https://blog.kernelstub.dev/tags/mathematics/Recent content in Mathematics on Prepakis Georgios | Kernelstub | Security ResearcherHugoen-USTue, 14 Jan 2025 00:00:00 +0000https://blog.kernelstub.dev/posts/advanced-cryptography-concepts-via-classical-to-post-quantum/Tue, 14 Jan 2025 00:00:00 +0000https://blog.kernelstub.dev/posts/advanced-cryptography-concepts-via-classical-to-post-quantum/<p>Cryptography has a strange history for a field that&rsquo;s now load-bearing for the entire internet. A lot of the number theory underneath it was developed by mathematicians who were doing pure math for its own sake, with zero interest in secrets or spies. Then, starting in the 1970s, people realized that certain &ldquo;hard&rdquo; problems in number theory (the kind that are easy to state but brutal to solve at scale) were exactly what you needed to build systems where two strangers could agree on a secret over a public channel, or where you could prove your identity without ever handing over a password. This post is a walk through that stack, from the classical number-theoretic foundations, through the protocols built on top of them, and finally into the post-quantum schemes that exist because a sufficiently large quantum computer would tear a hole through most of what came before.</p>