Pseudo-random number generators (PRNG) play main important role in
many security and cryptographic applications which require the output to be unpre-
dictable and this is directly related to the quality of the generated random sequences.
The design of such random sequences generators is not an easy task. Elliptic Curve
Cryptography (ECC) is a relatively recent branch of cryptography which is based on
the arithmetic on elliptic curves and security of the hardness of the Elliptic Curve Dis-
crete Logarithm Problem (ECDLP). Elliptic curve cryptographic schemes are public-
key mechanisms that provide encryption, digital signature and key exchange capabili-
ties. Elliptic curve algorithms are also applied to generation of sequences of pseudo-
random numbers. In the present work, we propose a method of generating sequences
based on multiplication of points of elliptic curves over finite fields which is driven by a
chaotic map. The random sequence generated using our method has been subjected to
a battery of statistical tests developed by National Institute of Standards and Technol-
ogy (NIST). The results show that the proposed generator can generate pseudo-random
numbers effectively as standard generators with good randomness properties makes it
suitable for both classical and elliptic curve cryptography.