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Achieving Fairness in Private Contract Negotiation. Keith Frikken and Mikhail Atallah Purdue University March 2, 2005. Overview. Introduction/Motivation Related Work Framework Protocols Extensions Summary. Overview. Introduction/Motivation Related Work Framework Protocols

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Achieving fairness in private contract negotiation l.jpg

Achieving Fairness in Private Contract Negotiation

Keith Frikken and Mikhail Atallah

Purdue University

March 2, 2005


Overview l.jpg
Overview

  • Introduction/Motivation

  • Related Work

  • Framework

  • Protocols

  • Extensions

  • Summary

FC 2005


Overview3 l.jpg
Overview

  • Introduction/Motivation

  • Related Work

  • Framework

  • Protocols

  • Extensions

  • Summary

FC 2005


Introduction l.jpg
Introduction

  • Alice and Bob wish to negotiate a contract

  • Contract consists of many clauses

    • How to distribute revenue

    • Where are specific tasks performed

  • Alice and Bob have constraints on the acceptability of a clause

  • Naïve solution:

    • Alice and Bob reveal constraints to one another

    • Reveals unnecessary information

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Goals

  • Alice and Bob would like to create a protocol that determines an agreement that is:

  • Valid: satisfies both party’s constraints

  • Fair: neither party can control the outcome

  • Efficient: No clause is replaceable by another that is better for both parties

  • Semi-honest (Honest but Curious)

FC 2005


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Overview

  • Introduction/Motivation

  • Related Work

  • Framework

  • Protocols

  • Extensions

  • Summary

FC 2005


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Related Work

  • Automated Negotiations

    • [Grosof et al, 1999]

    • [Governatori et al, 2000]

  • Secure Protocols

    • [Yao, 1982]

    • [Yao, 1986]

    • [Goldreich et al, 1987]

    • [Katz and Ostrovsky, 2004]

    • [Malkhi et al, 2004]

  • Secure Protocols for Set Intersection

    • [Freedman et al, 2004]

FC 2005


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Building Blocks

  • Homomorphic Encryption:

    • E(x)*E(y)=E(x+y)

    • E(x)y=E(xy)

    • Semantic Security

    • [Paillier, 1999] and [Damgård and Jurik, 2001]

  • Secure Circuit Evaluation

    • [Yao, 1986]

    • Any 2-ary circuit with m gates and n inputs can be evaluated securely with:

      • O(m) communication and pseudo-random functions

      • O(n) 1-out-of-2 OTs

      • O(1) rounds

FC 2005


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Overview

  • Introduction/Motivation

  • Related Work

  • Framework

  • Protocols

  • Extensions

  • Summary

FC 2005


Framework l.jpg
Framework

  • A clause is a public set S={s0,…,sN-1}

  • Alice (Bob) have constraints on the acceptability of a clause, represented by AS (BS)

  • A term xS is acceptable if xA∩B

  • A clause is satisfiable if A∩B≠

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Framework(cont.)

  • A negotiation is a set of clauses S0,…,Sk-1

  • A negotiation is satisfiable if all of its terms are satisfiable

  • A contract is a sequence of terms x0,…,xk-1 (where xiSi)

  • A contract is valid if all terms are acceptable to all parties

FC 2005


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Overview

  • Introduction/Motivation

  • Related Work

  • Framework

  • Protocols

  • Extensions

  • Summary

FC 2005


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Protocol Template

  • Two Parts:

    • Protocol for determining if a clause is satisfiable

    • Protocols for computing a fair agreement (where neither party has control)

  • Extend these to the negotiation level

    • Satisfiability: Conjunction

    • Valid: Can compute independently

FC 2005


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Protocol for Satisfiability

  • Trivial reduction from Set Disjointness (i.e., a clause is satisifiable if the sets are not disjoint)

  • Suppose Alice forms a list of binary values a0,…,aN-1 where ai is true is Alice finds the ith term acceptable

  • Bob similarly forms b0,…,bN-1

  • Equivalent to i=0 to N-1 (ai  bi)

  • Easily evaluated with a circuit with O(N) gates and O(N) inputs

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Finding a fair term

  • Input: Alice has binary values a0,…,aN-1 and Bob has b0,…,bN-1. It is known that i such that aibi. Furthermore, Alice and Bob have exchanged semantically-secure homomorphic encryption systems EA and EB

