Design of Practical and Provably Good Random Number Generators

doi:10.1006/jagm.1998.0952

Journal of Algorithms

Volume 29, Issue 2, November 1998, Pages 358-389

https://doi.org/10.1006/jagm.1998.0952 Get rights and content

Abstract

We present a construction for a family of pseudo-random generators that are very fast in practice, yet possess provable statistical and cryptographic unpredictability properties. Such generators are useful for simulations, randomized algorithms, and cryptography.

Our starting point is a slow but high quality generator whose use can be mostly confined to a preprocessing step. We give a method of stretching its outputs that yields a faster generator. The fast generator offers smooth memory–time–security trade-offs and also has many desired properties that are provable. The slow generator can be based on strong one-way permutations or block ciphers. Our implementation based on the block cipher DES is faster than popular generators.

References (52)

E. Bach
Realistic analysis of some randomized algorithms
J. Comput. System Sci.
(1991)
B. Chor et al.
On the power of two point based sampling
J. Complexity
(1989)
G.L. Miller
Riemann's hypothesis and tests for primality
J. Comput. System Sci.
(1976)
M.O. Rabin
Probabilistic algorithms for testing primality
J. Number Theory
(1980)
W. Aiello et al.
Practical and provable pseudorandom generators
5th Annual ACM–SIAM Symp. Disc. Alg.
(1995)
M. Ajtai et al.
Deterministic simulation of logspace
19th Annual ACM Symp. Theory Computing
(1987)
N. Alon
Eigenvalues and expanders
Combinatorica
(1986)
N. Alon et al.
Simple constructions of almostk
31st Annual IEEE Symp. Found. Comp. Sci.
(1990)
E. Biham et al.
Differential analysis of DES-like crypto system
Advances in Cryptology—CRYPTO90
(1990)
L. Blum et al.
Comparison of two pseudorandom number generators
Advances in Cryptology—Crypto82
(1983)

M. Blum et al.

How to generate cryptographically strong sequences of pseudorandom bits

SIAM J. Comput.

(1984)

J. Boyar

Inferring sequences produced by pseudorandom number generators

J. Assoc. Comput. Mach.

(1989)

F.R.K. Chung

Spectral Graph Theory

(1997)

I.H. Dinwoodie

A probability inequality for the occupation measure of a reversible Markov chain

Ann. Appl. Probab.

(1995)

A.M. Ferrenberg et al.

Monte Carlo simulations: Hidden errors from “good” random number generator

Phys. Rev. Lett.

(Dec. 1992)

A.M. Frieze et al.

Reconstructing truncated integer variables satisfying linear congruences

SIAM J. Comput.

(1988)

J.-B. Fischer et al.

An efficient pseudorandom generator provably as secure as syndrome decoding

Advances in Cryptology, EUROCRYPT96

(1996)

O. Gabber et al.

Explicit constructions of linear-sized superconcentrators

J. Comput. System Sci.

(1981)

D. Gillman

A Chernoff bound for random walks in expander graphs

IEEE Symp. Found. Comp. Sci.

(1993)

O. Goldreich et al.

On the existence of pseudorandom generators

29th Annual IEEE Symp. Found. Computing

(1988)

O. Goldrich et al.

Hard core bit for any one way function

J. Symbolic Logic

(1993)

O. Goldreich et al.

Security preserving amplification of hardness

31st Annual IEEE Symp. Found. Comp. Sci.

(1990)

J. Hastad et al.

Pseudorandom generation from one-way functions

21st Annual ACM Symp. on Theory Computing

(1989)

R. Impagliazzo et al.

Efficient cryptographic schemes provably as secure as subset sum

30th Annual IEEE Symp. Found. Comp. Sci.

(1989)

R. Impagliazzo et al.

How to recycle random bits

IEEE Symp. Found. Comp. Sci.

(1989)

Cited by (0)

^☆: A preliminary version of this work was presented at the Sixth 1–9).

^☆☆: U. Maurer

^†: E-mail:[email protected].

^‡: Work done while at Boston University Computer Science Department, and as a summer student at Bell Communications Research. E-mail:[email protected].

^§: Work done while at Bell Communications Research. E-mail:[email protected].

^f1: [email protected]

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Regular ArticleDesign of Practical and Provably Good Random Number Generators☆,☆☆

Abstract

J. Comput. System Sci.

J. Complexity

J. Comput. System Sci.

J. Number Theory

Practical and provable pseudorandom generators

5th Annual ACM–SIAM Symp. Disc. Alg.

Deterministic simulation of logspace

19th Annual ACM Symp. Theory Computing

Eigenvalues and expanders

Combinatorica

Simple constructions of almostk

31st Annual IEEE Symp. Found. Comp. Sci.

Differential analysis of DES-like crypto system

Advances in Cryptology—CRYPTO90

Comparison of two pseudorandom number generators

Advances in Cryptology—Crypto82

How to generate cryptographically strong sequences of pseudorandom bits

SIAM J. Comput.

Inferring sequences produced by pseudorandom number generators

J. Assoc. Comput. Mach.

Spectral Graph Theory

A probability inequality for the occupation measure of a reversible Markov chain

Ann. Appl. Probab.

Monte Carlo simulations: Hidden errors from “good” random number generator

Phys. Rev. Lett.

Reconstructing truncated integer variables satisfying linear congruences

SIAM J. Comput.

An efficient pseudorandom generator provably as secure as syndrome decoding

Advances in Cryptology, EUROCRYPT96

Explicit constructions of linear-sized superconcentrators

J. Comput. System Sci.

A Chernoff bound for random walks in expander graphs

IEEE Symp. Found. Comp. Sci.

On the existence of pseudorandom generators

29th Annual IEEE Symp. Found. Computing

Hard core bit for any one way function

J. Symbolic Logic

Security preserving amplification of hardness

31st Annual IEEE Symp. Found. Comp. Sci.

Pseudorandom generation from one-way functions

21st Annual ACM Symp. on Theory Computing

Efficient cryptographic schemes provably as secure as subset sum

30th Annual IEEE Symp. Found. Comp. Sci.

How to recycle random bits

IEEE Symp. Found. Comp. Sci.

Regular Article
Design of Practical and Provably Good Random Number Generators☆,☆☆