Hierarchical key assignment for black-box tracing with efficient ciphertext size

We propose a hierarchical key-assignment method to reduce the ciphertext size in a black-box tracing scheme presented at ASIA-CRYPT 2004. Applying the proposed method to this scheme, the ciphertext size is reduced from O(root n) to O(k+log(n/k)) without a substantial increase in the decryption-key size, where k, n denote the maximum number of colluders in a coalition and the total number of receivers respectively. The resulting scheme also supports black-box tracing and enjoys the following properties: Even if a pirate decoder does not respond any further queries when it detects itself being examined, the pirate decoder can be traced back to a person who participated in its construction. A tracer's key, which is necessary for black-box tracing, is public.