Lower bounds for collusion-secure fingerprinting

Chris Peikert, Abhi Shelat, Adam Smith

Research output: Contribution to conferencePaper

32 Citations (Scopus)

Abstract

Collusion-secure fingerprinting codes are an important primitive used by many digital watermarking schemes [1, 10, 9]. Boneh and Shaw [3] define a model for these types of codes and present an explicit construction. Their code has length O(c3 log(1/cε)) and attains security against coalitions of size c with ε error. Boneh and Shaw also present a lower bound of Ω(c log(1/cε)) on the length of any collusion-secure code. We give new lower bounds on the length of collusion-secure codes by analyzing a weighted coin-flipping strategy for the coalition. As an illustration of our methods, we give a simple proof that the Boneh-Shaw construction cannot be asymptotically improved. Next, we prove a general lower bound: no secure code can have length o(c2 log(1/cε)), which improves the previous known bound by a factor of c. In particular, we show that any secure code will have length Ω(c2 log(1/cε)) as long as log(1/ε) ≥ Kk log c, where K is a constant and k is the number of columns in the code (in some sense, a measure of the code's complexity). Finally, we describe a general paradigm for constructing fingerprinting codes which encompasses the construction of [3], and show that no secure code that follows this paradigm can have length o(c3/log c log(1/cε)) (again, by showing a lower bound for large values of ln(1/ε)). This suggests that any attempts at improvement should be directed toward techniques that lie outside our algorithm.

Original languageEnglish (US)
Pages472-479
Number of pages8
StatePublished - Jan 1 2003
EventConfiguralble Computing: Technology and Applications - Boston, MA, United States
Duration: Nov 2 1998Nov 3 1998

Other

OtherConfiguralble Computing: Technology and Applications
CountryUnited States
CityBoston, MA
Period11/2/9811/3/98

Fingerprint

Collusion
Fingerprinting
Lower bound
Digital watermarking
Coalitions
Paradigm
Digital Watermarking

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Cite this

Peikert, C., Shelat, A., & Smith, A. (2003). Lower bounds for collusion-secure fingerprinting. 472-479. Paper presented at Configuralble Computing: Technology and Applications, Boston, MA, United States.
Peikert, Chris ; Shelat, Abhi ; Smith, Adam. / Lower bounds for collusion-secure fingerprinting. Paper presented at Configuralble Computing: Technology and Applications, Boston, MA, United States.8 p.
@conference{53379480925c462397e026324bf55e81,
title = "Lower bounds for collusion-secure fingerprinting",
abstract = "Collusion-secure fingerprinting codes are an important primitive used by many digital watermarking schemes [1, 10, 9]. Boneh and Shaw [3] define a model for these types of codes and present an explicit construction. Their code has length O(c3 log(1/cε)) and attains security against coalitions of size c with ε error. Boneh and Shaw also present a lower bound of Ω(c log(1/cε)) on the length of any collusion-secure code. We give new lower bounds on the length of collusion-secure codes by analyzing a weighted coin-flipping strategy for the coalition. As an illustration of our methods, we give a simple proof that the Boneh-Shaw construction cannot be asymptotically improved. Next, we prove a general lower bound: no secure code can have length o(c2 log(1/cε)), which improves the previous known bound by a factor of c. In particular, we show that any secure code will have length Ω(c2 log(1/cε)) as long as log(1/ε) ≥ Kk log c, where K is a constant and k is the number of columns in the code (in some sense, a measure of the code's complexity). Finally, we describe a general paradigm for constructing fingerprinting codes which encompasses the construction of [3], and show that no secure code that follows this paradigm can have length o(c3/log c log(1/cε)) (again, by showing a lower bound for large values of ln(1/ε)). This suggests that any attempts at improvement should be directed toward techniques that lie outside our algorithm.",
author = "Chris Peikert and Abhi Shelat and Adam Smith",
year = "2003",
month = "1",
day = "1",
language = "English (US)",
pages = "472--479",
note = "Configuralble Computing: Technology and Applications ; Conference date: 02-11-1998 Through 03-11-1998",

}

Peikert, C, Shelat, A & Smith, A 2003, 'Lower bounds for collusion-secure fingerprinting', Paper presented at Configuralble Computing: Technology and Applications, Boston, MA, United States, 11/2/98 - 11/3/98 pp. 472-479.

Lower bounds for collusion-secure fingerprinting. / Peikert, Chris; Shelat, Abhi; Smith, Adam.

2003. 472-479 Paper presented at Configuralble Computing: Technology and Applications, Boston, MA, United States.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Lower bounds for collusion-secure fingerprinting

AU - Peikert, Chris

AU - Shelat, Abhi

AU - Smith, Adam

PY - 2003/1/1

Y1 - 2003/1/1

N2 - Collusion-secure fingerprinting codes are an important primitive used by many digital watermarking schemes [1, 10, 9]. Boneh and Shaw [3] define a model for these types of codes and present an explicit construction. Their code has length O(c3 log(1/cε)) and attains security against coalitions of size c with ε error. Boneh and Shaw also present a lower bound of Ω(c log(1/cε)) on the length of any collusion-secure code. We give new lower bounds on the length of collusion-secure codes by analyzing a weighted coin-flipping strategy for the coalition. As an illustration of our methods, we give a simple proof that the Boneh-Shaw construction cannot be asymptotically improved. Next, we prove a general lower bound: no secure code can have length o(c2 log(1/cε)), which improves the previous known bound by a factor of c. In particular, we show that any secure code will have length Ω(c2 log(1/cε)) as long as log(1/ε) ≥ Kk log c, where K is a constant and k is the number of columns in the code (in some sense, a measure of the code's complexity). Finally, we describe a general paradigm for constructing fingerprinting codes which encompasses the construction of [3], and show that no secure code that follows this paradigm can have length o(c3/log c log(1/cε)) (again, by showing a lower bound for large values of ln(1/ε)). This suggests that any attempts at improvement should be directed toward techniques that lie outside our algorithm.

AB - Collusion-secure fingerprinting codes are an important primitive used by many digital watermarking schemes [1, 10, 9]. Boneh and Shaw [3] define a model for these types of codes and present an explicit construction. Their code has length O(c3 log(1/cε)) and attains security against coalitions of size c with ε error. Boneh and Shaw also present a lower bound of Ω(c log(1/cε)) on the length of any collusion-secure code. We give new lower bounds on the length of collusion-secure codes by analyzing a weighted coin-flipping strategy for the coalition. As an illustration of our methods, we give a simple proof that the Boneh-Shaw construction cannot be asymptotically improved. Next, we prove a general lower bound: no secure code can have length o(c2 log(1/cε)), which improves the previous known bound by a factor of c. In particular, we show that any secure code will have length Ω(c2 log(1/cε)) as long as log(1/ε) ≥ Kk log c, where K is a constant and k is the number of columns in the code (in some sense, a measure of the code's complexity). Finally, we describe a general paradigm for constructing fingerprinting codes which encompasses the construction of [3], and show that no secure code that follows this paradigm can have length o(c3/log c log(1/cε)) (again, by showing a lower bound for large values of ln(1/ε)). This suggests that any attempts at improvement should be directed toward techniques that lie outside our algorithm.

UR - http://www.scopus.com/inward/record.url?scp=0038077509&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038077509&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:0038077509

SP - 472

EP - 479

ER -

Peikert C, Shelat A, Smith A. Lower bounds for collusion-secure fingerprinting. 2003. Paper presented at Configuralble Computing: Technology and Applications, Boston, MA, United States.