ABSTRACT
This chapter introduces some ideas from modern cryptography which makes use of congruences and Fermat’s Theorem as well as Euler’s Function and Euler’s Theorem. A simple technique is called linear encryption, which in this case would involve using a modulus of 26 and two keys, a multiplier m (which must be relatively prime to 26) and an adder b. Fermat’s Theorem tells us that if a is a non-zero element of Zp, then ap-1=1(modp). The point is that we need shared secure keys to communicate, but, ironically, we need other keys to communicate our desired keys, and so on.
