Two Faces of Cryptography — RSA and the Quantum Threat

From Caesar's cipher, through the public-key revolution of RSA in 1977, to Shor's 1994 algorithm threatening RSA itself — the mathematical arms race between making and breaking secrets.

About 22 min·5 nodes

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STEP 1 · Concept~BCE 300Alexandria· Publication

Prime Number Theorem

The prime-counting function π(x) is asymptotic to x/ln(x). Gauss recalled an early table-based observation in an 1849 letter; Hadamard and de la Vallée Poussin proved the theorem independently in 1896.

↓2.1-thousand-year span

STEP 2 · Concept1801Göttingen· Publication

Modular Arithmetic

The arithmetic of clocks — wrapping around at a modulus. The basic language of number theory and cryptography.

↓180-year span

STEP 3 · Concept1977Cambridge, MA· Discovery

Cryptography and Information

The mathematics of secrets — from Caesar ciphers to quantum key distribution. Information security is fundamentally a question of which math is hard.

↓17 years later

STEP 4 · Concept1994Bell Labs· Discovery

Quantum Algorithms

Algorithms using quantum superposition — Shor 1994 cast a shadow on RSA security.

↓Next step

STEP 5 · RiverNo location

The River of Cryptography

Caesar → al-Kindi's frequency analysis → changing alphabets in Alberti, Bellaso, and Vigenère → Polish and Bletchley Enigma networks → Shannon's theory of secrecy → Diffie–Hellman and RSA public keys → post-quantum cryptography — two millennia of keeping and breaking secrets.

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