Some Results for Multiparty Computation
Author
Gundersen, Jaron Skovsted
Term
4. term
Education
Publication year
2018
Submitted on
2018-09-05
Pages
31
Abstract
This thesis presents selected results related to multiparty computation (MPC) with an emphasis on their practical impact on protocols. First, it studies limitations in linear ramp secret sharing and obtains improved bounds on privacy and reconstruction thresholds as well as the threshold gap. Methodologically, a linear secret sharing scheme is represented by a pair of linear codes, allowing the thresholds to be characterized via relative generalized Hamming weights; known bounds on these weights then yield sharper bounds on the thresholds. Because many MPC protocols rely on secret sharing, the implications for (strongly) multiplicative secret sharing are also discussed. Second, the thesis introduces an oblivious transfer (OT) extension that generalizes a known binary protocol to linear codes over arbitrary finite fields. Examples demonstrate that the same number of OTs can be obtained from fewer underlying (expensive) base OTs than before, often at the cost of increased communication in other parts of the protocol; the trade-offs are illustrated and compared. Finally, the thesis outlines further work on squares of matrix-product codes and their potential relevance to MPC.
Dette speciale præsenterer udvalgte resultater om multiparty computation med fokus på, hvordan de påvirker praktiske protokoller. Først behandles begrænsninger i lineær ramp secret sharing, hvor vi opnår forbedrede grænser for privacy- og rekonstruktions-thresholds samt threshold gap. Metodisk repræsenteres et lineært secret sharing-scheme ved to lineære koder, hvorefter thresholds udtrykkes via relative generaliserede Hamming-vægte; kendte grænser for disse vægte oversættes dermed til skærpede grænser for thresholds. Da mange MPC-protokoller bygger på secret sharing, diskuteres også følgerne for (stærkt) multiplicative secret sharing. Dernæst præsenteres en oblivious transfer (OT) extension, der generaliserer en kendt protokol fra binære til lineære koder over vilkårlige legemer. Eksempler viser, at man kan simulere samme antal OTs ud fra færre underliggende (dyrere) OTs end tidligere, om end med en ofte øget kommunikationskompleksitet i andre dele af protokollen; afvejningerne mellem disse effekter illustreres og sammenlignes. Specialet afsluttes med forslag til videre arbejde, herunder resultater om kvadrater af matrix-produkt-koder og deres potentielle rolle i MPC.
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