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Algebraic graphs D(n, q) and their analog graphs D(n, K), where K is a finite commutative ring were used successfully in Coding Theory (as Tanner graphs for the construction of LDPC codes and turbo-codes) and in Cryptography (stream-ciphers, public-keys and tools for the key-exchange protocols. Many properties of cryptography algorithms largely depend on the choice of finite field Fq or commutative ring K. For practical implementations the most convenient fields are F and rings modulo Z modulo 2m. In this paper the reader can find the first results about the comparison of D(n, 2m) based stream-ciphers for m = 8, 16, 32 implemented in C++. They show that performance (speed) of algorithms gets better when m is increased.
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Rocznik
Tom
Strony
81--93
Opis fizyczny
Bibliogr. 17 poz., rys.
Twórcy
autor
- College of Science Sultan Quaboos University, Sultanate of Oman
autor
- Institute of Mathematics, University of Maria Curie Sklodowska, pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland
autor
- College of Science Sultan Quaboos University, Sultanate of Oman
autor
- College of Science Sultan Quaboos University, Sultanate of Oman
Bibliografia
- [1] Lazebnik F., Ustimenko V., Some Algebraic Constructions of Dense Graphs of Large Girth and of Large Size, DIMACS series in Discrete Mathematics and Theoretical Computer Science 10 (1993): 75.
- [2] Kim J. L., Peled U. N., Perepelitsa I., Pless V., Friedland S., Explicit construction of families of LDPC codes with no 4-cycles, Information Theory, IEEE Transactions 50(10) (2004): 2378.
- [3] Ustimenko V. A., Coordinatisation of regular tree and its quotients, in ”Voronoi’s impact on modern science”, eds P. Engel and H. Syta, book 2, National Acad. of Sci, Institute of Matematics (1998): 228.
- [4] Kotorowicz J., Ustimenko V. A., On the implementation of cryptoalgorithms based on algebraic graphs over some commutative rings, Condenced Matters Physics, Special Issue: Proceedings of the international conferences ”Infinite particle systems, Complex systems theory and its application”, Kazimerz Dolny, Poland, 2006, 11, 2(54) (2008): 347.
- [5] Ustimenko V., Touzene A., CRYPTALL-a System to Encrypt All types of Data, Notices of Kiev Mohyla Academy (2004): 57.
- [6] Touzene A., Ustimenko V., Graph Based Private Key Crypto System, International Journal on Computer Research, Nova Science Publisher 13(4) (2006): 12.
- [7] Klisowski M., Ustimenko V., On the public keys based on the extremal graphs and digraphs, International Multi–conference on Computer Science and Informational Technology, October 2010, Wisla, Poland, CANA Proceedings.
- [8] Wróblewska A., On some properties of graph based public keys, Albanian Journal of Mathematics 2(3) (2008): 229.
- [9] Ustimenko V., Algebraic graphs and security of digital communications, Institute of Computer Science, University of Maria Curie Sklodowska in Lublin (2011): 151 (supported by European Social Foundation), available at the UMCS web.
- [10] Ustimenko V., CRYPTIM: Graphs as Tools for Symmetric Encryption, In Lecture Notes in Computer Science, Springer 2227 (2002): 278.
- [11] Ustimenko V., Graphs with special arcs and Cryptography, Acta Applicandae Mathematicae (1974): 117.
- [12] Koblitz N., A Course in Number Theory and Cryptography, Second Edition, Springer (1994).
- [13] Koblitz N., Algebraic Aspects of Cryptograph, Springer (1998).
- [14] Hasan M. A., Look-Up Table-Based Large Finite Field Multiplication in Memory Constrained Cryptosystems, IEEE Trans. Comp. 49 (7) (2000): 749.
- [15] Ustimenko V., Woldar A., Extremal properties of regular and affine generalized polygons as tactical configurations, Europ. J. Com. 24 (2003): 99.
- [16] Dijkstra E., Note on two problems in connection with graphs, Num. Math. 1 (1959): 269.
- [17] Plank J. (n.d.), Fast Galois Field Arithmetic Library in C/C++. Retrieved October 28 (2009), from The University of Tennessee, College of Art and Science: http://www.cs.utk.edu/ plank/plank/papers/CS-07-593.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8a7c43d5-1f29-4cbe-90be-0f5f64c8a497