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MATH-211 Introduction to Cryptography
Offered academic year 2010-2011
In this introductory course we begin by looking at how the ancient Roman military send secret messages. We then survey cryptography from Roman times up to today's high tech world. Students will learn how to encrypt messages and how to attempt to break codes. We will discuss the efficiency and security level of different encryption methods. To make the discussion rigorous, we will need tools/concepts/results from
mathematics.
Mathematical content: mappings and inverse mappings, modular arithmetic, the additive group Z/n, the multiplicative group Z*/n, Euler's phi function, Fermat's Little theorem and Euler's generalization, primitve roots, discrete logarithms.
Cryptographic content: classical ciphers and their decryption (shift, affine, and Vigenere ciphers), key exchange protocols (main
example: Diffie-Hellman), public key ciphers (main example: RSA).
An important mathematical thrust will be to show students that there are
alternative arithmetic systems in which familiar objects such as inverses, products, and logarithms have strange properties, and that these are the right tools for cryptography.
Credits: 3
Prerequisites: None
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