Distributed Identity Authentication with Lenstra–Lenstra–Lovász Algorithm–Ciphertext Policy Attribute-Based Encryption from Lattices: An Efficient Approach Based on Ring Learning with Errors Problem

Abstract

In recent years, research on attribute-based encryption (ABE) has expanded into the quantum domain. Because a traditional single authority can cause the potential single point of failure, an improved lattice-based quantum-resistant identity authentication and policy attribute encryption scheme is proposed, in which the generation of random values is optimized by adjusting parameters in the Gaussian sampling algorithm to improve overall performance. Additionally, in the key generation phase, attributes are processed according to their shared nature, which reduces the computational overhead of the authorization authority. In the decryption phase, the basis transformation of the Lenstra–Lenstra–Lovász (LLL) lattice reduction algorithm is utilized to rapidly convert shared matrices into the shortest vector form, which can reduce the computational cost of linear space checks. The experimental results demonstrate that the proposed method not only improves efficiency but also enhances security compared with related schemes.

Keywords

• lattice cryptography
• encryption of policy attributes
• identity authentication
• Lenstra–Lenstra–Lovász lattice reduction algorithm