Algebra for Cryptologists pp 251-276 | Cite as

# Number Theory in Public Key Cryptography

## Abstract

We have already dealt with two of the most important applications of number theory, namely the difficulty of factoring as used in the RSA public key system, and the difficulty of the discrete logarithm problem in Diffie–Hellman key establishment and ElGamal encryption. It is worthwhile recalling that until as recently as 1976, when Diffie and Hellman’s famous paper appeared, it was generally thought to be impossible to encrypt a message from Alice to Bob, if Alice and Bob had not previously obtained a secret key. Until then number theory was seen as the “Queen of Mathematics”, which is how Gauss described it, and as one would like a queen to be, this could (somewhat rudely) be construed as meaning “beautiful, but of no practical value”.