Motivating Example: Microsoft Product Key
•When Windows or Microsoft office are installed, the user is required to enter a 25-digit alphanumeric antipiracy code.
•This code (“key”) must be short.
•The computer must be able to quickly recognize whether or not this is a valid key, without giving away any clue as to how to manufacture additional valid keys.
•Otherwise thieves would copy the software CDs and illegally resell them with new codes.  Key=CA$H.
•Future attacks will be faster.  How can one keep the key short, yet still keep up with the attackers?
•This requires new methods and cryptosystems.  Serious mathematics involved in design.
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