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Remarks on Pseudorandom Binary Sequences Over Elliptic Curves

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Języki publikacji
EN
Abstrakty
EN
In the paper the pseudorandomness of binary sequences defined over elliptic curves is studied and both the well-distribution and correlation measures are estimated. The paper is based on the Kohel-Shparlinski bound and the Erdös-Turan-Koksma inequality.
Słowa kluczowe
Rocznik
Strony
301--308
Opis fizyczny
Bibliogr. 22 poz., tab.
Twórcy
autor
  • Alfred Renyi Institute of Mathematics Budapest, Pf. 127, H-1364 Hungary, merai@cs.elte.hu
Bibliografia
  • [1] N. Alon, Y. Kohayakawa, C. Mauduit, C. G. Moreira, V. R¨odl, Measures of pseudorandomness for finite sequences: typical values, Proc. Lond. Math. Soc. (3) 95 (2007), no. 3, 778-812.
  • [2] R. M. Avanzi, H. Cohen, C. Doche, G. Frey, T. Lange, K. Nguyen and F. Vercauteren, Handbook of Elliptic and Hyperelliptic Curve Cryptography, CRC Press, 2005.
  • [3] Z. Chen, Elliptic curve analogue of Legendre sequences, Monatsh. Math. 154 (2008) no. 1, 1-10.
  • [4] Chen, Z., Li, S., Xiao, G. Construction of pseudorandom binary sequences from elliptic curves by using discrete logarithm, Lecture Notes in Comput. Sci., 4086, Springer, Berlin, (2006), 285-294.
  • [5] Z. Chen, G. Xiao, 'Good' pseudo-random binary sequences from elliptic curves. Cryptology ePrint Archive, Report 2007/275, http://eprint.iacr.org/
  • [6] M. Drmota, R. F. Tichy, Sequences, Discrepancies and Applications, Springer, Berlin, 1997.
  • [7] E. El Mahassni, I. E. Shparlinski, On the uniformity of distribution of congruential generators over elliptic curves, In Proc. Intern. Conf. on Sequences and Their Applications, Bergen 2001, Springer-Verlag, London, (2002) pp. 257-264.
  • [8] L. Goubin, C. Mauduit, A. S´ark¨ozy, Construction of large families of pseudorandom binary sequences, J. Number Theory 106 (2004), 56-69.
  • [9] G. Gong, T. A. Berson, D. R. Stinson, Elliptic curve pseudorandom sequence generators, in: Selected Areas in Cryptography (Kingston, ON, 1999), Springer, 2000, 34-48.
  • [10] G. Gong, C. C. Y. Lam, Linear recursive sequences over elliptic curves, in: Sequences and their Applications (Bergen, 2001), Springer, 2002, 182-196.
  • [11] S. Hallgren, Linear congruential generators over elliptic curves, Tech. Report CS-94-143, Carnegie Mellon Univ., 1994
  • [12] F. Hess, I. E. Shparlinski, On the linear complexity and multidimensional distribution of congruential generators over elliptic curves. Des. Codes Cryptogr. 35 (2005), 1, 111-117.
  • [13] D. Kohel, I. E. Shparlinski, Exponential sums and group generators for elliptic curves over finite fields, Proc. Algorithmic Number Theory Symposium, Leiden, 2000, LNCS 1838, Berlin: Springer-Verlag, 395-404.
  • [14] T. Lange, I. E. Shparlinski, Distribution of some sequences of points on elliptic curves. J. Math. Cryptol. 1 (2007), 1 1-11.
  • [15] H. Liu, T. Zhan, X. Wang, Large families of elliptic curve pseudorandom binary sequences, Acta Arith. 140 (2009), 135-144.
  • [16] C. Mauduit, H. Niederreiter and A. S´ark¨ozy, On pseudorandom [0, 1) and binary sequences, Publ. Math. Debrecen 71 (2007), 305-324.
  • [17] C. Mauduit, A. S´ark¨ozy, On finite pseudorandom binary sequences I: Measures of pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997) 365-377.
  • [18] A. J. Menezes, P.C. van Oorschot, S. A. Vanstone, Handbook of applied cryptography, CRC Press, Boca Raton, FL, 1997.
  • [19] L. Mérai, Construction of pseudorandom binary sequences over elliptic curves using multiplicative characters, to appear in Publ. Math. Debrecen.
  • [20] I. E. Shparlinski, Pseudorandomnumber generators from elliptic curves. Recent trends in cryptography, 121-141, Contemp. Math., 477, Amer. Math. Soc., Providence, RI, 2009.
  • [21] J.H. Silverman, The arithmetic of elliptic curves, Springer, Berlin 1995.
  • [22] A. Topuzo˘glu, A.Winterhof, Pseudorandomsequences. Topics in geometry, coding theory and cryptography, 135-166, Algebr. Appl., 6, Springer, Dordrecht, 2007.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0024-0020
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