Why strong cryptography is needed?

If encryption/decryption algorithm is not "strong" enough, the bad guy can still get the message content without knowing the key. This is called 'Cryptanalysis'. One usual method of cryptanalysis is exhaustive search, which means trying all possible keys to decrypt the message. For example, if there are only 16 possible keys, then the bad guy can make use of a powerful computer to decrypt an encrypted message with all 16 possible keys.

Therefore, in order to protect the message, a "strong" encryption algorithm is needed. One condition is that the key length should be long enough so there

are many possible keys. Other conditions involves advanced mathematical properties.

What is the importance of public key infrastructure in electronic commerce?

Electronic commerce transactions are mainly based on Internet. There are two main security issues:
1. You need to identify the other party ("On Internet, nobody knows that you are a dog")
2. You don't want your information to be read by others.
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