Research And Implementation On LWE-based Cryptosystem

Unlike other public key cryptosystems, lattice-based cryptosystems are still safe under quantumcomputers. Basic module in lattice-based cryptosystem is basic algebra. As a result, lattice-basedcryptosystems are more efficient and become a new way of improving the efficiency of public keycryptosystems. At present, LWE-based cryptosystems are the most efficient cryptosystems withsecurity proof in lattice-based cryptography, so they become a focus in research.But there are still many problems in LWE-based cryptosystems: Most LWE-based cryptosystemsonly statisfy CPA security, cryptosystems in genearl lattices are still inefficient, and there’s littlepractical research on LWE-based cryptosystems. We research on these problems, general methods forconstructing CCA security cryptosystems, and LWE-based cryptosystems, the main contributions ofour work are as follows:(1)A CCA2cryptosystem based on LWE-based IBE scheme. CCA2cryptosystem based onstrong one-time unforgeable signature and IBE scheme will increase key size and introduce morecomputing expense in encryption/decryption. We first research on the LWE-based IBE scheme andthen proposed an improved IBE-based CCA2cryptosystem by using MAC and encapsulation scheme.This new cryptosystem is more efficient without sacrificing security.(2)A CCA2cryptosystem in ideal lattice. By using the general method for constructing CCA2cryptosystem, we propose a CCA2cryptosystem in ideal lattice based on preimage sampleable fuction.In contrast with cryptosystem in geneal lattice, this new cryptosystem decreases public key size and isfaster without sacrificing security.(3) By using GPU, we implement multi bit LWE cryptosystem. Multi bit LWE-basedcryptosystem is easily parallel, and GPU implementation has universality. Based on this experiment,we analyze error rate, key generation and encrytion/decryption. The experiment shows that practicalerror rate is as expected, and compared with CPU implementation, we get hardware speedup fromGPU.