Moving Cryptography Forward

by Raine Conor

RCR's latest area of focus has been on researching ways to break cryptosystems that have strength based on the difficulty of factoring large integers. If you can reduce a large integer down to its prime factors, then you can break the cryptosystem. It is a simple concept, yet when the integer is large enough, there is no efficient algorithm known.

Using creativity and logical deduction, RCR has developed a specialized algorithm that is capable of efficiently factoring integers of cryptographic significance. For a technical analysis of this algorithm please visit this page.

Starting Small

The size of numbers used to encrypt messages is astronomically large. An example of one of these numbers looks like this:
18229021800499389179810999984147294316694481152259999178780074391429829111773881276038281122549654793695493293264207027376776682362226410733793123117211189262610875849497690435072434819643299230953875973012904516275649075242502330535166202977871076698326460570645695302887174347984232777274357996755103073370058925661345782916623908813122753869187282565276059526610380429671250747371523249129041042163813118053400537221212684975928016171244322844087003229657728793172722938168054943184764356498974298899669556165909647342688587153673679901583046195388386919521461435059782679160323429508745816818692733354205358568651
These numbers are difficult to comprehend, so we decided to focus on researching the nature of these numbers starting in the 4 to 6 digit range, then scale up to test new discoveries. This made thinking about these numbers easier, and led to algorithms that are just as valid for any size number.

Thinking About Numbers Differently

Numbers are a piece of language that we use to describe things. Numbers can be represented as a diagram by graphing them. This allows us to create visual descriptions of ideas, data, or physical objects using numbers.

Manipulations to graphs often have an equivalent mathematical function. This connection between numbers and images helped us invent our algorithm by giving us a way to utilize imagination as a mathematical tool. We did this by taking a graph of the number system we were working with, modifying the graph as if it were a physical object, then modifying the respective formulas accordingly.

Identifying Patterns

Once we had a visual representation of a number set, we searched for patterns. We searched for them visually first, and when there was a promising lead, we tested them computationally to get a sense how it can be written mathematically and if the pattern is reproducible for a larger set of numbers.

Conclusion

Breaking encryption moves cryptography forward by initiating discussion about the discovered vulnerability and hopefully the invention or adoption of a stronger system. Our research into integer factorization opens the door for new ideas to explore in the field. The algorithm that was born out of this research is just the beginning of a new generation of efficient factoring algorithms.

Read the technical analysis of our patented factoring algorithm here, or if you are interested in testing it in your facility, please contact us to request access to our source code.

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