Lower bounds for collusion-secure fingerprinting

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/ )) and attains security against coalitions of size c with error. Boneh and Shaw also present a lower bound of Ω(c log(1/c )) on the length of any collusion-secure code. We give new lower bounds on the length of collusion-secure codes by analyzing a weighted coinflipping strategy for the coalition. As an illustration of our methods, we give a simple proof that the BonehShaw construction cannot be asymptotically improved. Next, we prove a general lower bound: no secure code can have length o(c2 log(1/c )), 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/c )) as long as log(1/ ) ≥ Kk log c, where K is a constant and k is the number of columns in the cod...

• Type: Conference
• Year: 2003
• Where: SODA
• Authors: Chris Peikert, Abhi Shelat, Adam Smith
• Keywords: Algorithms, Collusion-secure Codes, Lower Bound, Secure Code, SODA 2003