The birth of public-key cryptography is associated with the Diffie-Hellman 
protocol which was motivated by the belief that the discrete logarithm problem 
is hard. The two most important number-theoretic problems that are thought to 
be hard are the factorization problem and the DL problem, and most 
computational problems used as assumptions to obtain cryptographic security 
reductions are related to one of these problems. The security of the first 
public-key encryption scheme, RSA, is related through the RSA assumption to the 
integer factorization problem but it was not clear how to define an encryption 
scheme similarly related to the DL problem. 
(J. L. G. Pardo - Introduction to Cryptography with Maple)