## 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(c^{3} 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(c^{2} 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(c^{2} 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(c^{3}/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 language | English (US) |
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Pages | 472-479 |

Number of pages | 8 |

State | Published - 2003 |

Event | Configuralble Computing: Technology and Applications - Boston, MA, United States Duration: Nov 2 1998 → Nov 3 1998 |

### Other

Other | Configuralble Computing: Technology and Applications |
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Country/Territory | United States |

City | Boston, MA |

Period | 11/2/98 → 11/3/98 |

## All Science Journal Classification (ASJC) codes

- Software
- General Mathematics