Quote - Noooooooooooooo.

The whole basis of public key encryption is that the process of encrypting a message with a public key is easily done, while the reverse (decrypting it) is not, unless you have the private key

The reverse is not decrypting, is to follow the algorithm in the reverse direction..

Quote - It may seem intuitive to believe that by reverse engineering the key-checking algorithm that one can then create a program to generate valid keys, but this is not necessarily the case (it actually is possible, given enough time.  However "enough time" could turn out to be months or even years of processing time on even the fastest computers).

They believe that the existence of so huge number of possible combinations would make impossible to decrypt in "enough time", that's the failure of the system.
Decryption is based on the use of intelligence and not by use of brute force of trying all the possible combinations. Nobody that discovers a program key use a computer running for years to try all the possible combinations, even a year is too much time because the program will be obsolete and a newer version was released.
Keys are discovered by the use of intelligence, human intelligence and not stupid computer intelligence, and many can be discovered in less than an hour of human work looking at the code.

All the software encryption and protection is flawed, it is flawed because all the mathematical theories involved are used out of context and wrongly applied.
In first place most of the programmers that do the protection have no idea of what are doing and have no mathematical background to deal with advanced theories, they only pick an algorithm from some software library or take it from some book and then put it in the software.
Next comes the company managers that have no idea at all what are doing, they live in Hollywood! The result is a joke.

There's a huge difference in the use of encryption in serious applications as war times and the use in common software.
The purpouse of encrypting a message is to send it without the enemy know what it is. You encrypt the message with a key using some encryption algorithm, who decrypt the message use the same or other key using some decryption algorithm.
It can look to be the same but you soon will see that software protection use it out of context:
War/spy message
You send a crypted message, the key that you use has a very short life, you only use this key for only this message or very few messages. The next message you send will be with other key, you can't give enough time your enemy to decode the key and of course your next message will not be the same as the previous one.
The enemy when intercept your coded message put to work their team of brains and use all the spies information to decode your message.
In the decrypting process there don't exist a point where you can say that you discovered the key.
You can think that you decoded when the recovered message makes some sense, but you cannot be sure.
You can also reach a point when the recovered message have no meaning to you, you continue trying to decrypt it. You hit the right key but you ignored it because you wasn't able to understand the meaning of the message.
In resume, you never are sure if you discovered the key.
Software serial number
The key and the message are always exactly the same, it never change and continue to exist until the pass of time is able to destroy all the existent CD copies of this software. A ten year old software you always can open it with a ten year old key.
The war messages are different , "move the troops to place xxx", "target is at location xxx:yyy", "meet person xxx at place yyy"
The encrypted software messages are very simple and always the same: "the key is valid, you can proceed further with the installation"
You can be 100% sure when you found the right key and 100% sure when the key is wrong.
The message transmited can be resumed to YES or NO. Only one bit of message!!!!!
The enemy  or spy needs the message and a decrypting machine.
The message and all the elements needed to decode the message are present in the software..

Stupidity also evolves!