This article presents Axiom, a DTLS-based approach to efficiently secure multicast group communication among IoT-constrained devices. Axiom provides an adaptation of the DTLS record layer, relies on key material commonly shared among the group members, and does not require one to perform any DTLS handshake. We made a proof-of-concept implementation of Axiom based on the tinyDTLS library for the Contiki OS and used it to experimentally evaluate performance of our approach on real IoT hardware. Results show that Axiom is affordable on resource-constrained platforms and performs significantly better than related alternative approaches.