Pseudorandom Generators: A Primer

A Primer on Pseudorandom Generators

MSTg: Cryptographically strong pseudorandom number generator and its realization

Random covers for finite groups have been introduced in [5, 9], and [18], and used for constructing public key cryptosystems. The primer [10] introduces a new approach for constructing pseudorandom number generators, called MSTg, based on random covers for large finite groups. In particular, on the class of elementary abelian 2-groups they allow a very efficient realization. The crucial point t...

Security Frameworks for Pseudorandom Number Generators

In the cryptographic system a pseudorandom number generator is one of the basic primitives. We survey theoretically secure pseudorandom bit generators which are provably secure under certain reasonable number theoretic assumptions and some practical pseudorandom number generators based on assumptions about symmetric crypto-primitives. Recently, there was a noticeable result for the concrete sec...

Pseudorandom Generators for Read-Once ACC

We consider the problem of constructing pseudorandom generators for read-once circuits. We give an explicit construction of a pseudorandom generator for the class of read-once constant depth circuits with unbounded fan-in AND, OR, NOT and generalized modulo m gates, where m is an arbitrary fixed constant. The seed length of our generator is poly-logarithmic in the number of variables and the er...

Pseudorandomness

We postulate that a distribution is pseudorandom if it cannot be told apart from the uniform distribution by any eecient procedure. This yields a robust deenition of pseudorandom generators as eecient deterministic programs stretching short random seeds into longer pseudorandom sequences. Thus, pseudorandom generators can be used to reduce the randomness-complexity in any eecient procedure. Pse...