol. 1-2, pp. 15-32
2000.
[14] D. Gligoroski, Stream Cipher based on Quasigroup string
transformations in ZZP
*, arXiv:cs.CR/0403043, Macedonian Academy of
Science and Arts, annual Proceedings in Mathematical and Technical
Sciences, 2004.
[15] Kościelny, C.: Generating Quasigroups for cryptographic applications,
Int. J. Appl. Math. Sci., Vol. 12, No.4, pp. 559-569, 2002.
[16] Kościelny, C.: A method of constructing quasigroup-based streamciphers.
Appl. Math. and Comp. Sci. vol 6,pp. 109-121, 1996.
[17] Roman Barták, On generators of Random Quasigroup Problems, In proc.
Of ERCIM 05 workshop, pp. 264-278, 2006.
[18] M Hassinen, S Markoviski, Differential Cryptanalysis of the
quasigroup cipher, Proceedings of the Finnish Data Processing Week,
Petrozavodsk, Russia. Petrozavodsk State University, (2004).
[19] D. Gligoroski, S. Markovski, Cryptographic potentials of quasigroup
transformations, Talk at EIDMA Cryptography Working Group, Utrecht,
2003.
[20] McKay, B.D., Rogoyski, E.:Latin squares of order 10, Electronic J.
Comb.2,1995, http://ejc.math.gatech.edu:8080/Journal/journalhome.html
@article{"International Journal of Information, Control and Computer Sciences:60473", author = "Deepthi Haridas and S Venkataraman and Geeta Varadan", title = "Block Cipher Based on Randomly Generated Quasigroups", abstract = "Quasigroups are algebraic structures closely related to
Latin squares which have many different applications. The
construction of block cipher is based on quasigroup string
transformation. This article describes a block cipher based
Quasigroup of order 256, suitable for fast software encryption of
messages written down in universal ASCII code. The novelty of this
cipher lies on the fact that every time the cipher is invoked a new set
of two randomly generated quasigroups are used which in turn is
used to create a pair of quasigroup of dual operations. The
cryptographic strength of the block cipher is examined by calculation
of the xor-distribution tables. In this approach some algebraic
operations allows quasigroups of huge order to be used without any
requisite to be stored.", keywords = "quasigroups, latin squares, block cipher and
quasigroup string transformations.", volume = "4", number = "11", pages = "1743-5", }
