First Advisor

Fang Song

Date of Award

5-26-2017

Document Type

Thesis

Degree Name

Bachelor of Science (B.S.) in Physics and University Honors

Department

Physics

Subjects

Quantum theory, Hashing (Computer science), Collisions (Nuclear physics)

DOI

10.15760/honors.421

Abstract

This work proves an improved lower bound for the quantum query complexity of collision- finding in hash functions whose images are distributed according to a non-uniform distribution. Recent work by [TTU16] applied the leftover hash lemma to show that at least Omega(2k/9) quantum queries are necessary to find a collision when the image distribution has min-entropy k. In comparison, a result by [Zha15] implies that Omega(2k/3) quantum queries are necessary if the distribution is uniform. In this paper the lower bound complexity of [Zha15] is extended directly to the non-uniform case using a chain of reductions which convert collisions in min-entropy k distributions into collisions in the uniform distribution with constant probability. This result shows a minimum security guarantee for hash functions under more general assumptions in which the image distribution may not be uniform.

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Persistent Identifier

http://archives.pdx.edu/ds/psu/20427

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