Derandomization in Cryptography

Derandomization in Cryptography

We give two applications of Nisan–Wigderson-type (“non-cryptographic”) pseudorandom generators in cryptography. Specifically, assuming the existence of an appropriate NW-type generator, we construct: 1. A one-message witness-indistinguishable proof system for every language in NP, based on any trapdoor permutation. This proof system does not assume a shared random string or any setup assumption...

Pairwise Independence and Derandomization Pairwise Independence and Derandomization

This article gives several applications of the following paradigm, which has proven extremely powerful in algorithm design and computational complexity. First, design a probabilistic algorithm for a given problem. Then, show that the correctness analysis of the algorithm remains valid even when the random strings used by the algorithm do not come from the uniform distribution, but rather from a...

Resource Tradeoffs and Derandomization

We consider uniform assumptions for derandomization. We provide intuitive evidence that BPP can be simulated non-trivially in deterministic time by showing that (1) There is a simulation of P in POLY LOGSPACE that is successful against all polynomial-time adversaries infinitely often, or BPP ⊆ SUBEXP (2) There is a simulation of P in SUBPSPACE that is successful against all polynomialtime adver...

44 Randomization and Derandomization

FRAMEWORK AND ANALYSIS Most randomized incremental algorithms in the literature follow the framework sketched here for the computation of the trapezoidal map: the structure to be computed is maintained while the objects defining it are inserted in random order. To insert a new object, one first has to find a “conflict” of that object (the location step), then local updates in the structure are ...

Randomization and derandomization