On the saddle-point solution and the large-coalition behavior of fingerprinting games

Huang, Yen-Wei

Permalink

https://hdl.handle.net/2142/16836 Copy

Description

Title

On the saddle-point solution and the large-coalition behavior of fingerprinting games

Author(s)

Huang, Yen-Wei

Issue Date

2010-08-20T17:59:20Z

Director of Research (if dissertation) or Advisor (if thesis)

Moulin, Pierre

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

• fingerprinting
• traitor tracing
• capacity
• game theory
• minimax theorem
• Jeffreys' prior
• saddle-point problems

Abstract

We study a fingerprinting game in which the number of colluders and the collusion channel are unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value of a sequence of maximin games with mutual information as their payoff functions. However, these games generally do not admit saddle-point solutions and are very hard to solve numerically. Here under the so-called Boneh-Shaw marking assumption, we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point solution. If the maximal coalition size is $k$ and the fingerprinting alphabet is binary, we show that the capacity is in $\Theta(1/k^2)$. Furthermore, we prove rigorously that the asymptotic capacity is $1/(k^2 2 \ln2)$ and we confirm our earlier conjecture that Tardos' choice of the arcsine distribution asymptotically maximizes the mutual information payoff function while the interleaving attack minimizes it. Along with the asymptotic behavior, numerical solutions to the game for small $k$ are also presented.

Graduation Semester

2010-08

Permalink

http://hdl.handle.net/2142/16836

Copyright and License Information

Copyright 2010 Yen-Wei Huang

Owning Collections