01Overview

In 1976 Diffie and Hellman proposed public-key cryptography and a key-exchange protocol: two parties agree on a shared key over a public channel that an eavesdropper cannot compute. In 1977 Rivest, Shamir and Adleman built RSA, using the hardness of factoring large integers for both encryption and signatures.

Public-key cryptography solved the key-distribution problem of symmetric ciphers and became the basis of digital signatures, certificates and TLS. In 1985 Koblitz and Miller proposed elliptic-curve cryptography, reaching the same security with much shorter keys. Today RSA and ECC carry almost every secure connection — and quantum computing threatens both.

02History

  1. 1976

    Diffie–Hellman

    Public-key cryptography and key exchange.

  2. 1977

    RSA

    The difficulty of factoring large integers.

  3. 1985

    Elliptic-curve cryptography

    Shorter keys for the same strength.

  4. 1991

    PGP

    Public-key encryption for individuals.

03Core concepts

Public and private keys

The public key may be published for encryption or verification; the private key stays secret.

Key exchange

Agree on a shared session key over an insecure channel.

Digital signature

Sign with the private key, verify with the public one, proving origin and integrity.

04Hands-on

Do it once — it beats reading it ten times

Implement Diffie–Hellman over a small prime by hand, then exchange a message with a classmate

05Self-check

Say it in your own words first, then open the answer. Whatever you cannot explain is what to review next.

Can you explain "Public and private keys"?

The public key may be published for encryption or verification; the private key stays secret.

Can you explain "Key exchange"?

Agree on a shared session key over an insecure channel.

Can you explain "Digital signature"?

Sign with the private key, verify with the public one, proving origin and integrity.

What problem did it solve, and why was there nothing better at the time?

Go back to the history section: how was this done before, and what did it cost?

If you had to build it today, how would you break it down?

Use the hands-on task above: write a plan of at most three steps before you start.

06Key people

W

Whitfield Diffie

1944 –

Co-inventor of public-key cryptography and key exchange.

R

Ron Rivest

1947 –

Co-inventor of RSA.

07Further reading

  • New Directions in CryptographyDiffie & Hellman · 1976
  • Applied CryptographyBruce Schneier · 1993