基于R-LWE的公钥加密方案

摘要

An improved method of generating trapdoor on ideal lattice was proposed by a stronger regularity bound theorem, then with R-LWE encryption algorithm and strongly unforgeable one-time signature tool from ideal lattice, an adaptive chosen-ciphertext attack (CCA) secure PKE scheme under the standard model was designed. The new PKE scheme supported public ciphertext integrity verification, could achieve block encryption and had a high encryp-tion/decryption speed and a low encryption blowup factor, whose security proved reduced to decisional R-LWE as-sumption tightly. The construction is the first CCA-secure PKE cryptosystem completely based on hard problems from ideal lattice.%　　根据一个更紧凑的均匀性定理提出了一种改进的理想格上陷门生成方法；然后结合 R-LWE 加密算法和理想格上强不可伪造一次签名工具，在标准模型下设计了一个适应性选择密文攻击(CCA)安全的公钥加密方案。新方案可实现块加密，可支持公开的密文完整性验证，具有加解密速度快、密文扩展率低的优势，其安全性可以高效地归约为判定性R-LWE困难性假设。新方案是第一个完全基于理想格上困难问题构造的CCA安全公钥加密方案。