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Shamir's secret sharing scheme using floating point arithmetic

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Date Issued:
2012
Summary:
Implementing Shamir's secret sharing scheme using floating point arithmetic would provide a faster and more efficient secret sharing scheme due to the speed in which GPUs perform floating point arithmetic. However, with the loss of a finite field, properties of a perfect secret sharing scheme are not immediately attainable. The goal is to analyze the plausibility of Shamir's secret sharing scheme using floating point arithmetic achieving the properties of a perfect secret sharing scheme and propose improvements to attain these properties. Experiments indicate that property 2 of a perfect secret sharing scheme, "Any k-1 or fewer participants obtain no information regarding the shared secret", is compromised when Shamir's secret sharing scheme is implemented with floating point arithmetic. These experimental results also provide information regarding possible solutions and adjustments. One of which being, selecting randomly generated points from a smaller interval in one of the proposed schemes of this thesis. Further experimental results indicate improvement using the scheme outlined. Possible attacks are run to test the desirable properties of the different schemes and reinforce the improvements observed in prior experiments.
Title: Shamir's secret sharing scheme using floating point arithmetic.
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Name(s): Finamore, Timothy.
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Issued: 2012
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: ix, 35 p. : ill. (some col.)
Language(s): English
Summary: Implementing Shamir's secret sharing scheme using floating point arithmetic would provide a faster and more efficient secret sharing scheme due to the speed in which GPUs perform floating point arithmetic. However, with the loss of a finite field, properties of a perfect secret sharing scheme are not immediately attainable. The goal is to analyze the plausibility of Shamir's secret sharing scheme using floating point arithmetic achieving the properties of a perfect secret sharing scheme and propose improvements to attain these properties. Experiments indicate that property 2 of a perfect secret sharing scheme, "Any k-1 or fewer participants obtain no information regarding the shared secret", is compromised when Shamir's secret sharing scheme is implemented with floating point arithmetic. These experimental results also provide information regarding possible solutions and adjustments. One of which being, selecting randomly generated points from a smaller interval in one of the proposed schemes of this thesis. Further experimental results indicate improvement using the scheme outlined. Possible attacks are run to test the desirable properties of the different schemes and reinforce the improvements observed in prior experiments.
Identifier: 794228861 (oclc), 3342048 (digitool), FADT3342048 (IID), fau:3851 (fedora)
Note(s): by Timothy Finemore.
Thesis (M.S.)--Florida Atlantic University, 2012.
Includes bibliography.
Electronic reproduction. Boca Raton, Fla., 2012. Mode of access: World Wide Web.
Subject(s): Signal processing -- Digital techniques -- Mathematics
Data encryption (Computer science)
Computer file sharing -- Security measures
Computer algorithms
Numerical analysis -- Data processing
Persistent Link to This Record: http://purl.flvc.org/FAU/3342048
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU