Cryptanalysis of Bohio et al.\u27s ID-Based Broadcast Signcryption (IBBSC) Scheme for Wireless Ad-hoc Networks

Broadcast signcryption enables the broadcaster to simultaneously encrypt and sign the content meant for a specific set of users in a single logical step. It provides a very efficient solution to the dual problem of achieving confidentiality and authentication during content distribution. Among other alternatives, ID-based schemes are arguably the best suited for its implementation in wireless ad-hoc networks because of the unique advantage that they provide - any unique, publicly available parameter of a user can be his public key, which eliminates the need for a complex public key infrastructure. In 2004, Bohio et al. [4] proposed an ID-based broadcast signcryption (IBBSC) scheme which achieves constant ciphertext size. They claim that their scheme provides both message authentication and confidentiality, but do not give formal proofs. In this paper, we demonstrate how a legitimate user of the scheme can forge a valid signcrypted ciphertext, as if generated by the broadcaster. Moreover, we show that their scheme is not IND-CCA secure. Following this, we propose a fix for Bohio et al.\u27s scheme, and formally prove its security under the strongest existing security models for broadcast signcryption (IND-CCA2 and EUF-CMA). While fixing the scheme, we also improve its efficiency by reducing the ciphertext size to two elements compared to three in [4]