ABSTRACT
One approach to eliminating these disadvantages is to introduce
schemes or maybe reduce the security of the existing efficient schemes on those assumptions. Despite this approach being certainly fascinating, we are still left in practice with the issue that a new assumption turns out to be not as reasonable as it appeared on first sight. Furthermore, it is also unclear how to determine when the new assumption should be introduced to prove the security of the existing schemes. Thus, it is desirable to prove the security of the schemes on older and widely accepted problems rather than newer ones.
