Hardware Implementation of a Cryptographically Secure Pseudo-Random Number Generators Based on Koblitz Elliptic Curves

In this brief, a cryptographically secure pseudo-random number generator based on the NIST Koblitz elliptic curve K-163 is implemented. A 3-stage pipelined multiplier is adopted to speed up point additions. In addition, Frobenius map and point additions are performed in parallel to reduce the clock cycles required for scalar multiplication. By expanding the multiplier with a multiplexer, exponentiation and multiplication can be executed simultaneously, thus greatly reducing the clock cycles needed for inversion. Implementation results on Xilinx Virtex-4 show that the frequency of the multiplier is up to 248 MHz, therefore it takes only 2.21 us for scalar multiplication over K-163. The cryptographically secure pseudo-random number generator can produce 452 Kbit random number every second.