{"title":"GF(2m)中的GPU加速椭圆曲线密码","authors":"A. E. Cohen, K. Parhi","doi":"10.1109/MWSCAS.2010.5548560","DOIUrl":null,"url":null,"abstract":"This paper presents the Graphics Processing Unit (GPU) accelerated version of the LSB Invariant scalar point multiplication for binary elliptic curves. This method was implemented using the CUDA programming language for nVidia graphics cards. With a parallel factor of (length+1) and López-Dahab projective coordinate P<inf>i</inf>'s, on an nVidia GTX 285 graphics card precomputation takes 190.203995 ms while the actual scalar point multiplication takes 173.121002 ms for GF(2<sup>163</sup>). With a parallel factor of (length+1)*(length) and López-Dahab projective coordinate P<inf>i</inf>'s, on an nVidia GTX 285 graphics card precomputation of 2<sup>i</sup>P points takes 9.545 ms while the actual scalar point multiplication takes 10.743 ms (∼93.0839 kP/s) for GF(2<sup>163</sup>). With a parallel factor of (length+1)*(length) and affine coordinate P<inf>i</inf>'s, on an nVidia GTX 285 graphics card precomputation takes 140.078003 ms for GF(2<sup>163</sup>) while the actual scalar point multiplication takes 10.363000 ms (∼96.4972 kP/s) for GF(2<sup>163</sup>).","PeriodicalId":245322,"journal":{"name":"2010 53rd IEEE International Midwest Symposium on Circuits and Systems","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":"{\"title\":\"GPU accelerated elliptic curve cryptography in GF(2m)\",\"authors\":\"A. E. Cohen, K. Parhi\",\"doi\":\"10.1109/MWSCAS.2010.5548560\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents the Graphics Processing Unit (GPU) accelerated version of the LSB Invariant scalar point multiplication for binary elliptic curves. This method was implemented using the CUDA programming language for nVidia graphics cards. With a parallel factor of (length+1) and López-Dahab projective coordinate P<inf>i</inf>'s, on an nVidia GTX 285 graphics card precomputation takes 190.203995 ms while the actual scalar point multiplication takes 173.121002 ms for GF(2<sup>163</sup>). With a parallel factor of (length+1)*(length) and López-Dahab projective coordinate P<inf>i</inf>'s, on an nVidia GTX 285 graphics card precomputation of 2<sup>i</sup>P points takes 9.545 ms while the actual scalar point multiplication takes 10.743 ms (∼93.0839 kP/s) for GF(2<sup>163</sup>). With a parallel factor of (length+1)*(length) and affine coordinate P<inf>i</inf>'s, on an nVidia GTX 285 graphics card precomputation takes 140.078003 ms for GF(2<sup>163</sup>) while the actual scalar point multiplication takes 10.363000 ms (∼96.4972 kP/s) for GF(2<sup>163</sup>).\",\"PeriodicalId\":245322,\"journal\":{\"name\":\"2010 53rd IEEE International Midwest Symposium on Circuits and Systems\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"29\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 53rd IEEE International Midwest Symposium on Circuits and Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MWSCAS.2010.5548560\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 53rd IEEE International Midwest Symposium on Circuits and Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MWSCAS.2010.5548560","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 29
摘要
本文提出了基于图形处理器(GPU)的二元椭圆曲线的LSB不变标量点乘法加速算法。该方法是在nVidia显卡上使用CUDA编程语言实现的。在nVidia GTX 285图形卡上，并行因子(长度+1)和López-Dahab投影坐标Pi's，预计算需要190.203995 ms，而实际的标量点乘法需要173.121002 ms。在nVidia GTX 285显卡上，并行因子(长度+1)*(长度)和López-Dahab投影坐标Pi's，预计算2iP点需要9.545 ms，而实际标量点乘法需要10.743 ms (~ 93.0839 kP/s)。在nVidia GTX 285显卡上，并行因子(长度+1)*(长度)和仿射坐标Pi的情况下，GF(2163)的预计算时间为140.078003 ms，而GF(2163)的实际标量点乘法时间为10.363000 ms (~ 96.4972 kP/s)。
GPU accelerated elliptic curve cryptography in GF(2m)
This paper presents the Graphics Processing Unit (GPU) accelerated version of the LSB Invariant scalar point multiplication for binary elliptic curves. This method was implemented using the CUDA programming language for nVidia graphics cards. With a parallel factor of (length+1) and López-Dahab projective coordinate Pi's, on an nVidia GTX 285 graphics card precomputation takes 190.203995 ms while the actual scalar point multiplication takes 173.121002 ms for GF(2163). With a parallel factor of (length+1)*(length) and López-Dahab projective coordinate Pi's, on an nVidia GTX 285 graphics card precomputation of 2iP points takes 9.545 ms while the actual scalar point multiplication takes 10.743 ms (∼93.0839 kP/s) for GF(2163). With a parallel factor of (length+1)*(length) and affine coordinate Pi's, on an nVidia GTX 285 graphics card precomputation takes 140.078003 ms for GF(2163) while the actual scalar point multiplication takes 10.363000 ms (∼96.4972 kP/s) for GF(2163).
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