This paper introduces aggregate and verifiably encrypted signatures based on bilinear maps. Aggregate signatures allow the combination of multiple signatures into a single short signature, enabling efficient verification of multiple signatures on distinct messages from different users. The authors construct an efficient aggregate signature scheme based on a recent short signature scheme using bilinear maps. This scheme works in groups where the Decision Diffie-Hellman (DDH) problem is easy, but the Computational Diffie-Hellman (CDH) problem is hard. The scheme uses a pair of groups and a bilinear map to enable efficient aggregation. Aggregate signatures are useful for reducing the size of certificate chains and message size in secure routing protocols like SBGP. The authors also show that aggregate signatures can be used to create verifiably encrypted signatures, which allow a verifier to test that a given ciphertext is the encryption of a signature on a given message. These signatures are used in contract-signing protocols. Additionally, the authors show that similar ideas can be used to extend short signature schemes to give simple ring signatures. The paper also discusses the security models and applications of aggregate signatures, including their use in certificate chains and secure routing protocols. The authors prove the security of their aggregate signature scheme and show that it provides efficient and secure signatures. The paper concludes with a discussion of the implications of their work and the potential applications of aggregate and verifiably encrypted signatures.This paper introduces aggregate and verifiably encrypted signatures based on bilinear maps. Aggregate signatures allow the combination of multiple signatures into a single short signature, enabling efficient verification of multiple signatures on distinct messages from different users. The authors construct an efficient aggregate signature scheme based on a recent short signature scheme using bilinear maps. This scheme works in groups where the Decision Diffie-Hellman (DDH) problem is easy, but the Computational Diffie-Hellman (CDH) problem is hard. The scheme uses a pair of groups and a bilinear map to enable efficient aggregation. Aggregate signatures are useful for reducing the size of certificate chains and message size in secure routing protocols like SBGP. The authors also show that aggregate signatures can be used to create verifiably encrypted signatures, which allow a verifier to test that a given ciphertext is the encryption of a signature on a given message. These signatures are used in contract-signing protocols. Additionally, the authors show that similar ideas can be used to extend short signature schemes to give simple ring signatures. The paper also discusses the security models and applications of aggregate signatures, including their use in certificate chains and secure routing protocols. The authors prove the security of their aggregate signature scheme and show that it provides efficient and secure signatures. The paper concludes with a discussion of the implications of their work and the potential applications of aggregate and verifiably encrypted signatures.