There have been a number of Scientific discoveries that seemed to be purely scientific curiosities that later turned out to be incredibly useful. Hertz famously commented about the discovery of radio waves: “I do not think that the wireless waves I have discovered will have any practical application.”
Are there examples like this in math as well? What is the most interesting “pure math” discovery that proved to be useful in solving a real-world problem?
prime number factorization is the basis of assymetric cryptography. basically, if I start with two large prime numbers (DES was 56bit prime numbers iirc), and multiply them, then the only known solution to find the original prime numbers is guess-and-check. modern keys use 4096-bit keys, and there are more prime numbers in that space than there are particles in the universe. using known computation methods, there is no way to find these keys before the heat death of the universe.
DES is symmetric key cryptography. It doesn’t rely on the difficulty of factorizing large semi-primes. It did use a 56-bit key, though.
Public key cryptography (DSA, RSA, Elliptic Curve) does rely on these things and yes it’s a 4096-bit key these days (up from 1024 in the older days).
RSA mostly uses 4096 bit keys nowadays. DSA is no longer used (or shouldn’t be lol). Ed25519 uses 256 bit keys.
thank you