Number Theory, Polynomials, and the Advanced
Encryption Standard
Joshua Holden
Rose-Hulman Institute of Technology
http://www.rose-hulman.edu/~holden
Joshua Holden (RHIT) Number Theory, Polynomials, and the AES 1 / 15

Question What does cryptography have to do with number theory?
Joshua Holden (RHIT) Number Theory, Polynomials, and the AES 2 / 15

Question What does cryptography have to do with number theory?
Answer Everything.
Joshua Holden (RHIT) Number Theory, Polynomials, and the AES 2 / 15

Shift (Caesar) ciphers, atbash cipher modular arithmetic
Affine ciphers gcds, Euclidean algorithm, modular inverses
Pohlig-Hellman exponentiation cipher Fermat’s Little Theorem,
primality testing
Rivest-Shamir-Adleman (RSA) Euler’s phi functi