Targeted Pseudorandom Generators, Simulation Advice Generators, and Derandomizing Logspace

Brains and pseudorandom generators

In a pioneering classic, Warren McCulloch and Walter Pitts proposed a model of the central nervous system; motivated by EEG recordings of normal brain activity, Chvátal and Goldsmith asked whether or not this model can be engineered to provide pseudorandom number generators. We supply evidence suggesting that the answer is negative.

Robust Pseudorandom Generators

Let G : {0, 1} → {0, 1} be a pseudorandom generator. We say that a circuit implementation of G is (k, q)-robust if for every set S of at most k wires anywhere in the circuit, there is a set T of at most q|S| outputs, such that conditioned on the values of S and T the remaining outputs are pseudorandom. We initiate the study of robust PRGs, presenting explicit and non-explicit constructions in w...

Pseudorandom Generators: A Primer

Cryptanalysis of Pseudorandom Generators

As a motivating application for the study of lattice in cryptography we consider the construction of pseudorandom generators. We recall that a pseudorandom generator is a program G(x) (computable in deterministic polynomial time) that maps bitstrings x ∈ {0, 1} to longer strings G(x) ∈ {0, 1} such that, if x is chosen uniformly at random and kept secret, then the output G(x) will “look” random ...

Empirical Pseudorandom Number Generators

The most common pseudorandom number generator or PRNG, the linear congruential generator or LCG, belongs to a whole class of rational congruential generators. These generators work by multiplicative congruential method for integers, which implements a ”grow-and-cut procedure”. We extend this concept to real numbers and call this the real congruence, which produces another class of random number...