基于多离散对数问题的公钥密码的分析

本文对一个特定群生成元系中元素的阶数的选取做了讨论，对多离散对数问题和基于它的公钥加密方案做了分析.指出在原文所述情况下，多离散对数问题可转化为离散对数问题，从而，该问题存在亚指数时间解，并导致相关私钥在大多数情况下是亚指数时间不安全的.本文进一步指出，在几乎任何情况下，密文还原问题都可转化为离散对数问题，从而，它也存在亚指数时间解.所以，要把离散对数问题和ElGamal公钥密码改造成抗Shor量子算法攻击的，还需做更深入的、持久的探索.

Analysis of a Public-Key Cryptograph Based on Multi-Discrete Logarithm Problems

The paper discusses the selection of orders of elements in one generator set for a specified group,and analyzes multi-discrete logarithm problems (MDLP) and a public key encryption scheme based on the MDLP.The paper points out that under the circumstances described by the original paper,the MDLP may be transformed into a discrete logarithm problem,which manifests that there exists a sub-exponential time solution for the MDLP,and causes a related private key insecure in sub-exponential time in most cases.Further,in almost any case,a ciphertext inversion problem may be transformed into a discrete logorithm problem,which illustrates that there also exists a sub-exponential time solution to the ciphertext.Therefore,to convert a discrete logarithm and the ElGamal cryptosystem into those which are resistant to the Shor quantum alg.orithm attack,the people still need to make deeper and longer explorations.