94 - The Transformation of Beautiful Mathematics into Unbreakable RSA Encryption

In this episode, Momo sits down with his friend and long-time flatmate, Sohail, a mathematician, for a relaxed conversation about RSA cryptography—how it works and why it was revolutionary. Sohail breaks down the math behind RSA with clear, accessible examples and shares bonus fun facts about mathematics, broken predictions, and the future of math in an open-source world. --- Hardy writes: "The 'real' mathematics of the 'real' mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly 'useless'." A similar quote is attributed to Gauss, Sohail’s beloved mathematician. He jokingly said "I must have committed blasphemy by attributing it to someone else." Here’s the exact quote: "Mathematics is the queen of the sciences, and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but under all circumstances she is entitled to first rank." --- 00:58 – Sohail’s background in mathematics 03:23 – Math and real-world applications 08:11 – Asymmetric cryptography (like public-key cryptography) vs. symmetric cryptography (like the Caesar cipher) 11:18 – Remembering Gauss and Gauss Junior 15:55 – Is asymmetric cryptography mind-blowing? 17:53 – Why RSA cryptography was ground-breaking 21:01 – Explaining RSA through the “suitcase” analogy 25:09 – The math behind RSA 32:18 – What kinds of functions can be used in RSA? 34:58 – Clock-like modular functions in RSA 40:59 – Fermat’s Little Theorem as the basis of RSA 48:11 – A more complex function than Fermat’s Little Theorem used in RSA 50:43 – How your password reaches your bank securely using RSA 59:41 – Do my function and my bank’s function need to match in RSA? 01:01:19 – The importance of prime numbers in cryptography 01:04:06 – Accessible resources for math enthusiasts 01:05:40 – Nuance: which exponentiation operations are invalid in RSA 01:10:25 – Can a hacker intercept and decode an RSA-encrypted message? 01:12:28 – Why the move to elliptic curves? 01:14:00 – Other real-world applications of number theory 01:19:03 – The future of mathematics --- Fermat's little theorem explanation: https://en.wikipedia.org/wiki/Fermat's_little_theorem The channel for explaining math concepts in simple words, 3Blue1Brown. This source doesn’t explain Fermat’s Little Theorem, but it is an accessible source for math enthusiasts without specialized training. https://www.youtube.com/@3blue1brown Enigma Cipher Center, the cryptography museum in Poznan, Poland https://csenigma.pl/en/ My Nostr post about the internet and cryptography: https://primal.net/e/nevent1qqs9x3rxx3s9fhg6jwzvafgh6vvvxe658junc0vt4lphmcdl4w9ccrs9rk8dd --- 🟩 To help spread knowledge and information, you're free to reuse the content on this page—no permission needed. 🟩 --- Follow Momo: https://linktr.ee/mktahmasbi --- Buy me a coffee ☕️ http://coff.ee/roundthefire