Black Hat Physical Device Security: Exploiting Hardware and Software

Appendix B: Factoring By Quadratic Relationships A Construction

Introduction

Given the talk about factoring in the chapter on authentication I thought it worth while to show some of the methods that I have employed with relative ease and little mathematical education should you desire to delve into becoming an amateur mathematician. I know that there are tried and true methods, of which some offer only statistical probability of a number being prime or not, but I enjoy attempting to find a linear solution. At present, I'm likely far (if ever) from finding a solution to the world's biggest mathematical problem, however, maybe my work can shed light for someone else out there.

Below we denote exponential raises by using the ? symbol. 2 ? 2 means two to the second power. X ? Y means X to an unknown power of Y. In all examples, X will always refer to the column, in diagrams especially, and Y will always refer to the row. Z will always refer to an arbitrary value or the value in the graph that can be calculated by X ?2 ? Y ?2.

Relationships of a Square

Here are a few equations that we can merge together to demonstrate a simple example of the process of factoring or developing provable relationships by using them together. This table contains the answers to the equation Z = X ? 2 ? Y ? 2. The answers in the dotted boxes represent the answer Z.

Table B.1:

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