On ring-like structures related to symmetric cryptosystems

• Autorzy: Dorninger D. , Länger H. , Mączyński M.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to study cryptographic systems denned as algebras (A,+alfa,+beta,p,s) of type (2,2,0,0) satisfying the axiom (x+alfa p)+beta S = x for all x is an element of A. Some standard and non-standard examples of such systems are given. In particular, we study the systems for which + alfa = + beta= + and p = s where the operation + is the addition operation of a generalized Boolean quasiring (GBQR). We investigate the structure of these algebras revealing their relation to orthomodular lattices and characterize the systems for which s (which is interpreted as coding and decoding key) commutes with all elements of A. By applying direct products to cryptographic algebras one can construct complicated cryptographic systems which may be of importance for practical use. (Then the keys are sequences whose components may be selected at random like in an XOR2 protocol.)

Słowa kluczowe

EN

cryptographic algebra; completely symmetric cryptographic GBQR; finite incidence structure; symmetric cryptographic GBQR

PL

algebra kryptograficzna; kryptosystemy symetryczne; kryptografia GBQR; skończone zależności struktur

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 265--276
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Dorninger D.

• Vienna University of Technology, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria

autor

Länger H.

• Vienna University of Technology, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria

autor

Mączyński M.

• Warsaw University of Technology, Faculty of Mathematics and Information Science, Plac Politechniki 1, 00-661 Warsaw, Poland

Bibliografia

• [1] D. Dorninger, H. Länger and M. Mączyński, The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232.
• [2] D. Dorninger, H. Länger and M. Mączyński, On ring-like structures occurring in axiomatic quantum mechanics, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279-289.
• [3] D. Dorninger, H. Länger and M. Mączyński, On ring-like structures induced by Mackey's probability function, Rep. Math. Phys. 43 (1999), 499-515.
• [4] D. Dorninger, H. Länger and M. Mączyński, Lattice properties of ring-like quantum logics, Intern. J. Theor. Phys. 39 (2000), 1015-1026.
• [5] D. Dorninger, H. Länger and M. Mączyński, Concepts of measures on ring-like quantum logics, Rep. Math. Phys. 47 (2001), 167-176.
• [6] D. Dorninger, H. Länger and M. Mączyński, Ring-like structures with unique symmetric difference related to quantum logic, Discuss. Math. General Algebra Appl. 21 (2001), 239-253.
• [7] G. Kalmbach, Orthomodular Lattices, Academic Press, London 1983.
• [8] H. Lausch and W. Nöbauer, Algebra of Polynomials, North-Holland, Amsterdam, and Amer. Elsevier, New York, 1973.
• [9] A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton 1997. (http://www.cacr.math.uwaterloo.cafhac/)