基于RLWE困难假设的NTRU型代理重加密方案

NTRU-Type Proxy Re-Encryption Scheme Based on RLWE Difficult Assumption

NTRU(number theory research unit)作为基于格公钥密码体制的经典分支,具有实用性强、尺寸小、计算速度快的优势,在第三轮NIST后量子密码算法标准化的评估中成功入围.自2015年Nuñez提出第一个基于NTRU的代理重加密方案以来,如何构造可证明安全的高可用性NTRU代理重加密方案,成为NTRU代理重加密体制研究发展的重难点问题.本文首先基于BI-NTRU-LPR公钥加密方案构造了单密钥的IND-CPA安全的NTRU公钥加密变体,与目前已有的NTRU变体相比私钥尺寸更小.基于此变体设计了在标准模型下可证明安全的新型NTRU代理重加密方案,其IND-CPA安全性可以归约到D-RLWE困难问题,进一步完善了NTRU代理重加密体制.新方案较目前格上基于LWE的代理重加密方案,密钥尺寸小,结构简洁,计算复杂度低,是一个单向、多跳、抗合谋攻击的高可用性代理重加密方案.

NTRU(number theory research unit),as a classical branch of lattice based public key cryptosystem,has the advantages of strong practicability,small size and fast computing speed,and has been successfully shortlisted in the third round of evaluation of NIST post quantum cryptography algorithm standardization.Since Nuñez proposed the first NTRU based proxy re-encryption scheme in 2015,how to construct a provable security and high availability NTRU proxy re-encryption scheme has become a key and difficult problem in the research and development of NTRU proxy re-encryption systems.This paper constructs a single key IND-CPA secure NTRU public key encryption variant based on BI-NTRU-LPR public key encryption scheme.Compared with the existing NTRU variant,the size of the private key of the designed scheme is smaller.Based on this variant,a new provable security NTRU proxy re-encryption scheme is designed,and the IND-CPA security of the scheme is reduced to the D-RLWE problem,which further improves the NTRU proxy re-encryption scheme.Compared with other existing proxy re-encryption schemes based on LWE,the designed scheme has smaller key size,simpler structure and lower computational complexity.It is a high availability proxy re-encryption scheme with Uni-directional,multi hop and anti collusion attack.