A.2. The ElGamal public key system
ElGamal’s scheme [28] is based on the difficulty of computing discrete logarithms. This is currently considered to be intractable and comparable to the problem of factoring large numbers that underlies RSA. It is quite easy to understand – really no more complicated than RSA and probably about as easy to implement. As far as is currently known (in the open world at any rate) it is cryptographically about as strong as RSA.
A large prime p along with a primitive root a modulo p are made publicly available. A primitive root is one that ‘generates’ the entire field, so taking successive powers of a modulo p will yield all the integers from 1 to p − 1. For a prime p it can be shown that there always exists a primitive ...
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