Cryptography Across 1500 Years

From Caesar's shift cipher through Al-Khwarizmi, Vigenère, Shannon, RSA, and quantum algorithms — a journey showing that secrecy is exactly the question of which mathematics is hard.

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STEP 1 · Mathematician~825Baghdad· Main activity

Al-Khwarizmi

A ninth-century mathematician, astronomer, and geographer who worked under Abbasid patronage in Baghdad. His exact birthplace is unknown: the nisba al-Khwarizmi may connect him or his ancestry with Khwarazm, but it does not establish modern Khiva as his birthplace. His al-jabr wa-l-muqābala organized practical inheritance, surveying, and trade problems into six types of linear and quadratic equations explained in words and geometry. The title supplied the word algebra, while the Latin transmission of a different work on Indian calculation turned his name, Algoritmi, into algorithm. He did not invent symbolic algebra or the computer; the richer story is how translated books preserved one author in two modern words.

↓980-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.

↓150-year span

STEP 3 · Mathematician1948Bell Labs· Teaching and work

Claude Shannon

A mathematician and engineer whose 1937 thesis applied Boolean algebra to relay switching circuits. His 1948 paper quantified information and established coding limits for noisy channels. Under stated probabilistic conditions and with long codes, rates below capacity can achieve arbitrarily small error probability—not magically error-free communication in every channel.

↓29 years later

STEP 4 · 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.

↓Next step

STEP 5 · ConceptNo location

Elliptic Curves

A nonsingular cubic curve whose points carry a group law. Elliptic curves connect ancient questions about rational solutions, nineteenth-century elliptic functions, modern number theory, and selected cryptographic systems.

↓Next step

STEP 6 · Concept1994Bell Labs· Discovery

Quantum Algorithms

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

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