Network Security: Private Communication in a Public World, Second Edition

8. Math with AES and Elliptic Curves

8.1. Introduction

We've seen a plethora of techniques for performing secret key and public key cryptography, and the number theory behind some of the public key algorithms. These public key schemes are based on the difficulty of factoring large integers, or the difficulty of calculating discrete logarithms over Z_p*. While these problems still seem intractable, some significant progress has been made, and that makes cryptographers nervous.

So cryptographers have started exploiting somewhat different mathematical structures to use as the basis for cryptographic schemes. In this chapter we'll explore the mathematics needed to properly understand Rijndael/AES (described algorithmically in §3.5 Advanced Encryption ...