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#number-theory
1 articles
01
2026-09-23
·
Security
·
FREE
·
PAPER
·
20 min read
RSA from Scratch — The Number Theory Behind Public Keys
RSA lets you publish a key that locks but cannot unlock. This builds it from congruence arithmetic up: key generation, the two modular exponentiations, and a line-by-line proof from Euler's theorem of why the message comes back — then a worked example small enough to check by hand, why factoring is the security assumption, and why textbook RSA must never be shipped without padding.