Modern cryptography

Modern cryptography emerged twice—once in secret, once in public—and the secret version came first. In 1970, James Ellis at Britain's GCHQ proposed "non-secret encryption," inspired by a classified World War II paper on adding noise to voice communications. Ellis had the concept but not the mathematics. In 1973, Clifford Cocks—a new hire told about Ellis's idea—solved it in thirty minutes using prime factorization. The following year, Malcolm Williamson discovered key exchange while trying to find flaws in Cocks's work. For 24 years, the trio watched in silence as Americans independently solved the same problems.

The public breakthrough came in November 1976, when Whitfield Diffie and Martin Hellman published "New Directions in Cryptography." Their key exchange protocol let strangers establish a shared secret over public channels—solving a problem that had plagued cryptography for millennia. The following year, Ronald Rivest, Adi Shamir, and Leonard Adleman created RSA, the first practical public-key encryption system based on the difficulty of factoring large primes.

The adjacent possible was computational. The Cook-Levin theorem (1971) and Richard Karp's NP-completeness paper (1972) established that certain problems were computationally infeasible, providing theoretical foundations for cryptographic hardness. Computer networks like ARPANET created demand for secure communication between strangers who couldn't meet to exchange keys.

The cascade built the infrastructure of digital commerce. SSL, developed at Netscape in 1994-1995, enabled secure web transactions; the first occurred on August 11, 1994, when a Sting CD was purchased online. Certificate authorities like VeriSign (1995) verified website identities. Let's Encrypt (2016) democratized HTTPS by offering free certificates, pushing Chrome's encrypted traffic from 30% in 2015 to 95% by 2020. Bitcoin (2009) combined elliptic curve cryptography with blockchain, enabling trustless digital transactions. Every HTTPS connection, every cryptocurrency transaction, every digitally signed document uses mathematics that GCHQ discovered first but the world learned from Diffie, Hellman, and RSA.