A novel portable hardware architecture of the Elliptic Curve Method of factoring, designed and optimized for application in the relation collection step of the Number Field Sieve, is described and analyzed. A comparison with an earlier proof-of-concept design by Pelzl, Simka, et al. has been performed, and a substantial improvement has been demonstrated in terms of both the execution time and the area-time product. The ECM architecture has been ported across five different families of FPGA devices in order to select the family with the best performance to cost ratio. A timing comparison with the highly optimized software implementation, GMP-ECM, has been performed. Our results indicate that low-cost families of FPGAs, such as Spartan-3 and Spartan-3E, offer at least an order of magnitude improvement over the same generation of microprocessors in terms of the performance to cost ratio.
As part of the Jefferson Laboratory (JLab) 12 GeV accelerator upgrade, the experimental physics Hall B detector system requires two superconducting magnets-a torus and a solenoid. The specifications required maximum space for the detectors which led to the choice of conduction cooling for each magnet. The torus consists of six trapezoidal 'race-track'-type coils connected in series with an operating current of 3770 A. The solenoid is an actively shielded 5 Tesla magnet consisting of five coils connected in series operating at 2416 A. Within the hall the two magnets are located in close proximity to each other and are surrounded by particle detectors. We describe the philosophy behind the instrumentation selection and control design that accounts for this proximity and other challenging working conditions. We describe the choice of sensor technologies, as well as the control and data acquisition methods. The magnet power and cryogenic control sub-systems are implemented using Allen Bradley Control-Logix 1756-L72 programmable logic controllers (PLCs). Sensor instrumentation readbacks are routed into the PLC via National Instruments cRIO hardware (field programmable gate arrays or FPGA/RT application) using a JLab-designed FPGA-based multi-sensor-excitation-chassis. Configuration, monitoring, and alarm handlers for the magnet systems are provided via an experimental physics instrumentation and control system interface. Failure modes and effects analysis and the requirement to monitor critical parameters during operation guided the selection of instrumentation and associated hardware. The design of the quench protection and voltage tap sub-systems was driven by the anticipated level of voltages developed during a magnet quench. The primary-hardwired quench detection and protection sub-system together with the secondary PLC based protection sub-system is also discussed. The successful commissioning and subsequent performance of these magnets demonstrates the robustness of the design and implementation approach that was adopted by the JLab team and serves as an excellent 'how to' guide for future projects of this size and complexity.
A novel portable hardware architecture of the Elliptic Curve Method of factoring, designed and optimized for application in the relation collection step of the Number Field Sieve, is described and analyzed. A comparison with an earlier proof-of-concept design by Pelzl, Šimka, et al. has been performed, and a substantial improvement has been demonstrated in terms of both the execution time and the area-time product. The ECM architecture has been ported across five different families of FPGA devices in order to select the family with the best performance to cost ratio. A timing comparison with the highly optimized software implementation, GMP-ECM, has been performed. Our results indicate that low-cost families of FPGAs, such as Spartan-3 and Spartan-3E, offer at least an order of magnitude improvement over the same generation of microprocessors in terms of the performance to cost ratio, without the use of embedded FPGA resources, such as embedded multipliers.
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