As the importance of information security is widely recognized today, development of cryptography in practical use is rapidly taking place. On the other hand, however, many cases have been reported, where problems are found in the cryptographic systems already in use, or where the cryptographic systems are broken. Causes for a cryptographic system to get corrupted can be: defects in cryptographic algorithm designs; defects in implementation; defects in attack models and definitions of security; progress in computers and attack algorithms; inapplicability due to the change of environment. It is to be noted that the cryptographic system that has been created in the circumstance where there can be some kind of defects is generally vulnerable to breakdown. In the world of cryptography, we should regard ”Anything that can happen, happens.”