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Education for all
Number theory may be one of the “purest” branches of mathematics, but it has turned out to be one of the most useful when it comes to computer security. For instance, number theory helps to protect sensitive data such as credit card numbers when you shop online. This is the result of some remarkable mathematics research from the 1970s that is now being applied worldwide.
Sensitive data exchanged between a user and a Web site needs to be encrypted to prevent it from being disclosed to or modified by unauthorized parties. The encryption must be done in such a way that decryption is only possible with knowledge of a secret decryption key. The decryption key should only be known by authorized parties.
In traditional cryptography, such as was available prior to the 1970s, the encryption and decryption operations are performed with the same key. This means that the party encrypting the data and the party decrypting it need to share the same decryption key. Establishing a shared key between the parties is an interesting challenge. If two parties already share a secret key, they could easily distribute new keys to each other by encrypting them with prior keys. But if they don’t already share a secret key, how do they establish the first one?
This challenge is relevant to the protection of sensitive data on the Web and many other applications like it. Your computer doesn’t initially share any secret keys with Web sites. How then do you encrypt data you are sending to the site? You might eventually set up a password, and the password could then be used to derive an encryption key. But how do you protect the password from interception when you’re first setting it up?