Secure Multi-Party Computations using Secret Sharing Schemes - A coding theoretical approach
Translated title
Sikkert Distribueret Beregninger med Secret Sharing Ordninger - En kodnings teoretisk tilgang
Author
Sorknæs, Johan Milton
Term
4. term
Education
Publication year
2016
Submitted on
2016-09-12
Pages
88
Abstract
Denne kandidatafhandling undersøger sikker flerpartsberegning (MPC), hvor flere deltagere sammen beregner et resultat uden at afsløre deres private input. Vi anvender hemmelighedsdelingsordninger (SSS) baseret på lineære koder til at beskytte data. Vi præsenterer både passivt sikre protokoller (sikre mod ærlige‑men‑nysgerrige deltagere) og aktivt sikre protokoller (sikre mod ondsindet adfærd) og giver eksempler med lineære SSS'er, herunder en ramp‑version af Masseys SSS (en variant med separate grænser for privatliv og rekonstruktion). Først beskriver vi en aktivt sikker MPC‑protokol med lineær SSS, som kun tillader addition og skalarmultiplikation. For at understøtte generelle beregninger introducerer vi multiplikative og stærkt multiplikative SSS'er, som muliggør sikker multiplikation og dermed protokoller for enhver funktion under passiv eller aktiv sikkerhed. Da multiplikative SSS'er og deres tilhørende matricer er svære at konstruere, giver vi flere konkrete eksempler. Afslutningsvis præsenterer vi en passivt sikker protokol, der reducerer deltagernes kommunikation ved at gruppere multiplikationer.
This thesis studies secure multi‑party computation (MPC), where several participants jointly compute a result without revealing their private inputs. We use secret sharing schemes (SSS) built from linear codes to protect data. We present both passively secure protocols (secure against honest‑but‑curious participants) and actively secure protocols (secure against malicious behavior), and give examples using linear SSS, including a ramp version of Massey’s SSS (a variant with separate privacy and reconstruction thresholds). We first describe an actively secure MPC protocol with linear SSS that supports only addition and scalar multiplication. To handle general computations, we introduce multiplicative and strongly multiplicative SSSs, which enable secure multiplication and therefore passively and actively secure protocols for any function. Because multiplicative SSSs and their associated matrices are hard to construct, we provide several concrete examples. Finally, we present a passively secure protocol that reduces communication between participants by grouping multiplications.
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