安全多方计算以及密钥共享.pdf

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Introduction

The problem

Motivation and applications

Basic Terminology

Corrupted parties

Definitions of security

Protocols for Multi-Party Computations

Overview

Passive secure protocol

Active secure protocol

Appendix

Secure Multi-Party Computations Secure Multi-Party Computations An Introduction Christian Zielinski Last updated in 2015 1 / 52

Secure Multi-Party Computations Outline 1 Introduction The problem Motivation and applications 2 Basic Terminology Corrupted parties Deﬁnitions of security 3 Protocols for Multi-Party Computations Overview Passive secure protocol Active secure protocol References 2 / 52

Secure Multi-Party Computations Introduction Outline 1 Introduction The problem Motivation and applications 2 Basic Terminology Corrupted parties Deﬁnitions of security 3 Protocols for Multi-Party Computations Overview Passive secure protocol Active secure protocol References 3 / 52

Secure Multi-Party Computations Introduction The problem Secure multi-party computations • Consider n parties, with private inputs x1, . . . , xn • They want to compute a function f (x1, . . . , xn) in a secure way • Security means here • Privacy: The respective inputs remain private • Correctness: The output is guaranteed to be correct • Fairness: Each party learns the result • This should even hold when some parties try to cheat • The following presentation is primarily based on Ref. [1, 2] 4 / 52

Secure Multi-Party Computations Introduction The problem Questions at hand • How to carry out computations without revealing the inputs? • How to deal with cheating (corrupted) parties? • How to deﬁne security formally? • What is the upper limit of corrupted parties allowed? • How does this bound depend on the assumption made about the attacker? 5 / 52

Secure Multi-Party Computations Introduction Motivation and applications Motivation and applications • Multi-party computations (MPCs) have a wide range of applications • Auctions • Several parties are bidding for a product • Winning party and maximum bid should be determined, without revealing bids of other parties • Electronic voting schemes • Each party votes for a candidate • Only the result is made public, the votes remain secret • Yao’s Millionaires’ Problem, c.f. Ref. [3] • A group of millionaires wants to ﬁnd out who is the richest • Nobody wants to reveal how wealthy they are 6 / 52

Secure Multi-Party Computations Basic Terminology Outline 1 Introduction The problem Motivation and applications 2 Basic Terminology Corrupted parties Deﬁnitions of security 3 Protocols for Multi-Party Computations Overview Passive secure protocol Active secure protocol References 7 / 52

Secure Multi-Party Computations Basic Terminology Corrupted parties Adversaries • To discuss secure MPCs, we have to deﬁne security • Hence we have to make assumptions about cheating parties • Typically one models them by considering an adversary • This adversary can take over (corrupt) certain subsets of parties • We assume one adversary, assuming the worst-case scenario of coordinated corrupted parties (monolithic adversary) • We assume that at the beginning of the protocol honest (i.e. not corrupted) parties do not know which parties are corrupted 8 / 52

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