TENSOR HASHING

One way to hash values is to consider more advanced math. Tensors are more sophisticated but they are easy to understand.

Consider the vector of say (x,y) which is simply the coordinates on a sheet of paper. A vector of (x,y,z) simple extends above and below the sheet of paper. Vectors can have as many indexes as desired without limit.

The matrix is a set of rows and columns of numbers. In one sense it’s clear that a vector for rows and a vector for columns is called the cross product. A spreadsheet is more or less a glorified matrix.

The box takes the matrix one step higher with layers of more matrices. The cross product of a matrix and a vector gives the box.

Now that the basic ideas are presented a new way of looking at the objects is to consider the number of indices. The integer is called a zero order tensor while the vector is a first order tensor and the matrix is a second order tensor. This can be extended indefinitely as well.

Abstract algebra deals with groups, rings and fields. A field is just like the integers or real numbers etc. A group is a set such as the row permutations of the identity matrix which is closed under multiplication. Rings work like integers in which addition and multiplication are defined but unlike integers some rings may not be commutative etc. The example matrix is closed but its not commutative.

In more advanced math the idea of a finite field comes into discussion. Generally operators such as addition are done modolo to keep the result with the field. The boolean algebra is the simplest but finite fields are possible for any range needed.

Using tensor algebra it is possible to use multiple tensor products to hash anything so badly as to be unrecognizable over any desired field. The noncommutative nature of matrix algebra makes it ideal for a one way function that is impossible to reverse.

Using a square matrix as the salt can be generated quite easily. The product of two square matrices can grind the salt as much as desired over a finite field. The password can be mapped into a rectangular matrix that is the same height as the salt matrix. The product will be the same size as the password matrix and this will be the hashed result. The product can also be applied multiple times over the finite field.

Semirings are rings where an additive or multiplicative inverse may not be defined. Matrix inversion is complicated and attempts to simplify it have left much to be desired. If the determinant is not zero then AB=BA=I. Realistically inversion attempt will fail to remain within the finite field causing errors which make the algorithm more secure in cases where the seed is stolen.

Using boxes makes it even more brutal. The square box seed is very robust and it’s a noncommutative ring. There is no limited to the order of the tensor.

The NSA will no doubt have fits over this article as there is no way to crack this. The seed is random and there size of the square salt matrix is unknown as well. Then the finite field is unknown. This makes the tensor hash safe from any quantum analysis as the finite field and noncommutative nature of the ring make it secure. This is a true one way algorithm.

This algorithm is copyrighted and patent pending.