Quantum Search for Scaled Hash Function Preimages

09/01/2020
by   Sergi Ramos-Calderer, et al.
0

We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our implementation provides the means to assess with precision the scaling of the number of gates and depth of a full-fledged quantum circuit designed to find the preimages of a given hash digest. The detailed construction of the quantum oracle shows that the presence of AND gates, OR gates, shifts of bits and the reuse of the initial state along the computation, require extra quantum resources as compared with other hash functions based on modular additions, XOR gates and rotations. We also track the entanglement entropy present in the quantum register at every step along the computation, showing that it becomes maximal at the inner core of the first action of the quantum oracle, which implies that no classical simulation based on Tensor Networks would be of relevance. Finally, we show that strategies that suggest a shortcut based on sampling the quantum register after a few steps of Grover's algorithm can only provide some marginal practical advantage in terms of error mitigation.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

02/22/2022

Applying Grover's Algorithm to Hash Functions: A Software Perspective

Quantum software frameworks provide software engineers with the tools to...
11/15/2021

Query and Depth Upper Bounds for Quantum Unitaries via Grover Search

We prove that any n-qubit unitary can be implemented (i) approximately i...
09/11/2019

Efficient template matching in quantum circuits

Given a large and a small quantum circuit, we are interested in finding ...
01/20/2022

The Accuracy vs. Sampling Overhead Trade-off in Quantum Error Mitigation Using Monte Carlo-Based Channel Inversion

Quantum error mitigation (QEM) is a class of promising techniques for re...
10/13/2021

The Straddling Gates Problem in Multi-partite Quantum Systems

It is well known that an arbitrary n-qubit quantum state |Ψ⟩ can be prep...
05/01/2020

ROS: Resource-constrained Oracle Synthesis for Quantum Computers

We present a completely automatic synthesis framework for oracle functio...
05/06/2020

A Quantum Algorithm To Locate Unknown Hashes For Known N-Grams Within A Large Malware Corpus

Quantum computing has evolved quickly in recent years and is showing sig...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.