Watermarking Cryptographic Data

This paper presents a novel watermarking scheme, which is designed for cryptographic data such as keys, cipher-texts, and signatures. Such a cryptographic data is defined carefully based on its mathematical structure in order to provide correctness and security. Thus, in general, cryptographic data has no redundancy and modified data cannot work for intended use. We first show a general solution to this problem by focusing on cryptographic data of the recent major cryptosystems called pairing-based schemes. We then present an example of construction for one of the most known pairing-based schemes. We also prove that both correctness and security remain satisfied even if cryptographic data is watermarked.