| We present some new public and innovative private key cryptosystems based on the collection process for the lower central series of the free product of finitely many Burnside groups of finite rank and of exponent 2. These groups are residually nilpotent, and their lower central series may be investigated using efficient group-theoretic algorithms. This allows us to create new and innovative methods for encrypting and decrypting data via computational group theory. We refer to the general methodology as collective encryption. We have performed various experiments centered on collective encryption and have related our methods to contemporary advances in cryptology. Applying the recent test by Ueli Maurer we demonstrate that the encrypted data appears fairly random. Computational experiments allow us to pose a conjecture about the complexity of our algorithm. We also state several open problems and indicate directions and methodology for future research. |
