PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Cryptography and canonical number systems in quadratic fields

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Konferencja
International Conference on Computer Vision and Graphics ICCVG 2006 (25-27.09.2006 ; Warsaw, Poland)
Języki publikacji
EN
Abstrakty
EN
This paper proposes an encryption method based on representation of messages in the canonical number systems (CNS) in quadratic fields. The essence of the encryption method is conversion of the representation of integers from the conventional number system to their representation in the CNS in a certain quadratic field. A sufficiently wide range of CNS with a given number of digits ensures resistance of the method to "accidental guessing" of the secret keys. Nonlinear nature of the conversion ensures its resistance to frequency analysis.
Rocznik
Strony
363--372
Opis fizyczny
Bibliogr. 14 poz., tab., wykr.
Twórcy
autor
autor
  • Image Processing Systems Institute of RAS 151, Molodogvardejskaya St., 443001, Samara, Russia, vicanfed@mail.ru
Bibliografia
  • [1] Bellman R., Shapiro H. N.: The distribution of squarefree integers in small intervals. Duke Math. J., 21, 629-637, 1954.
  • [2] Kátai I., Kovács B. Kanonische Zahlensysteme in der Théorie der quadratischen Zahlen. Acta Sci. Math. (Szeged), 42, 99-107, 1980.
  • [3] Kátai I., Kovács B.: Canonical number systems in imaginary quadratic fields. Acta Math. Acad. Sci. Hungaricae, 37, 159-164, 1981.
  • [4] Gilbert W. J.: Fractal geometry derived from complex bases. Math. Intelligencer, 4, 78-86, 1982.
  • [5] Gilbert W. J.: Arithmetic in complex bases. Math. Mag. 57, 77-81, 1984.
  • [6] Gilbert W. J.: The Fractal Dimension of sets derived from complex bases. Canad. Math. Bull., 29, 495-500, 1986.
  • [7] Lenstra H. W. Jr.: Algorithms in algebraic number theory. Bull. Amer. Math. Soc, 26, 211-244, 1926.
  • [8] Thuswardner J. M.: Elementary properties of canonical number systems in quadratic fields. Applications of Fibonacci Numbers, F.T.Howard (Ed.), 7 Kluwer, 405-409, 1998.
  • [9] Akiyama S. Petho A.: On canonical number systems, Theoret. Comp. Sci., 270, 921-933, 2002.
  • [10] Chernov V.: Factorization ambiguity in algebraic number fields: Schônhage-Strassen Algorithm. Abstracts of fourth European congress of mathematics, Stockholm, Sweden. http://www.math.kth.Se/4ecm/abstracts/6.l.pdf, 2004.
  • [11] Chernov V.: 3D Generalization for LFSR random point generator. Proceedings of the Second IASTED Int. Multi-Conference "Signal and Image Processing" Novosibirsk, Russia, 122-125, 2005.
  • [12] Chernov V.: Discrete orthogonal transforms with "chaotic" basis functions set. ICGST International Conference on Graphics, Vision and Image Processing (GVIP-05), Cairo, Egypt, http://www.icgst.com/GVIP05/conference/participants.html (PID: P1150535127), 2005.
  • [13] Weisstein E. W.: Squarefree. From MathWorld - a Wolfram Web Resource. http://mathworld.wolfram.com/Squarefree.html, 2005.
  • [14] Chernov V.: Fast uniform distribution of sequences for fractal sets. Proceedings of International Conference on Computer Vision and Graphics. Computational Imaging and Vision, Warsaw, Poland, 12, 709-714, 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA1-0025-0013
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.