Abstract: Signature-based authentication is a core cryptographic primitive essential for most secure networking protocols. A new signature scheme, MSS, allows a client to efficiently authenticate herself to a server. The new scheme is modeled in an offline/online model where client online time is premium. The offline component derives basis signatures that are then composed based on the data being signed to provide signatures efficiently and securely during run-time. MSS requires the server to maintain state and is suitable for applications where a device has long-term associations with the server. MSS allows direct comparison to hash chains-based authentication schemes used in similar settings, and is relevant to resource-constrained devices, e.g., IoT. MSS instantiations are derived for two cryptographic families, assuming the hardness of RSA and decisional Diffie-Hellman (DDH) respectively. Then used is the new scheme to design an efficient time-based one-time password (TOTP) protocol.