The Cayley-Purser algorithm is a public-key cryptography algorithm that relies on the fact that matrix multiplication is not commutative. It was devised by Sarah Flannery (then age 16), inspired by ideas of Michael Purser, for a Young Scientist competition in 1998. Flannery named the algorithm after Purser and Arthur Cayley (the inventor of matrices). The Cayley-Purser algorithm uses only modular matrix multiplication instead of modular exponentiation, and is much faster than other public-key algorithms for large moduli (e.g., about 20 times faster than RSA encryption for a 200-digit modulus). While the algorithm at first seemed to be as secure as RSA, it was subsequently shown that messages encrypted with this algorithm can be readily decrypted by knowledge of public data alone.

public-key cryptography | RSA encryption