  The purpose of this paper is to describe and analyze the Cayley-Purser
algorithm, which is a public-key cryptosystem proposed by Flannery in 1999. I
will present two attacks on it, one of which is apparently new. I will also
examine a variant of the Cayley-Purser algorithm that was patented by Slavin in
2008, and show that it is also insecure.
