A Method for Application of a Quantum Search Algorithm to Classical Databases

TL;DR

This paper introduces a novel method for applying Grover's quantum search algorithm directly to classical databases by mapping database elements to indices, enabling true database searches and demonstrating potential cryptographic vulnerabilities.

Contribution

It presents the first approach to perform genuine database searches with Grover's algorithm through index-to-element mapping, expanding its practical application scope.

Findings

Feasibility of applying Grover's algorithm to classical databases.

Potential for quantum attacks on Diffie-Hellman cryptosystems.

Demonstration of a new quantum search methodology.

Abstract

Grover's algorithm is normally presented as a method of searching a database, however it would be more accurately described as a method of identifying elements of an interval of the integers which satisfy some logical clause - an example might be identifying binary strings which correspond to the solutions of a Sudoku problem. In this paper we present the first method of performing a true database search using Grover's search algorithm, by first creating a mapping from a set of indices in the range 0:2^n-1 to a set of database elements, then applying the clause to these elements. We then demonstrate the feasibility of an attack against the Diffie-Hellman cryptosystem based on a Grover's search of a database of candidate solutions generated via the number field sieve algorithm.