On Some Properties of Pseudorandom Sequences

Abstract: 

Pseudorandom sequences are used in many fields such that simulation, cryptography, etc. Normally, they are assocciated with a Monte Carlo rule, where the elements of the sequence should "appear" to be uniformily distributed and independent one from each other. They can be used in combination of better distributed sets of points and obtain some advantages. In the first part of the talk, we review a construction called hybrid sequences, which combine pseudorandom sequences and uniform distribution sequences.

Then, we move to applications of pseudorandom sequences in cryptography, where  pseudorandom sequences  in many protocols.

We mention some of them:

1)  Anonymous speech,

2)  Authentication over an insecure channel,

3)  Key agreement.

All of these protocols are secure under the condition that this information should be "unpredictable''. Unfortunately true random numbers are hard to generate, mainly because of the deterministic nature of a computer. In this talk, we review several constructions of pseudorandom number sequences which pass certain specific tests. We introduce this tests and comment some equivalence between them.

Finally, we finish this talk with open problems in this area.