The entropy of a distributed computation random number generation from memory interleaving

Abstract

We ask to what extent processes communicating through shared memory can extract randomness from their underlying scheduler, e.g., to generate random numbers for cryptographic applications. We introduce the quantitative notions of entropy rate and information capacity of a distributed algorithm. Whilst the entropy rate measures the Shannon information that may pass from a given scheduler to the processes executing the algorithm, the information capacity measures the optimal entropy rate over all possible schedulers. We present a general method for computing these quantities by classifying distributed algorithms according to their pattern of shared memory accesses. We then address the issue of effectively extracting, online, the information produced by the scheduler into a meaningful format at every process. We present Duez, an algorithm solving this problem with an optimal memory consumption. Putting these principles into practice, we introduce Co-RNG, a random number generator that leverages the unpredictability of modern processors state. The power of Co-RNG comes from its simplicity. No specialized hardware is required: two concurrent threads actively perform successive reads and writes to shared memory locations. Another thread collects the sequences of values read by these two threads and seeks to reconstruct the interleaving of read and write operations. The resulting (Markovian) interaction scheme is then used to produce random bits. This simplicity yields a transparent behavior. If the hardware exhibits enough entropy, then Co-RNG efficiently extracts random numbers from it. We successfully experimented Co-RNG on various idle as well as loaded platforms, from laptops and desktops featuring Intel Core processors, to servers with Intel Xeon and AMD Opteron. Co-RNG passes all state-of-the-art random number generator statistical test suites while being faster than current I/O sampling based methods by 2–3 orders of magnitude.