ImPossibility of Unconditionally Private Auctions

1
(Im)Possibility of Unconditionally Private
Auctions

• Felix Brandt and Tuomas Sandholm
• Carnegie Mellon University

2
Overview

• Privacy in sealed-bid auctions
• Bidder-resolved auctions
• Secure multiparty computation
• Unconditional full privacy
• Main results
• Conclusion

3
Privacy in Sealed-Bid Auctions

• Classic setting Each bidder submits bid to
  auctioneer who then declares outcome (e.g.,
  winner and 1st- or 2nd-highest bid)
• Bidders are reluctant to reveal their bids to
  auctioneer
• Confidentiality of private information
• Significance for current auction and future
  negotiations
• In 2nd-price auctions bids are usually equal to
  valuations due to dominant strategy equilibrium

4
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
5
Privacy Classes

• Adversarys computational power
• Bounded by probabilistic polynomial computation?
  computational privacy
• Unbounded? unconditional privacy
• Number of agents adversary may corrupt
• Certain fraction of agents, e.g., n/2 or n/3?
  threshold privacy
• Any proper subset of agents? full privacy (or
  (n-1)-privacy)

6
Multiparty Computation

• Classic possibility results

unb.
Unconditional full privacy
computational power
(pr. ch.)
some functions
any function
poly
Brandt, FC03 3-round computationally fully
private Vickrey auction protocol
(intract.)
n/2
n
untrustworthy parties
7
What is wrong with computational privacy?

• presumes P?NP(unknown)
• presumes average-case hardness(largely
  unexplored field)
• presumes NP-hardness of some problem, e.g.,
  factoring(unknown for most common problems)
• no eternal privacy

8
Example of Unconditionally Fully Privately
Computable Function

• Modular sum f(x1,,xn)S xi mod m

2
x1 x2 x3 (mod 10)
2
4
Agent 1
Agent 2
Agent 3
0
9
x1 3
7 1 5 (mod 10)
5
1
7 (mod 10)
6
9
Main Theorems

• Which auction types can be emulated privately?
• Disregard ties in order to obtain general results

? (exp. rounds)

• ?

• ?
• (if ngt2)

• ?
• (if ngt2)

10
Robustness of 2nd-price Impossibility

• Theorem 2nd-price auction can not be emulated
  privately even when
• only protecting a single losing bid(hiding the
  highest bid is possible, anonymized English
  auction)
• revealing second-highest bidders identity
• limiting the size of curious coalitions to n/2
• allowing positive error probability (conjectured)

11
Conclusion

• No distributed protocol that privately computes
  2ndprice auction outcome (without relying on
  computational intractability)
• Dutch-style protocol for 1st-price auction (no
  more efficient protocol)
• Future work
• Construct minimum information-revelation
  2nd-price protocol