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Efficient PrivacyPreserving Protocols for MultiUnit Auctions

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Significance for current auction and future negotiations ... Cryptographic single-unit auction protocols ... One additional round for discriminatory auction ... – PowerPoint PPT presentation

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Title: Efficient PrivacyPreserving Protocols for MultiUnit Auctions


1
Efficient Privacy-Preserving Protocols for
Multi-Unit Auctions
  • Tuomas Sandholm
  • Carnegie Mellon University

Felix Brandt Stanford University
2
Overview
  • Auctions (sealed-bid, multi-unit)
  • Privacy, correctness related work
  • Bidder-resolved auctions
  • Order statistic subprotocol
  • Secure multi-unit auction protocols
  • Analysis
  • Conclusion

3
Sealed-Bid Auctions
  • Each bidder submits sealed bid to auctioneer
  • Auctioneer opens all bids and declares outcome
    (i.e., allocation and prices)
  • English auction 2nd-price sealed-bid
    (Vickrey)Independent private values
  • Dutch auction 1st-price sealed-bid
  • Advantages Efficiency and privacy

4
Multi-Unit Auctions
  • M indistinguishable units of one item
  • Each bidder submits bid vector
    where denotes the price bidder i is willing to
    pay for jth unit (bidder is willing to pay
    for m units)
  • Auctioneer computes allocation that maximizes
    revenue (NP-complete)
  • Marginal decreasing valuations? tractable
  • Classic applications Treasury bills, electrical
    power, spectrum licenses
  • CS applications CPU time, network bandwidth

5
Common Pricing Schemes
  • Uniform-priceAll bidders pay same unit price
    given by (M1)st-highest bid
  • DiscriminatoryBidders pay what they bid (
    for mi units)
  • Generalized VickreyBidder who receives mi units
    pays sum of mi highest losing bids submitted by
    other bidders

6
Privacy and Correctness
  • Bidders are reluctant to reveal their bids to
    auctioneer
  • Confidentiality of private information
  • Significance for current auction and future
    negotiations
  • In (generalized) Vickrey auctions bids are
    usually equal to valuations due to dominant
    strategy equilibrium
  • Bidders doubt the correctness of the outcome
  • Especially in Vickrey auctions

7
Related Work
  • Cryptographic single-unit auction protocolsNaor
    et al 99, Abe et al 02, Lipmaa et al 02, Brandt
    03, etc.
  • 1st-, 2nd-, and (M1)st-price (unit demand)
  • Multiple auctioneers (either two (asymmetric MPC)
    or more (threshold MPC)
  • Cryptographic combinatorial auction
    protocolsSuzuki et al 02 and 03
  • Exponential worst-case complexity

8
Auctions without Auctioneers
  • Bidders jointly emulate virtual auctioneer,
    i.e., they jointly compute outcome function
    without revealing any information in addition to
    outcome

Auctioneer
Bidder 1
Bidder 2
Bidder 3
Bidder 1
Bidder 2
Bidder 3
9
Multiparty Computation (MPC)
  • General MPC is (still) inefficient
  • Special-purpose MPC auction protocols based on
  • Linear combinations
  • Random multiplications
  • Efficient implementation using homomorphic
    encryption (El Gamal) and standard ZK-proofs
  • Low round complexity
  • Communication complexity linear in number of
    prices

10
Vector Representation
  • Bids are expressed in unary notation
  • Linear combinations (multiplication with
    matrices)
  • Random multiplication matrix R

11
Order Statistic Subprotocol
  • Example
  • Extra work required due to possibility of ties
    involving mth-highest bid (total of m(N-m)
    vectors)

12
Compute Allocation
  • Additional vectors to enable tie-breaking

13
Compute Prices
  • Uniform-price auction
  • Discriminatory auction
  • Generalized Vickrey auction

14
Protocol Implementation
  • Round 1 Distributed generation of El Gamal keys
  • Round 2 Publishing El Gamal encryptions of bids
  • Round 3 Joint computation of outcome vectors
  • Round 4 Distributed decryption of outcome
  • One additional round for discriminatory auction
  • Two additional rounds for generalized Vickrey
    auction

15
Analysis
n bidders, M units, k prices
16
Conclusion
  • Fully private bidder-resolved constant-round
    protocols for all three common types of
    multi-unit auctions
  • Feasible for moderately-sized settings (tens of
    bidders, hundreds of prices)
  • Linearity in number of prices
  • High communication complexity
  • Straightforward adaptability to iterative
    auctions
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