This paper introduces a novel type of digital watermarking, which is mainly designed for embededing information into cryptographic data such as keys, ciphertexts, and signatures. We focus on a mathematical structure of the recent major cryptosystems called pairing-based schemes. We present a detection-type watermarking scheme by which a watermark is visible by anyone but unremovable without secret trapdoor. The important feature is that both correctness and security of cryptographic data remain satisfied even if the trapdoor is published.