  • Output: An index j such that ajbj and where neither Alice or Bob can control outcome

  • Semi-honest OT reduces to this problem

  • Circuit Complexity:

    • Both parties input permutations into the circuit which then permutes values (using composition of permutations) and then choose first agreement

    • O(N log N) input (unless using pseudorandom permutation)

    • O(N2) gates

  • Our protocol’s goal: O(N) modular exponentiations and O(N) communication

FC 2005


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Step 1 of Simplified Protocol

  • Input: Alice has binary values a0,…,aN-1 and Bob has b0,…,bN-1. It is known that i such that aibi.

  • Output: Bob learns EA(a0b0),…,EA(aN-1bN-1)

  • Step:

  • Alice sends to Bob EA(a0),…,EA(aN-1)

  • For each value bi, Bob does:

    • If bi=0, output EA(0)

    • If bi=1, output EA(ai)EA(0)

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Step 2 of Simplified Protocol

  • Input: Bob has EA(a0b0),…, EA(aN-1bN-1) and has a permutation ΠB

  • Output: Alice learns EB(a0b0),…, EB(aN-1bN-1) permuted with ΠB

  • Steps:

  • Bob permutes his input with ΠB

  • For each item EA(aibi) in the list:

    • Bob chooses a random value ri from {0,1}

    • If ri=0, he sets γi to EA(aibi), otherwise he γi sets it to EA(aibi)-1EA(1) (i.e., EA(1-(aibi))=EA(⌐(aibi)))

    • He sends Alice the ordered triple (γi,EB(ri),EB(1-ri))

  • For each triple (γi,EB(ri),EB(1-ri)):

    • Alice computes j=DA(γi)

    • If j=0 she sets her output to be EB(ri)

    • Otherwise sets her output to be EB(1-ri)

FC 2005


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Step 3 of Simplified Protocol

  • Input: Alice has EB(a0b0),…, EB(aN-1bN-1) permuted with ΠB, and she has two permutations Π’ and Π’’

  • Output: Bob gets a list of items permuted with Π’’Π’ΠB where one of them is marked as the agreement

  • Steps:

  • Alice permutes the items with Π’ (call this list α0,…,αN-1)

  • Alice computes a sequence of values: β0,…, βN-1, where β0=α0, and βi= αi*(βi-1)2

  • She computes a sequence of values: θ0,…, θN-1, where θi=(βi*EB(-1))q[i] where q[i] is a randomly chosen value

  • Alice permutes these values with Π’’ and sends them to Bob along with Π’’Π’

  • Bob decrypts the values and chooses the one that is 0 and computed the original index by inverting the permutations.

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Overview

  • Introduction/Motivation

  • Related Work

  • Framework

  • Protocols

  • Extensions

  • Summary

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Expressing Preferences

  • Alice and Bob assign a utility to each possible term (denoted by UA(x) and UB(x)) – assume utilities are distinct

  • A term t1 is inefficient if  a term t2 such that UA(t1)<UA(t2) and UB(t1)<UB(t2)

  • An efficient term is Pareto optimal

  • Desirable to only choose efficient terms

  • Set Disjointness reduces to finding a fair and efficient term

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Other Extensions

  • Interactive Negotiation

    • Feedback

    • Engage in the protocol several times relaxing constratints

  • Sparse sets: creating protocols with communication proportional to |A|+|B|

  • Dependent Clauses

    • Combine dependent clauses into a “super”-clause

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Overview

  • Introduction/Motivation

  • Related Work

  • Framework

  • Protocols

  • Extensions

  • Summary

FC 2005


Summary l.jpg
Summary

  • Introduce framework for contract negotiation

  • Introduced protocols for finding valid, fair, and efficient contracts

  • Future Work

    • Dependent Clauses

    • Multiple parties

    • Malicious Adversary Model

    • Multiple Negotiations with Inter-Clause Dependencies

    • Other negotiation strategies

FC 2005


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Acknowledgements

  • Anonymous Reviewers

  • Gov’t

    • NSF5, ONR, AFRL

  • Industry

    • Intel, Motorola, HP + the corporate sponsors of CERIAS

  • Foundation

    • Lilly Endowment

  • Purdue

    • CERIAS, Discovery Park

FC 2005


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