For secret message transfer through computer, every message is encrypted following a scrambling rule and the coded message is decrypted if the scrambling rule (i.e., the encryption key) is known. For a computer, the message (M), the key (K) and the coded message (C) are all numbers, expressed as strings of 0's and 1's. The one-way modulo function (which enables us to determine uniquely the RHS form the LHS, but not the other way round) and the difficulty of the obtaining two large prime factors (p and q) of a number N = p × q are combined to create an asymmetric key. Different keys are used for encryption and decryption.

Public Key and Private Key

Everybody knows my public key (like my telephone number). Anyone can send me an encrypted message using my public key, but only I can decipher it by using my private key.

RSA, or Rivest, Shamir, Adleman, algorithm, reported in 1976. depends on the difficulty of getting back two very large prime numbers p and q from their product N.

N (known to all) serves as the public key and p, q (known only to me) comprise my private key.

Martin Gardner (1977) asked the readers of Scientific American to find the two prime factors of a large number consisting of 129 digits.