Hardware implementation of a point multiplication algorithm based on parallel scheduling

Abstract

针对gf(2M)域椭圆曲线点乘算法计算速度慢,硬件实现成本高的问题,提出一种改进的并行调度算法以及专用的硬件调度结构。通过合并点乘算法中底层模乘、模逆及模平方算法,降低底层运算单元硬件成本。同时对点乘算法进行模乘和模平方两路并行调度分解,以提高运算速度。并针对点乘调度算法的特点,设计专用的硬件调度结构,以减少调度复杂性。STrATIXIII系列的fPgA原型实现结果表明,通过这些方式使点乘运算速度得到提高。AnimprovedparallelschedulingalgorithmandspecifichardwareschedulingstructureispresentedinthispaperforsolvingtheproblemoflowspeedandhighhardwarecostofpointmultiplicationalgorithmofellipticcurveoverGF(2m).Mergingtheunderlyingmodularmultiplication,modularinversionandmodularsquarealgorithmisusedtoreducethecostofhardwareimplementation.Thenaparallelschedulinghasbeenmadetopointmultiplicationalgorithmwithmodularmultiplicationandmodularsquareforincreasingcomputingspeed.Besides,specifichardwareschedulingstructureisdesignedtoreducethecomplexityaccordingtothefeatureofpointmultiplication.TheresultshowsthatpointmultiplicationmoduleintroducedbythispaperhasreachedanexcellentcostperformancebothonspeedandhardwareresourcesonFPGAofStratixIIIseries.国家自然科学基金项目(61274133); 福建省自然科学基金项目(2010J05143