In this paper, we first show that recently proposed five CLS and CLAS schemes are insecure against universal forgery attacks, type I attacks, type II attacks or malicious-but-passive-KGC attacks. We discuss their security flaws, causes and countermeasures. We then present design principles to prevent various algebraic attacks including our attacks. The design principles will help in the construction of secure CLS and CLAS schemes against the previous attacks and potential attacks.
