Improved Trapdoors and Public Key Search Encryption Based on Middle-Product LWE
Yufan Yao, Jianhua Wang, Ke Wang +3 more
Abstract Middle-product learning with errors (MP-LWE) was proposed in 2017 by Rosa et al., it is considered to be a method that combines the high efficiency of the R-LWE with the security guarantee of the ordinary LWE. Following the idea of this problem, in the TCC 2019, Alex Lombardi et al. further studied the method of constructing identity-based encryption (IBE) scheme on the premise of the MP-LWE. They introduced several major technologies, these include the introduction of a new leftover hash lemma and the instan-tiation of a brand-new variant of lattice trapdoor corresponding to MP-LWE. The idea of instantiation of trapdoor is very novel, but the equation can not be solved correctly by using the trapdoor. In the current work, we have improved the research results of the Lombardi et al., that is, we re-instantiate the trapdoor matching MP-LWE and use it to construct a new IBE scheme. Further, we also use the classical transformation of Abdalla et al. to transform the constructed IBE scheme into a MP-LWE-based public key search encryption scheme (PEKS). Compared to IBE and PEKS schemes from LWE, our scheme is more effective, and their ciphertexts and keys size are only O˜(n) in size (for identities of size n bits). Compared to IBE and PEKS schemes from ring-LWE, our schemes have similar efficiency
•Jul 17, 2023•1 citation