Paper 2019/285

SpaceFlip : Unbound Geometry Cryptography

Gideon Samid

Abstract

A geometry is a measure of restraint over the allowed 0.5n(n-1) distances between a set of n points (e.g. the metric and topological spaces). So defined, geometries lead to associated algebra. The complexities of such algebras are used to build cryptographic primitives. We propose then to push geometries to the limit -- unbound geometries -- where any two points may be assigned an arbitrary distance value, which may reflect a planning process or a randomized assignment. Regarding these distances as a cryptographic key, one could use the resultant algebras to carry out cryptographic missions. We define the mathematical framework for this aim, then present a few cryptographic primitives. Most effective implementation is through the new technology for “rock of randomness” establishing random distances through 3D printed molecular compounds. Security is proportional to the size of the ‘rock’. We use the term SpaceFlip to collectively refer to the unbound geometry, its associated algebra and the cryptographic tools derived from it.

Note: This article focuses on the cryptographic aspects of a multi-disciplinary research. The geometry described herein, reflects a borderline nanoscale 3D printing of a macromolecular compound, designed to fit into mobile phones and various other communication ports. The data is kept implicitly in the chemical structure of the chip, not as hackable bits. See "Rock of Randomness" published by the Materials Research Society of America.