A standard signature scheme generates a signature σ against a message m. An aggregate signaturescheme takes n many signatures σi ∀i ∈ n and generates a single σagg against n many messages or a single message. Most existing work on aggregate signatures fails to provide a detailed proof of security under different attacks. This creates a problem in assessing the weakness of the newly proposed signatures or even gauging the strength of existing signature schemes. In this thesis, we establish the unforgeability against Key-only-atack (uf-koa) in Random Oracle Model(ROM). We also prove the stronger notion of security in Elliptic-Curve Generic Group Model(EC-GGM). We reveal the underlying geometry of ECDSA and show how to manipulate it in order to generalize ECDSA for aggregate signatures. This thesis work proposes the first schemes that don’t require pairing-friendly elliptic curves to achieve efficient and secure aggregate signatures. This work presents two non-interactive ECDSA aggregate signatures which are constant-sized with commu- nication complexity same as space complexity.