  Pseudorandom bit generators (PRBG) can be designed to take the advantage of
some hard number theoretic problems such as the discrete logarithm problem
(DLP). Such type of generators will have good randomness and unpredictability
properties as it is so difficult to find an easy solution to the regarding
mathematical dilemma. Hash functions in turn play a remarkable role in many
cryptographic tasks to achieve various security strengths. In this paper, a
pseudorandom bit generator mechanism that is based mainly on the elliptic curve
discrete logarithm problem (ECDLP) and hash derivation function is proposed.
The cryptographic hash functions are used in consuming applications that
require various security strengths. In a good hash function, finding whatever
the input that can be mapped to any pre-specified output is considered
computationally infeasible. The obtained pseudorandom bits are tested with NIST
statistical tests and it also could fulfill the up-to-date standards. Moreover,
a $256 \times 256$ grayscale images are encrypted with the obtained
pseudorandom bits following by necessary analysis of the cipher images for
security prove.
