HRA-secure attribute-based threshold proxy re-encryption from lattices

Abstract

Proxy re-encryption (PRE) allows a semi-trust proxy with a re-encryption key to transform a ciphertext encrypted under one key to an encryption of the same message under another key. Attribute-based proxy re-encryption (AB-PRE) is a generalization of PRE which enables fine-grained access control and delegation of encrypted data. However, traditional AB-PRE suffers from the single point of failure as it relies on a single proxy to perform ciphertext transformations. To resolve this problem, this paper introduces a new primitive called attribute-based threshold proxy re-encryption (AB-TPRE), that utilizes multiple (N) proxies for the transformations. In AB-TPRE, the re-encryption key is split into N shares, with each proxy receiving one share to generate a transformed ciphertext share. Only when a threshold (t) number of transformed ciphertext shares are combined can the transformed ciphertext be correctly generated. Furthermore, to address the security risk of shares leakage, we introduce a share updatable property that allows the re-encryption key shares to be refreshed. We propose a construction of AB-TPRE from lattices, and prove its security against the honest re-encryption attacks under the learning with errors (LWE) assumption, which is assumed to be quantum secure since up to now there is no known quantum algorithm to solve LWE in polynomial time.