摘要
目前的公钥加密方案受到来自量子计算的威胁,研究在量子计算下安全的公开加密算法具有重要的意义.本文提出了遍历矩阵的概念,并给出了遍历矩阵的性质.同时提出了基于有限域上遍历矩阵的双侧幂乘问题(TEME:Two-side Ergodic Matrices Exponentiation),并证明了求解TEME问题是NP完全的.据此,本文提出了一个新的公钥加密方案,并在标准模型下,证明了该方案基于TEME问题的安全性,即该方案具有适应性选择密文攻击下的不可区分性.
The current public key encryption schemes are vulnerable under the threat from quantum computing,it is necessary to research secure public key encryption algorithm under quantum computing.The concept of ergodic matrices and its property are given,and a new difficult problem named Two-side Ergodic Matrices Exponentiation（TEME） is proposed,which is proved at least NP-complete.Accordingly,we present a new public key encryption scheme based on ergodic matrices,and proved it is secure based on the TEME problem in the standard model,that is,the INDistinguishability against adaptively Chosen Ciphertext Attack（IND-CCA）.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2010年第8期1908-1913,共6页
Acta Electronica Sinica
基金
国家教育部博士点基金(No.20050183032)
关键词
公钥密码
遍历矩阵
NP完全
可证明安全性
public key cryptography
ergodic matrix
NP-Complete
proved security
