What I Learned About Cryptography as a Math Major

Most people never think about cryptography. You send a message, log into an app, or make a payment, and everything just works. But behind the scenes, a lot of that security depends on mathematics, especially ideas involving prime numbers.

When I studied mathematics, cryptography was one of the areas that made everything feel real. It was one of the first times I saw abstract math directly connect to systems people actually use every day.

At a high level, modern encryption works because of asymmetry. It is easy to take two very large prime numbers and multiply them together. But if you only have the result, it is extremely difficult to figure out which two primes were used.

That one idea is part of the foundation behind systems like RSA encryption. You can think of it like a lock: locking something is easy, but unlocking it without the key is extremely difficult. That difficulty gap is what helps keep data secure.

What stood out to me was not just the math itself, but how intentional it is. These systems are not random. They are carefully designed around problems that are computationally hard to reverse.

That changed how I viewed mathematics. It stopped feeling like something confined to a classroom and started feeling like something quietly protecting real people in real systems.

Another thing I learned is that security is not permanent. The strength of encryption depends on what computers are capable of. As computing power increases, and especially as quantum computing develops, some of the assumptions we rely on today may eventually change.

That does not mean everything suddenly becomes insecure overnight. It means systems have to evolve. There is already active work being done on post-quantum cryptography, which focuses on designing methods that remain secure even if older assumptions stop holding.

What I took away from studying cryptography is this: mathematics is not just theoretical. It quietly protects almost everything we do online.

The systems we trust today are built on very specific mathematical ideas, and those ideas have to be constantly revisited, tested, and improved. That connection between abstract math and real-world impact is what made the subject meaningful to me.