Design And Analysis Of Lattice-Based Public Key Encryption Schemes

With the rapid development of Internet industry, the security of network communications has acquired much attention from all walks of life. As the cornerstone of defense in network security, public key encryption (PKE) plays an important role in providing security for network communications. However, continuous progress in quantum computer brings more and more challenges to the traditional security of public key encryption schemes and algorithms. Lattice-based public key encryption schemes are immune to quantum attacks so far, which make them one of the most important cryptographic technologies in the post-quantum era. This emerging field has good application prospects and high research value. In this paper, we focus on the design and analysis of lattice-based PKE schemes, and carry out work mainly in the following three aspects:First, we proposed one-way trapdoor function on the basis of lattice-based Learning with Rounding Problem (LWR Problem), construct three PKE schemes based on LWR Problem and give their security proofs. Compared with the existing structures, new schemes have many advantages such as smaller ciphertext size and lower computational complexity. In addition, we take further studies in multi-bit encryption and give the lower limit of ciphertext-plaintext ratio. On the hardness of Decisional Learning with Rounding Problem (DLWR Problem), these schemes are secure under the notion of indistinguishability against chosen plaintext attack (IND-CPA secure).For PKE schemes, the notion of indistinguishability against adaptive chosen ciphertext attack (IND-CCA2 secure) is a higher level of security. Based on the IND-CPA secure schemes, we investigate designs of IND-CCA2 secure schemes, come up with two schemes in the random oracle model and one scheme in standard model that are IND-CCA2 secure, and give the corresponding security proofs on the hardness of DLWR Problem. Compared with IND-CPA secure schemes, these schemes are less efficient, but the level of security has been improved significantly.The recently proposed memory leakage attack gives a higher demand of the notion of security for PKE schemes. Therefore, how to make schemes more resilient to key leakage attacks becomes one of the issues that we need to pay attention to. We focus on the leakage resilience of LWR Problem, trapdoor function and schemes proposed in this paper, give out the threshold of leakage percent for general leakage model as well as leakage bits for bounded-retrieval model. On this basis, we modify the trapdoor generation function and PKE schemes to construct a highly key leakage resilient PKE scheme, which guarantees security when 1-log β/log q of the entire private key (β, q are parameters of the scheme) is leaked.