Identity-based Signatures (IBS) are a form of digital signature scheme that enables the generation and verification of signatures based on a user’s identity, such as an email address, social security number, or any other unique identifier. Recent advancements in post-quantum cryptography have further strengthened IBS schemes, making them resilient against quantum computing threats and ensuring their applicability in future secure communications. At ProvSec’21, Shaw and Dutta introduced an identity-based signature obtained from the isogeny-based signature scheme CSI-FiSh by Beullens et al. at ASIACRYPT’19. Later, at PQCrypto’23, Chen et al. proposed a tightly secure \(\textsf{IBS}\) by utilising the tightly secure variant of CSI -FiSh, called Lossy CSI -FiSh, by Kaafarani et al. at PKC’20. In this paper, we generalise those results to obtain a framework for constructing an \(\textsf{IBS}\) scheme from cryptographic (non-abelian) group actions. Under the pseudorandom assumption of underlying group actions, we prove that our \(\textsf{IBS}\) is tightly secure in the random oracle model. Moreover, we also generalise a Forward-Secure Identity-based Signature (FSIBS) scheme from group actions. This scheme ensures past signatures remain unforgeable even if the current signing key is compromised. Our schemes can be instantiated from existing NIST’s post-quantum signature candidates such as \(\textsf {MEDS}, \textsf {LESS} \) and \(\textsf {ALTEQ} \) .