The paper introduces the concept of aggregate signatures, which allow multiple signatures from different users on distinct messages to be combined into a single, shorter signature. This aggregation process is useful for reducing the size of certificate chains and message sizes in protocols like Secure BGP (SBGP). The authors construct an efficient aggregate signature scheme based on bilinear maps, which are more powerful than general gap Diffie-Hellman groups. They also demonstrate that aggregate signatures can be used to create verifiably encrypted signatures, enabling users to verify that a given ciphertext is the encryption of a signature on a specific message. Additionally, the paper shows how similar ideas can be extended to construct simple ring signatures. The security of these schemes is analyzed in detail, and the authors provide concrete security proofs.The paper introduces the concept of aggregate signatures, which allow multiple signatures from different users on distinct messages to be combined into a single, shorter signature. This aggregation process is useful for reducing the size of certificate chains and message sizes in protocols like Secure BGP (SBGP). The authors construct an efficient aggregate signature scheme based on bilinear maps, which are more powerful than general gap Diffie-Hellman groups. They also demonstrate that aggregate signatures can be used to create verifiably encrypted signatures, enabling users to verify that a given ciphertext is the encryption of a signature on a specific message. Additionally, the paper shows how similar ideas can be extended to construct simple ring signatures. The security of these schemes is analyzed in detail, and the authors provide concrete security proofs.