In this paper, we propose the security notion of certificate-based signature that uses the same parameters and certificate revocation strategy as the encryption scheme presented at Eurocrypt 2003 by Gentry. Certificate-based signature preserves advantages of certificate-based encryption, such as implicit certification and no private key escrow. We present concrete certificate-based signature schemes derived from pairings on elliptic curves and prove their security in the random oracle model assuming that the underlying group is GDH. Additionally, we propose a concrete delegation-by-certificate proxy signature scheme which is derived from a certificate-based signature scheme after simple modifications. Our proxy scheme is provably secure in the random oracle model under the security notion defined by Boldyreva, Palacio and Warinschi.