Revocable Identity-Based Encryption from Codes with Rank Metric

TLDR: In this article, the authors proposed an identity-based encryption scheme from codes with efficient key revocation using a binary tree data structure to reduce the amount of work in terms of key updates for the key authority.

Abstract: In this paper, we present an identity-based encryption scheme from codes with efficient key revocation. Recently, in Crypto 2017, Gaborit et al. proposed a first identity-based encryption scheme from codes with rank metric, called RankIBE. To extract the decryption key from any public identity, they constructed a trapdoor function which relies on RankSign, a signature scheme proposed by Gaborit et al. in PQCrypto 2014. We adopt the same trapdoor function to add efficient key revocation functionality in the RankIBE scheme. Our revocable IBE scheme from codes with rank metric makes use of a binary tree data structure to reduce the amount of work in terms of key updates for the key authority. The total size of key updates requires logarithmic complexity in the maximum number of users and linear in the number of revoked users. We prove that our revocable IBE scheme is selective-ID secure in the random oracle model, under the hardness of three problems: the Rank Syndrome Decoding (RSD) problem, the Augmented Low Rank Parity Check Code (\(\textsf {LRPC}^+\)) problem, and the Rank Support Learning (RSL) problem.