Number-Theoretic-Transform (NTT) is a variation of Fast-Fourier-Transform (FFT) on finite fields. NTT is being increasingly used in blockchain and zero-knowledge proof applications. Although FFT and NTT are widely studied for FPGA implementation, we believe CycloneNTT is the first to solve this problem for large data sets (2^24, 64-bit numbers) that would not fit in the on-chip RAM. CycloneNTT uses a state-of-the-art butterfly network and maps the dataflow to hybrid FIFOs composed of on-chip SRAM and external memory. This manifests into a quasi-streaming data access pattern minimizing external memory access latency and maximizing throughput. We implement two variants of CycloneNTT optimized for DDR and HBM external memories. Although historically this problem has been shown to be memory-bound, CycloneNTT's quasi-streaming access pattern is optimized to the point that when using HBM (Xilinx C1100), the architecture becomes compute-bound. On the DDR-based platform (AWS F1), the latency of the application is equal to the streaming of the entire dataset log(N) times to/from external memory. Moreover, exploiting HBM's larger number of channels, and following a series of additional optimizations, CycloneNTT only requires log(N)/6 passes.

Distributed systems require strategies to detect and recover from failures. Many protocols for distributed systems employ a strategy based on leases, which grant a leaseholder access to data or services for a limited time (the lease period). Choosing an appropriate lease period involves tradeoffs among resource utilization, responsiveness, and system size. We investigate these issues for Jini Network Technology. First, we establish quantitative tradeoffs among lease period, bandwidth utilization, responsiveness, and system size. Then, we consider two self-adaptive algorithms that enable a Jini system, given a fixed allocation of resources, to vary lease periods with system size to achieve the best responsiveness. We compare performance of these self-adaptive algorithms against each other, and against fixed lease periods. We find that one of the self-adaptive algorithms proves easy to implement and performs reasonably well. We anticipate that similar procedures could add self-adaptive capability to other distributed systems that rely on leases.