IB Math HL Internal Assessment - Integer Factorization
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Abstract
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Since a young age, I’ve already been obsessed with computers. When I grew older, I realized that mathematics is the core of computer science. Many things in computers work because of the beauty of mathematics. One day, I wondered how could data be securely transferred through the Internet? How would passwords be sent over the Internet without others knowing? How would such public information be encrypted such that only the sending and the receiving party can understand the message without being intercepted and hacked? Therefore, I am going to focus on Public Key Cryptography, more specifically RSA encryption. As I know through previous research on this topic, this method of encryption is all based on mathematics. After further investigation, I found out there are many advanced mathematical areas that are applied to make RSA encryption work in modern day computer systems: Modular Arithmetic, Fermat’s Little Theorem, et cetera. The mathematical topics involved in this exploration are Algebra and Discrete Mathematics. After finding the general topic I want to do, I will create an aim for my exploration. I will explore the use of mathematics in making this widely encryption method work, and also try and crack the RSA encryption by creating my own computer program, automatically doing mathematical functions for me.

IB Math HL Internal Assessment - Integer Factorization
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Limitations
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The code can only factorize a 9-digit number. You also need to manually calculate the ceiling of square root n.

Abstract
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Since a young age, I’ve already been obsessed with computers. When I grew older, I realized that mathematics is the core of computer science. Many things in computers work because of the beauty of mathematics. One day, I wondered how could data be securely transferred through the Internet? How would passwords be sent over the Internet without others knowing? How would such public information be encrypted such that only the sending and the receiving party can understand the message without being intercepted and hacked? Therefore, I am going to focus on Public Key Cryptography, more specifically RSA encryption. As I know through previous research on this topic, this method of encryption is all based on mathematics. After further investigation, I found out there are many advanced mathematical areas that are applied to make RSA encryption work in modern day computer systems: Modular Arithmetic, Fermat’s Little Theorem, et cetera. This requires me to self-study areas of mathematics that I am unfamiliar with, namely Discrete Mathematics. In this exploration, I will be using Algebra and Discrete Mathematics as the mathematical topics.

The aim for my exploration is to attempt to hack RSA. Finding the private keys with only the public keys. I will explore the use of mathematics in making this widely used encryption method work, and also try and crack the RSA encryption by creating my own computer program, automatically doing mathematical functions for me.

Update Abstract and add limitations
Update Abstract and add limitations