The maths behind the code: number theory, linear algebra, and the proofs that make crypto work.
A deep-dive into the full cryptographic stack powering every HTTPS connection — RSA-OAEP, AES-GCM, ECDHE key exchange, and a working TLS 1.3 handshake simulation, all built in pure Python from first principles.
JavaScript cannot do RSA with numbers. Not slowly, not imprecisely — at all. The largest modulus a Number can handle is 26 bits and RSA needs 2048, and the failure is silent. Here's the implementation that works and why.
Finding a matrix inverse is very useful not only in Computer Science but when solving equations by hand. However, using the formula Adj(A) / det(A) can be
RSA Encryption has always been amazing to me. It allows you to publish an encryption key – also known as e – without having to compromise your decryption key – known
Part 1 used 15-bit primes and only encrypted integers. Making it usable means generating 1024-bit primes and chunking bytes — and the standard way to do the second one silently destroys data on inputs the tests never cover.
Every HTTPS connection you have ever made runs on a 1978 paper. You can build the core of it in about fifty lines of Python — and then see exactly why those fifty lines would get you destroyed in production.
