The ever-growing number of Internet connected devices poses several cybersecurity risks. Most of the exchanged data between the Internet of Things (IoT) devices are not adequately secured due to resource constraints on IoT devices. Attribute Based SignCryption (ABSC) is a powerful cryptographic mechanism suitable for distributed environments, providing flexible access control and data secrecy. However, it imposes high designcryption costs, and does not support access policy update (user addition/revocation). This paper presents PROUD, an ABSC solution, to securely outsource data designcryption process to edge servers in order to reduce the computation overhead on the user side. PROUD allows end-users to offload most of the designcryption overhead to an edge server and verify the correctness of the received partially designcrypted data from the edge server. Moreover, PROUD provides the access policy update feature with neither involving a proxy-server, nor re-signcrypting the signcrypted message and redistributing the users' secret keys. The access policy update feature in PROUD does not affect the size of the message received by the end-user which reduces the bandwidth and the storage usage. Our comprehensive theoretical and experimental analysis prove that PROUD outperforms existing schemes in terms of functionality, communication and computation overhead.