Elliptic curve analogues of a pseudorandom generator

Using the discrete logarithm in [7] and [9] a large family of pseudorandom binary sequences was constructed. Here we extend this construction. An interesting feature of this extension is that in certain special cases we get sequences involving points on elliptic curves.

[1]  András Sárközy,et al.  On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol , 1997 .

[2]  László Mérai Construction of large families of pseudorandom binary sequences , 2009 .

[3]  Rudolf Ahlswede,et al.  General Theory of Information Transfer and Combinatorics , 2006, GTIT-C.

[4]  On linear recursion and pseudorandomness , 2005 .

[5]  Tor Helleseth,et al.  Sequences and Their Applications - SETA 2006, 4th International Conference, Beijing, China, September 24-28, 2006, Proceedings , 2006, SETA.

[6]  A. Weil Sur les courbes algébriques et les variétés qui s'en déduisent , 1948 .

[7]  Joseph H. Silverman,et al.  The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[8]  Katalin Gyarmati,et al.  On a Fast Version of a Pseudorandom Generator , 2005, GTIT-C.

[9]  Katalin Gyarmati On a family of pseudorandom binary sequences , 2004, Period. Math. Hung..

[10]  Zhixiong Chen,et al.  Elliptic curve analogue of Legendre sequences , 2008 .

[11]  Shengqiang Li,et al.  Construction of Pseudo-random Binary Sequences from Elliptic Curves by Using Discrete Logarithm , 2006, SETA.

[12]  Rudolf Ahlswede,et al.  Large Families of Pseudorandom Sequences of k Symbols and Their Complexity - Part I , 2006, GTIT-C.

[13]  András Sárközy,et al.  Modular constructions of pseudorandom binary sequences with composite moduli , 2005, Period. Math. Hung..

[14]  Ning Zhang,et al.  Pseudo-Randomness of Discrete-Log Sequences from Elliptic Curves , 2007, Inscrypt.

[15]  András Sárközy,et al.  Construction of Pseudorandom Binary Sequences Using Additive Characters , 2004 .

[16]  Zhixiong Chen,et al.  'Good' Pseudo-Random Binary Sequences from Elliptic Curves , 2007, IACR Cryptol. ePrint Arch..

[17]  András Sárközy,et al.  A finite pseudorandom binary sequence , 2001 .