基于格上带舍入学习问题的抗选择密文攻击的公钥密码体制

CCA Secure Public Key Encryption Scheme Based on the Learning-with-Rounding Problem

基于格的密码体制具有可抵抗目前已知量子算法攻击、并行性好、由格上困难问题确保的可证安全性等优点,具有广泛的应用前景,受到了越来越多的关注。带舍入学习问题(learning with rounding问题,LWR问题)作为格上新兴问题,相关工作较少,研究价值较高。文章提出了两种基于该问题的公钥加密体制,给出了在随机谕示模型下的安全性证明。与现有基于该问题的体制相比,新体制可以达到适应性选择密文攻击下不可区分性(IND-CCA2)的安全性。

Lattice-based cryptography has promising prospects and has acquired much attention re- cently due to its potential advantages, such as resistance to cryptanalysis by quantum algorithms, as- ymptotic efficiency, and provable security with the hardness of lattice problems in the worst case. The emerging lattice-based problem, learning with rounding （LWR） problem, needs further investi- gation. Based on this problem two different public key encryption schemes are proposed and are proved secure against adaptively chosen cipher text attacks （IND-CCA2） under the hardness of LWR problem in the random oracle model. Existing schemes based on LWR problem can only reach chosen plaintext attack （CPA） security, which shows the main contribution.