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Optimal probabilistic fingerprint codes

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Gábor TardosAuthors Info & Claims

Journal of the ACM (JACM), Volume 55, Issue 2

Article No.: 10, Pages 1 - 24

https://doi.org/10.1145/1346330.1346335

Published: 15 May 2008 Publication History

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Abstract

We construct binary codes for fingerprinting digital documents. Our codes for n users that are ϵ-secure against c pirates have length O(c²log(n/ϵ)). This improves the codes proposed by Boneh and Shaw [1998] whose length is approximately the square of this length. The improvement carries over to works using the Boneh--Shaw code as a primitive, for example, to the dynamic traitor tracing scheme of Tassa [2005].

By proving matching lower bounds we establish that the length of our codes is best within a constant factor for reasonable error probabilities. This lower bound generalizes the bound found independently by Peikert et al. [2003] that applies to a limited class of codes. Our results also imply that randomized fingerprint codes over a binary alphabet are as powerful as over an arbitrary alphabet and the equal strength of two distinct models for fingerprinting.

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Tardos, G. 2003. Optimal probabilistic fingerprint codes. In Proceedings of the 35th Annual ACM Symposium on Theory of Computing (STOC). ACM, New York, 116--125.

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Cited By

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Barg AKabatiansky G(2025)FingerprintingEncyclopedia of Cryptography, Security and Privacy10.1007/978-3-030-71522-9_381(919-923)Online publication date: 8-Jan-2025
https://doi.org/10.1007/978-3-030-71522-9_381
Attias IDziugaite GHaghifam MLivni RRoy DSalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Information complexity of stochastic convex optimizationProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692151(2035-2068)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692151
Yan QYan HZhang L(2024) Synergistic Commutative Algorithm for Securing Vector Spatial Data via GD ‐ PBIBD Fingerprint Encoding and Data Encryption Transactions in GIS10.1111/tgis.13254Online publication date: 9-Oct-2024
https://doi.org/10.1111/tgis.13254
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Index Terms

Optimal probabilistic fingerprint codes
1. Mathematics of computing
  1. Information theory
    1. Coding theory
2. Security and privacy
  1. Cryptography
    1. Mathematical foundations of cryptography

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We construct binary codes for fingerprinting. Our codes for n users that are ε-secure against c pirates have length O(c² log(n/ε)). This improves the codes proposed by Boneh and Shaw [3] whose length is approximately the square of this length. Our codes ...
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Reviews

Reviewer: J Wolper

A fingerprint is a serial number embedded in a digital entity that enables tracing the source of a pirated version. A historical example is the introduction of small errors in low-order digits of tables of logarithms [1]. Pirates with multiple copies can identify where differences occur and, thus, alter part of the serial number. More pirates can alter the serial number even more, but information about the original serial numbers remains. This paper improves on previous results [1] that used a random matrix, by a clever choice of probability distribution of the bits in the matrix of serial numbers. The statistics of the distribution allow for a detailed analysis of the probability of accusing a pirate, which is high, and of the probability of accusing an innocent user, which is low. An accusation of piracy occurs when a score exceeds a certain threshold. The score is increased substantially when a bit is inconsistent with the distribution, and decreased when the bit is consistent. In other words, if 0 is expected but 1 is seen, add a lot to the score; if 0 is both expected and seen, subtract a little. Such results are seldom seen in the fingerprinting literature. In this paper, the codes constructed are shorter than those of Boneh and Shaw [1]. The probabilistic analysis is much more detailed and sophisticated than what is typically found in a computer science journal. Online Computing Reviews Service

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Published In

Journal of the ACM Volume 55, Issue 2

May 2008

282 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/1346330

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 May 2008

Accepted: 01 January 2008

Revised: 01 April 2004

Received: 01 August 2003

Published in JACM Volume 55, Issue 2

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Cited By

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Barg AKabatiansky G(2025)FingerprintingEncyclopedia of Cryptography, Security and Privacy10.1007/978-3-030-71522-9_381(919-923)Online publication date: 8-Jan-2025
https://doi.org/10.1007/978-3-030-71522-9_381
Attias IDziugaite GHaghifam MLivni RRoy DSalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Information complexity of stochastic convex optimizationProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692151(2035-2068)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692151
Yan QYan HZhang L(2024) Synergistic Commutative Algorithm for Securing Vector Spatial Data via GD ‐ PBIBD Fingerprint Encoding and Data Encryption Transactions in GIS10.1111/tgis.13254Online publication date: 9-Oct-2024
https://doi.org/10.1111/tgis.13254
Dang FJin XFu QLi LPeng GChen XLiu KLiu Y(2024)StreamingTag: A Scalable Piracy Tracking Solution for Mobile Streaming ServicesIEEE Transactions on Mobile Computing10.1109/TMC.2024.344541123:12(14530-14543)Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1109/TMC.2024.3445411
Zhang SZhu YZeng A(2024)Collusion-Resilient Privacy-Preserving Database FingerprintingIEEE Transactions on Information Forensics and Security10.1109/TIFS.2024.345574819(8306-8321)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TIFS.2024.3455748
Kamath GMouzakis ARegehr MSinghal VSteinke TUllman J(2024)A Bias-Accuracy-Privacy Trilemma for Statistical EstimationJournal of the American Statistical Association10.1080/01621459.2024.2443275(1-23)Online publication date: 20-Dec-2024
https://doi.org/10.1080/01621459.2024.2443275
Liu SPan HWang XZhao SLi Q(2024)A traceable and revocable broadcast encryption scheme for preventing malicious encryptors in Medical IoTJournal of Systems Architecture10.1016/j.sysarc.2024.103100149(103100)Online publication date: Apr-2024
https://doi.org/10.1016/j.sysarc.2024.103100
Boneh DPartap ARotem L(2024)Accountability for Misbehavior in Threshold Decryption via Threshold Traitor TracingAdvances in Cryptology – CRYPTO 202410.1007/978-3-031-68394-7_11(317-351)Online publication date: 18-Aug-2024
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Boneh DPartap ARotem L(2024)Traceable Secret Sharing: Strong Security and Efficient ConstructionsAdvances in Cryptology – CRYPTO 202410.1007/978-3-031-68388-6_9(221-256)Online publication date: 17-Aug-2024
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Steinke TNasr MJagielski MOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Privacy auditing with one (1) training runProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3668265(49268-49280)Online publication date: 10-Dec-2023
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