### An Elgamal type cryptosystem using the nim-field

Following on from my last post about Conway’s nimbers, here’s how to perform an Elgamal style encryption and decryption. Recall…

### Conway’s “Nimbers”

While hunting about for some material on finite fields, I came across Conway’s “Nim Field”, or the field of “nimbers”,…

### A simple block cipher

When teaching the various modes of encryption: electronic code book (ECB), cipher block chaining (CBC) and the rest, it’s nice…

### A quick-and-dirty cryptographic hash function

Cryptographic hash functions sit at the core of many secure applications. They are vital to digital signatures for example: rather…

### The NSH method for matrix inversion

We all know that systems of linear equations can be solved iteratively, using either the Jacobi or Gauss-Seidel methods. But…

### Using Sage in a lab

This semester I’ve decided to use Sage for my cryptography labs, having used first Maple (several years ago), then Maxima…

### Landau's function

A few weeks ago, when I was writing about the general group-theoretical version of the Elgamal cryptosystem, I was led…

### Elgamal encryption on general groups

The Elgamal cryptosystem can be defined on the multiplicative group for prime with primitive root as follows: Alice chooses a…

### An elliptic curve cryptosystem based on factoring

In an elliptic curve over a field, the points form a group with respect to the standard addition of points…

### Approximations with continued fractions

In an excellent blog post earlier this year, Dave Richeson commented on the approximation: . The reason for this is…