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 algorithm attack

the people still need to make deeper and longer explorations.