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1
Content available remote Finite directly indecomposable monogenic entropic quasigroups with quasi-identity
Bińczak G, Kaleta J.
Demonstratio Mathematica
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2012
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Vol. 45, nr 3
519-532
EN
In this paper we characterize finite directly indecomposable monogenic entropic quasigroups with quasi-identity.
2
Content available remote Finite simple monogenic entropic quasigroups with quasi-identity
Bińczak G, Kaleta J.
Demonstratio Mathematica
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2011
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Vol. 44, nr 1
17-27
EN
In this paper we describe finite simple monogenic entropic quasigroups with quasi-identity.
3
Content available remote Some necessary and sufficient conditions for parastrophic invariance of the associative law in quasigroups
Jaiyeola T. G.
Fasciculi Mathematici
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2008
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Nr 40
25-35
EN
Every quasigroup (S, ⋅) belongs to a set of 6 quasi-groups, called parastrophes denoted by (S, πi), i ∈ {1, 2, 3, 4, 5, 6}. It is shown that isotopy-isomorphy is a necessary and sufficient condition for any two distinct quasigroups (S, πi) and (S, πj), i, j ∈ {1, 2, 3, 4, 5, 6} to be parastrophic invariant relative to the associative law. In addition, a necessary and sufficient condition for any two distinct quasigroups (S, πi) and (S, πj), i, j ∈ {1, 2, 3, 4, 5, 6}. to be parastrophic invariant under the associative law is either if the πi-parastrophe of H is equivalent to the πi-parastrophe of the holomorph of the πiparastrophe of S or if the πi-parastrophe of H is equivalent to the πk-parastrophe of the πi-parastrophe of the holomorph of the πi-parastrophe of S, for a particular k ∈ {1, 2, 3, 4, 5, 6}.
4
Content available remote Generating quasigroups for cryptographic applications
Kościelny Cz.
International Journal of Applied Mathematics and Computer Science
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2002
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Vol. 12, no 4
559-569
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.
5
Content available remote A Quasigroup-Based Public-Key Cryptosystem
Kościelny Cz., Mullen G. L.
International Journal of Applied Mathematics and Computer Science
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1999
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Vol. 9, no 4
955-963
EN
A public-key cryptosystem, using generalized quasigroup-based streamciphers is presented. It is shown that such a cryptosystem allows one to transmit securely both a cryptogram and a secret portion of the enciphering key using the same insecure channel. The system is illustrated by means of a simple, but non-trivial, example.
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