  Parallel supercomputer-based Monte Carlo and stochastic simulations require
pseudorandom number generators that can produce distinct pseudorandom streams
across many independent processes. We propose a scalable class of parallel and
vectorizable pseudorandom number generators based on a non-cryptographic
version of the RSA public-key exponentiation cipher. Our method generates
uniformly distributed IEEE double-precision floating point pseudorandom
sequences on $[0,1)$ by encrypting pseudorandom sequences of 64-bit integer
messages by modular exponentiation. The advantages of the method are: the
method is parallelizable by parameterization with each pseudorandom number
generator instance derived from an independent 64-bit composite modulus, the
method is fully scalable on massively parallel computing clusters because of
the millions of available 32-bit prime numbers, the seeding and initialization
of the independent streams is simple, the periods of the independent instances
are all different and greater than $8.5\times 10^{37}$, and the method passes a
battery of intrastream and interstream correlation tests. The calculations in
each instance can be vectorized using steam splitting and can produce more than
$10^8$ pseudorandom numbers per second on each multicore CPU.
