大数乘法的GPU加速实现

大数乘法是公钥加密中最为核心的计算环节之一，快速实现大数乘法单元也是RSA、ElGamal、全同态等密码体制急需解决的问题之一。目前，基于C 的NTL GMP库函数虽然能在CPU上实现高精度的大数乘法，但其仍不能满足加密对实时性的要求。针对全同态加密应用需求，本文提出了一种基于Sch?nhage-Strassen算法的大数乘法GPU加速方法。通过比较相同实验平台下仅用CPU和GPU CPU异构方法实现的大数乘法运算，验证了本文设计方法的正确性和有效性。实验结果表明，采用本文方法实现的相同大数乘法运算所需的时间比在多核CPU平台实现所需的时间有12倍以上的加速。

GPU accelerated large number multiplication

Large number multiplication is one of the most important parts in public key encryption, which often consumes most of the computing time in RSA, homomorphic encryption and other cryptosystems. The NTL library based on C can achieve high precision multiplication on CPU platform, but it cannot meet the real-time requirement of a cryptosystem. For the application of fully homomorphic encryption, this paper presented a GPU-based acceleration of large number multiplication based on the Sch?nhage-Strassen algorithm. Accuracy of the GPU implementation is validated by comparing to the results obtained from the NTL library on the CPU. The experimental results of large number multiplication in different sizes show that the GPU implementation is about 12 times faster than using the NTL library on the multi-core CPU platform.