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Cryptographic hashing using chaotic hydrodynamics.

Abstract：

:Fluids may store and manipulate information, enabling complex applications ranging from digital logic gates to algorithmic self-assembly. While controllable hydrodynamic chaos has previously been observed in viscous fluids and harnessed for efficient mixing, its application to the manipulation of digital information has been sparsely investigated. We show that chaotic stirring of a viscous fluid naturally produces a characteristic signature of the stirring process in the arrangement of particles in the fluid, and that this signature directly satisfies the requirements for a cryptographic hash function. This includes strong divergence between similar stirring protocols' hashes and avoidance of collisions (identical hashes from distinct stirs), which are facilitated by noninvertibility and a broad chaotic attractor that samples many points in the fluid domain. The hashing ability of the chaotic fluidic map implicates several unexpected mechanisms, including incomplete mixing at short time scales that produces a hyperuniform hash distribution. We investigate the dynamics of hashing using interparticle winding statistics, and find that hashing starts with large-scale winding of kinetically disjoint regions of the chaotic attractor, which gradually gives way to smaller scale braiding of single-particle trajectories. In addition to providing a physically motivated approach to implementing and analyzing deterministic chaotic maps for cryptographic applications, we anticipate that our approach has applications in microfluidic proof-of-work systems and characterizing large-scale turbulent flows from sparse tracer data.

journal_name

Proc Natl Acad Sci U S A

journal_title

Proceedings of the National Academy of Sciences of the United States of America

authors

Gilpin W

doi

10.1073/pnas.1721852115

subject

Has Abstract

pub_date

2018-05-08 00:00:00

pages

4869-4874

issue

19

eissn

0027-8424

issn

1091-6490

pii

1721852115

journal_volume

115

pub_type

杂志文章

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