We successfully introduce a new efficient and secure cryptosystem by combining
two cryptographic assumptions namely the cube root extraction and the
discrete logarithm problem modulo a composite integer. It’s well known that
most of the existing schemes are based on single problems and if an adversary
could find an algorithm to solve the related problem the scheme is broken. Our
scheme is prevented from this problem since it’s based on two hard problems.
An adversary may break it if he is able to solve simultaneously the two related
problem which is very unlikely to happen. On the other hand, the new scheme
is as efficient as the El Gamal one and should be an alternative to the other
cryptosystems