# Mathematical Cryptography

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Category: Mathematics
Slides: 13
Updated: 2026-05-15T22:19:41.459Z
Tags: catalog, math, cryptography

## Summary

A substitution cipher maps each plaintext letter to a fixed ciphertext letter. Caesar's shift is a special case: c ≡ p + k (mod 26) . Key sections include: MATHEMATICAL CRYPTOGRAPHY; Substitution & the Statistics That Betray It; The One-Time Pad — Unbreakable, Unusable; Modular Arithmetic — Integers, Wrapped; Fermat & Euler — Why RSA Works; RSA (1977) — Factoring as a Trapdoor; Diffie–Hellman — A Secret in Public; Elliptic Curves — Same Idea, Smaller Keys; One-Way: SHA-256 and the Compression Trick; Signing — Authorship Without Disclosure.

## Slide Outline

1. MATHEMATICAL CRYPTOGRAPHY
2. Substitution & the Statistics That Betray It
3. The One-Time Pad — Unbreakable, Unusable
4. Modular Arithmetic — Integers, Wrapped
5. Fermat & Euler — Why RSA Works
6. RSA (1977) — Factoring as a Trapdoor
7. Diffie–Hellman — A Secret in Public
8. Elliptic Curves — Same Idea, Smaller Keys
9. One-Way: SHA-256 and the Compression Trick
10. Signing — Authorship Without Disclosure
11. Zero-Knowledge — Convince Without Revealing
12. Post-Quantum — Past the Reach of Shor
13. Where to Go Next

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