#### Primes, Modular Arithmetic, and Public Key Cryptography

(April 15, 2004)

#### __Introduction__

Every cipher we have worked with up to this point has been what is called a *symmetric key cipher*, in that the key with which you encipher a plaintext message is the same as the key with which you decipher a ciphertext message. As we have discussed from time to time, this leads to several problems. One of these is that, somehow, two people who want to use such a system must privately and secretly agree on a secret key. This is quite difficult if they are a long distance apart (it requires either a trusted courier or an expensive trip), and is wholly impractical if there is a whole network of people (for example, an army) who need to communicate. Even the sophisticated Enigma machine required secret keys. In fact, it was exactly the key distribution problem that led to the initial successful attacks on the Enigma machine.

However, in the late 1970’s, several people came up with a remarkable new way to solve the Continue reading

## Recent Comments