Short answers, pulled from the story.
Cryptography is the practice and study of techniques for secure communication in the presence of adversarial behavior. Its practical applications include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
Symmetric cryptography uses the same secret key to encrypt and decrypt a message, and was the only publicly known kind until June 1976. Public-key cryptography uses two mathematically related keys, a public key that can be freely distributed and a private key that stays secret.
Whitfield Diffie and Martin Hellman proposed public-key cryptography in a groundbreaking 1976 paper, including the Diffie-Hellman key exchange. The RSA algorithm was developed in 1978 by Ronald Rivest, Adi Shamir, and Len Adleman, though GCHQ cryptographers including James H. Ellis and Clifford Cocks had anticipated these ideas in secret around 1970 to 1974.
The one-time pad is the only theoretically unbreakable cipher, proven so by Claude Shannon. It holds only when the key material is truly random, never reused, kept secret from all attackers, and of equal or greater length than the message.
Frequency analysis is a cryptanalytic technique that breaks classical ciphers by using the statistical fingerprints that ciphertext reveals about plaintext. The Arab mathematician Al-Kindi described the first known use of it in his work Risalah fi Istikhraj al-Mu'amma.
Cryptography's potential as a tool for espionage and sedition has led many governments to classify it as a weapon and limit or prohibit its use and export. In the United States it was once placed on the Munitions List, and the 1999 Bernstein v. United States ruling held that printed cryptographic source code is protected free speech.
Estimates suggest a quantum computer could reduce the effort to break today's strongest RSA or elliptic-curve keys from millennia to mere seconds, rendering protocols such as TLS that rely on those keys insecure. Researchers are developing post-quantum cryptography whose security rests on problems believed to remain hard for both classical and quantum computers.