AdaCrypt - Vector Cryptography

Operational Overview

Factoring of Vectors. The vector to be factorised (factored if you prefer) is proposed as being the defining normal vector of a plane. If it is stipulated that this plane passes through the origin (0, 0, 0) then the plane is completely defined by the normal vector. This normal vector is a direction vector, or more precisely, a unit direction vector, not to be confused with a unit vector which is the vector quotient obtained when a vector is divided by its magnitude,

The factors of the vector then occur as pairs of vectors in the plane that always multiply out in ‘cross’ or ‘vector’ multiplication to give a product that is equal to the normal vector of the plane. Furthermore, the infinite set of all the possible factors occur as consecutive points on special number lines called factor lines in the same plane such that,

Vn × V(n-1) = N where N is the normal vector of the plane.
Vn is the position vector of any number ‘n’ on a factor-line in the plane.

The position vector that is used to define a number on a vector factor-line is called a Pn. A useful thing worth noting about a Pn is that it is comprised of a set of three coprime integers. It might be difficult to prove that it will always be so but results to date seem to indicate this.

In general vectors to be factored must have integer coefficients and for the cryptography being discussed here, they, ie the normal vectors, should be non-zero integer coefficient vectors.

Integrality of a Plane.
This means the disposition of the integer points, that is points that have integer coordinates that belong in the plane. The square mesh of integer (x, y defined) points on the standard X-Y plane is projected onto each inclined plane to form a mesh of diamond-shaped boxes with integer points at the corners of these boxes. Factoring of the normal vector of a plane also enables the equation of the general meshed-defined integers to be written in terms of the factors in addition to defining the factor lines themselves.

Intercepts
The intercepts provide a gateway to the plane and are conspicuous by the fact that the value of the associated coordinate (x, y or z) is zero at this point thus enabling some useful analysis to be made that leads to the equations of ‘factor lines’ and of the general mesh of integer points in that plane.

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