A method for obtaining digital signatures and public-key cryptosystems

TLDR

The system’s security relies on the difficulty of factoring the published modulus n. The paper proposes an encryption method where a publicly disclosed encryption key does not reveal the corresponding decryption key. Messages are encoded by computing M^e mod n, where n is the product of two large primes, and decoded with a secret exponent d satisfying e·d≡1 mod (p−1)(q−1). The method enables key distribution without secure channels, supports non‑forgeable digital signatures, and prevents signers from repudiating their signatures.

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 intented 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 primer 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 .