The encyclopedia · Software & IT · Technical decision · 1977–1978
RSA let anyone encrypt to you without sharing a secret first.
Rivest, Shamir and Adleman made the encrypting key public and the decrypting key private, so two strangers could trade secrets with no courier and no prior key.
Massachusetts Institute of Technology
the move
Before public-key cryptography, secure communication had a built-in trap: two parties who had never met had to first share a secret key, which itself needed a secure channel. Couriers, trusted phone calls and key tables were the expensive, leaky ways to do it.
Rivest, Shamir and Adleman's 1978 paper showed an encryption method with the property that publicly revealing an encryption key does not reveal the corresponding decryption key. A message is encoded as a number M raised to a public power e and reduced modulo a public product n of two large primes, and only the matching secret power d recovers it.
That one trick solved both problems at once. Couriers were no longer needed to transmit keys, and a message could be signed with the private key so anyone could verify it with the public key, giving unforgeable, non-repudiable signatures for electronic mail and funds transfer. Security rests on the difficulty of factoring the published modulus.
why it works
- Making the encryption key public removes the need to share a secret first.
- Factoring the modulus is hard, so publishing n does not expose the private key.
- The same math gives both confidentiality and signatures, so one scheme covered both uses.
- Its patent and the MIT paper turned public-key cryptography into a productizable standard.
what transfers
The key-distribution chicken-and-egg dissolves once the encryption operation is public and only the inverse of it stays secret.
what came after
RSA became the most widely deployed public-key scheme, securing web traffic, email and electronic payments for decades, and it made public-key cryptography the foundation of digital signatures and the public-key infrastructure. It also earned its authors the Turing Award in 2002.
references
- A Method for Obtaining Digital Signatures and Public-Key Cryptosystems
- Cryptographic communications system and method (U.S. Patent 4,405,829)
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