Structured signatures are digital signatures where relationship between signers is guaranteed in addition to the validity of individually generated data for each signer, and have been expected for the digital right management. Nevertheless, we mention that there is no scheme with a tight security reduction, to the best of our knowledge. Loosely speaking, it means that the security is downgraded against an adversary who obtains a large amount of signatures. Since contents are widely utilized in general, achieving a tighter reduction is desirable. Based on this background, we propose the first structured signature scheme with a tight security reduction in the conventional public key cryptography and the one with a rigorous reduction proof in the ID-based cryptography via our new proof method. Moreover, the security of our schemes can be proven under the CDH assumption which is the most standard. Our schemes are also based on bilinear maps whose implementation can be provided via well-known cryptographic libraries.