Instant messaging applications like WhatsApp and iMessage have been widely used to exchange public and private information for both individuals and organizations. At the same time, the asynchronicity nature of these applications also introduces various security issues. To this end, considerable efforts have been made to strengthen the security and privacy of these applications, where a major goal is to capture the forward secrecy of asynchronous messaging without sacrificing other reasonable security properties. In this paper, we mainly focus on forward-secure zero round-trip time (0-RTT) key exchange protocols. Such a protocol enables a user to send the encrypted application data along with the first protocol message, and thus is especially suitable for securing asynchronous messaging. Concretely, we introduce a new cryptographic primitive dubbed as puncturable identity-based matchmaking key encapsulation mechanism (PIB-MKEM). It captures the authenticity of ciphertexts, and also allo