On a connection between the complexities of the discrete logarithmization and the Diffie–Hellman problems

We prove that under some assumptions of a theoretical nature the complexity $L$ of the discrete logarithm problem in an arbitrary cyclic group of order $m$ is estimated in the rather general case in terms of the complexity $D$ of the Diffie–Hellman problem by the formula
$$ L \le \exp \left\{{\log D\log m\over \log\log m\log\log\log m}\right\}, $$
which gives a subexponential estimate for $L$ provided a polynomial estimate for $D$ is valid.