The  Weizmann  Institute  of  Science
                  Faculty of Mathematics and Computer Science


                            Computer Science Seminar

                                Igor Shparlinski
                            Department of Computing
                              Macquarie University
                               Sydney, Australia


                                 will speak on


                Pseudorandom Number Generators in Cryptography 
                          and Methods of Monte Carlo 

Abstract:
A survey of some number-theoretic properties, such as the period length,
distribution, linear complexity, of some most common pseudorandom number
generators will be given. In particular, the following generators will be
considered:

1. Power Generator $$ u_{x+1} = u_x^e (mod\ M),   x=0,1,2, ..., $$ which is
also known as the RSA generator if $gcd(e, \phi(M)) = 1$ and the Blum-Blum-Shub
generator if $e=2$

2. Inversive Generator $$ u_{x+1} = au_x^{-1} +b (mod\ M),   x=0,1,2, ... $$

3. Naor-Reingold Generator $$ u_x  = g^{a_1^{x_1}...a_n^{x_n}}
(mod\ p),x=0,1,2,
... $$ where $x=x_1...x_n$ is the binary representation of $x$ and $a_1, ...,
a_n$ are some integers.

Some cryptographic motivations and applications of these results will be
discussed as well.






                      The lecture will take place in the 
                     Lecture Hall, Room 1, Ziskind Building
                          on Monday, December 27, 1999
                                    at 14:30