This monograph gives a thorough treatment of the celebrated compositions of signature and encryption that allow for verifiability, that is, to efficiently prove properties about the encrypted data. This study is provided in the context of two cryptographic primitives: (1) designated confirmer signatures, an opaque signature which was introduced to control the proliferation of certified copies of documents, and (2) signcryption, a primitive that offers privacy and authenticity at once in an efficient way. This book is a useful resource to researchers in cryptology and information security, graduate and PhD students, and security professionals.