This article first describes a paper by Ling, Phan, and Stehle at the CRYPTO 2014 which presented the first encryption scheme for traitor tracing from lattice, and the scheme is almost as efficient as the learning with errors (LWE) encryption. However, their scheme is not constructed on an efficient trapdoor, that is, the trapdoor generation and preimage sampling algorithms are rather complex and not suitable for practice. This article is considered to use the MP12 trapdoor to construct an improved traitor tracing scheme. First, by using batch execution method, this article proposes an improved extracting algorithm for the user's key. Then, this article combines that with multi-bit encryption system to construct an efficient one-to-many encryption scheme. Furthermore, it is presented that a novel projective sampling family has very small hidden constants. Finally, a comparative analysis shows that the parameters of the scheme such as lattice dimension, trapdoor size, and ciphertext expansion rate, etc., all decrease in some degree, and the computational cost is reduced.
Hardness of k-LWE and Applications in Traitor Tracing
