Leakage-resilient attribute-based encryption scheme with large universe

Various leakage attacks in the actual environment allow attackers to obtain partial leakage of user secret information from cryptographic algorithms, resulting in traditional security no longer maintaining security in environments with leakage attacks. Cryptography researchers have proposed a series of cryptographic algorithms with leakage resilience to prevent the harm of leakage attacks on data security. The attribute-based encryption (ABE) scheme has received widespread attention and application in real-world environments due to its ability to provide fine-grained access control for data. However, in constructing existing leakage-resilient ABE schemes, the size of the system's public parameters is directly proportional to the size of the attribute set it can support, making it unable to be used in large attribute set environments. This paper proposes a new construction method for the leakage-resilient ABE scheme that supports large attribute sets. Firstly, to achieve better computational efficiency, this paper proposes a construction method for a leakage-resilient ABE scheme that supports large attribute sets on prime order groups and proves the security of this scheme based on the q-parallel bilinear Diffie Hellman exponent assumption. At the same time, performance analysis shows that our scheme has better computational, storage, and communication efficiency. Finally, to obtain a tight formal security proof, this paper proposes a construction method for a leakage ABE scheme that supports large attribute sets on composite order groups. It proves the security of the above scheme based on the improved assumption of subgroup determination on composite order groups.