According to the fundamental theorem of mathematics, the factorization is always unique—which is why factoring is of fundamental significance to cryptography. Because for large integers, factoring is a difficult problem (because there is no known method to carry it out quickly), its complexity forms the basis of the assumed security of public key cryptography. In brief, public key cryptography is a form of cryptography in which two digital keys are generated, one private and one public. These keys are used for encrypting messages; either one key is used to encrypt a message and another is used to decrypt it, or one key is used to sign a message and another is used to verify the signature. RSA, an algorithm described in 1977 by Ron Rivest, Adi Shamir, and Len Adleman, is a public key used widely in electronic business (or e-business).

See Also: Algorithm; Cryptography or “Crypto”; Key; RSA Public/Private Key Algorithm.