Secure simultaneous bit extraction from Koblitz curves

Secure pseudo-random number generators (PRNGs) have a lot of important applications in cryptography. In this paper, we analyze a new PRNG related to the elliptic curve power generator. The new PRNG has many desirable randomness properties such as long period, uniform distribution, etc. In particular, the proposed PRNG is provably secure under the l-strong Diffie–Hellman assumptions. An important feature of our PRNG is that many bits can be simultaneously output without significantly affecting its security. For instance, at 150-bit security, more than 100 bits can be output at each iteration, with a statistical distance from a uniform sequence less than 1 / 2 ¹⁵⁰. Our experimental results show that the new PRNG provides a secure and flexible solution for high security applications. Hence, our work is another step towards the construction of provably secure PRNGs in practice.