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A Method for Obtaining Digital Signatures and Public-Key Cryptosystems

Authors: R. L. Rivest, A. Shamir, L. Adleman

Published: April 1977

URL: https://people.csail.mit.edu/rivest/Rsapaper.pdf

Tags: 1970s Public Key Encryption

Abstract: An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences:

  1. Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intended recipient. Only he can decipher the message, since only he knows the corresponding decryption key.
  2. A message can be “signed” using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in “electronic mail” and “electronic funds transfer” systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two large secret prime numbers p and q. Decryption is similar; only a different, secret, power d is used, where e · d ≡ 1 (mod (p − 1) · (q − 1)). The security of the system rests in part on the difficulty of factoring the published divisor, n.