Paper 2022/307

An Anonymous Trace-and-Revoke Broadcast Encryption Scheme

Olivier Blazy and Sayantan Mukherjee and Huyen Nguyen and Duong Hieu Phan and Damien Stehle

Abstract

Broadcast Encryption is a fundamental cryptographic primitive, that gives the ability to send a secure message to any chosen target set among registered users. In this work, we investigate broadcast encryption with anonymous revocation, in which ciphertexts do not reveal any information on which users have been revoked. We provide a scheme whose ciphertext size grows linearly with the number of revoked users. Moreover, our system also achieves traceability in the black-box confirmation model. Technically, our contribution is threefold. First, we develop a generic transformation of linear functional encryption toward trace-and-revoke systems for 1-bit message space. It is inspired from the transformation by Agrawal {et al} (CCS'17) with the novelty of achieving anonymity. Our second contribution is to instantiate the underlying linear functional encryptions from standard assumptions. We propose a $\mathsf{DDH}$-based construction which does no longer require discrete logarithm evaluation during the decryption and thus significantly improves the performance compared to the $\mathsf{DDH}$-based construction of Agrawal {et al}. In the LWE-based setting, we tried to instantiate our construction by relying on the scheme from Wang {et al} (PKC'19) only to find an attack on this scheme. Our third contribution is to extend the 1-bit encryption from the generic transformation to $n$-bit encryption. By introducing matrix multiplication functional encryption, which essentially performs a fixed number of parallel calls on functional encryptions with the same randomness, we can prove the security of the final scheme with a tight reduction that does not depend on $n$, in contrast to employing the hybrid argument.