一种改进的基于上三角矩阵的密钥交换方案

摘要

公钥密码学提供了密钥交换机制，实现了不安全信道上的密钥交换。基于数论的公钥密码学密钥交换，需要进行大量的数学运算，在有限的资源下实现起来比较困难。为了解决这个问题，？lvarez 等人提出了一种基于上三角矩阵幂乘运算的密钥交换方案，Kamal 等人对？lvarez 等人的方案进行了分析，给出了一种可能的攻击方案。利用矩阵多项式幂乘运算改进？lvarez 等人的方案，并进行可行性验证和安全性分析。经验证及分析表明，改进方案安全可行。%Public-key cryptography provides key exchange mechanisms which achieves secret keys exchange between users over insecure communication channels.The key exchange of public key cryptography based on number theory requires a large number of arithmetical operations,which is difficult to implement in limited resources.To overcome this problem,?lvarez et al.proposed a key exchange scheme which is based on upper triangular matrices exponentiation operation.Kamal et al.analysed this scheme and presented a possible attack scheme.We improve ?lvarez et al.’s scheme by making use of exponentiation operation of matrices polynomial,and verify the feasibility and analyse the security as well.It is demonstrated through verification and analysis that the improved scheme is secure and feasible.