# Why use integer factorization to secure FACT0RN?

As it turns out, integer factoring is of immense interest to mathematicians and cryptography research. There are academics, professional societies and intelligence programs dedicated to factoring integers. Factorization is the process of breaking down a positive integer into smaller positive integers that are eventually broken down into their smallest factor, which are prime factors.

As an example, let’s use the number 60.

Factors of this number include 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30.

2 x 30 = 60

3 x 20 = 60

4 x 15 = 60

5 x 12 = 60

6 x 10 = 60

While these numbers are all factors, not all are prime factors (prime numbers are only divisible by 1 or the number itself). The prime factors for the integer 60 only consist of the prime factors 2, 3 and 5.

2 x 2 x 3 x 5 = 60

22 x 3 x 5 = 60

It sounds simple, boring, and useless but that is far from the truth!

It is easy to generate a large bit number (hundreds of digits) by multiplying two long prime integers, but it is more difficult to work backwards and know the prime factors that created our number. In fact, the privacy and security of top intelligence agencies, government and banks hinges on the difficulty of integer factoring. Security encryption provided by these large bit numbers is almost impossible to break using the currently available technology, including some of the world’s most powerful supercomputers.

Rights to privacy and secure communications are fundamental to the pillars of modern society, including intelligence work, finance and the digital world. The internet achieves secure, private messaging through various encryption methods. With the internet’s initial design, protocols such as HTTP did not consider security, which led to encrypted versions like HTTPS that allow us to browse online more securely. Protocols like HTTPS are often secured by RSA encryption that is actually based on prime factorisation.

Users can only access the public encrypted messages with private decryption keys. We have seen the devastating consequences that may occur with the breach of intelligence information or financial services. For example, DeFi protocols with weak encryption have lost billions of dollars in compromised security. Therefore, a strong encryption system is vital to prevent hacking. Put simply, strong encryption methods based on prime factorization helps to keep our vital information secure.

The FACT0RN blockchain aims to be the PoW blockchain that requires better mathematical theory, and by doing so, it can help to advance knowledge in mathematics, cryptography and security in a way that we can all benefit.

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