Showing papers by "Moni Naor published in 1989"

Universal one-way hash functions and their cryptographic applications

Abstract: We define a Universal One-Way Hash Function family, a new primitive which enables the compression of elements in the function domain. The main property of this primitive is that given an element x. We prove constructively that universal one-way hash functions exist if any 1-1 one-way functions exist.Among the various applications of the primitive is a One-Way based Secure Digital Signature Scheme, a system which is based on the existence of any 1-1 One-Way Functions and is secure against the most general attack known. Previously, all provably secure signature schemes were based on the stronger mathematical assumption that trapdoor one-way functions exist.

Bit Commitment Using Pseudo-Randomness

Abstract: We show how a pseudo-random generator can provide a bit commitment protocol. We also analyze the number of bits communicated when parties commit to many bits simultaneously, and show that the assumption of the existence of pseudo-random generators suffices to assure amortized O(1) bits of communication per bit commitment.

The probabilistic method yields deterministic parallel algorithms

Abstract: A method is provided for converting randomized parallel algorithms into deterministic parallel algorithms. The approach is based on a parallel implementation of the method of conditional probabilities. Results obtained by applying the method to the set balancing problem, lattice approximation, edge-coloring graphs, random sampling, and combinatorial constructions are presented. The general form in which the method of conditional probabilities is applied sequentially is described. The reason why this form does not lend itself to parallelization are discussed. The general form of the case for which the method of conditional probabilities can be applied in the parallel context is given. >

Efficient cryptographic schemes provably as secure as subset sum

Abstract: Very efficient constructions, based on the intractability of the subset sum problem for certain dimensions, are shown for a pseudorandom generator and for a universal one-way hash function. (Pseudorandom generators can be used for private key encryption, and universal one-way hash functions for signature schemes). The increase in efficiency in the construction is due to the fact that many bits can be generated/hashed with one application of the assumed one-way function. All the constructions can be implemented in NC using an optimal number of processors. >

Fast parallel algorithms for chordal graphs

Abstract: Techniques for parallel algorithms on chordal graphs are developed. An NC algorithm for recognizing chordal graphs is developed, as are NC algorithms for finding the following objects in chordal gr...

Bit commitment using pseudo-randomness (extended abstract)

Abstract: We show how a pseudo-random generator can provide a bit commitment protocol. We also analyze the number of bits communicated when parties commit to many bits simultaneously, and show that the assumption of the existence of pseudorandom generators suffices to assure amortized O(1) bits of communication per bit commitment.

On Dice and Coins: Models of Computation for Random Generation

Abstract: To distinguish between random generation in bounded, as opposed to expected, polynomial time, a model of Probabalisic Turing Machine (PTM) with the ability to make random choices with any (small) rational bias is necessary. This ability is equivalent to that of being able to simulate rolling any k-sided die (where |k| is polynomial in the length of the input). We would like to minimize the amount of hardware required for a machine with this capability. This leads to the problem of efficiently simulating a family of dice with as few different types of biased coins as possible.