Cryptography is the science of writing messages in a way that can be read by only the ones for whom they are intended. In our discussion, which will be given at an introductory level, we will give a brief history of the subject and introduce the notion of private key and public key systems of encryption. We will discover why prime factorization and prime numbers play such an important role in modern day cryptography (that is, since the 1970s) and create our own public key cipher. As a consequence we'll see a connection to computer algorithms and the unsolved P vs. NP completeness problem.

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