{"title":"二元多项式的快速乘法与即将到来的矢量化VPCLMULQDQ指令","authors":"Nir Drucker, S. Gueron, V. Krasnov","doi":"10.1109/ARITH.2018.8464777","DOIUrl":null,"url":null,"abstract":"Polynomial multiplication over binary fields $\\mathbb{F}_{2^{n}}$ is a common primitive, used for example by current cryptosystems such as AES-GCM (with $n=128)$. It also turns out to be a primitive for other cryptosystems, that are being designed for the Post Quantum era, with values $n\\gg 128$. Examples from the recent submissions to the NIST Post-Quantum Cryptography project, are BIKE, LEDAKem, and GeMSS, where the performance of the polynomial multiplications, is significant. Therefore, efficient polynomial multiplication over $\\mathbb{F}_{2^{n}}$, with large $n$, is a significant emerging optimization target. Anticipating future applications, Intel has recently announced that its future architecture (codename “Ice Lake”) will introduce a new vectorized way to use the current VPCLMULQDQ instruction. In this paper, we demonstrate how to use this instruction for accelerating polynomial multiplication. Our analysis shows a prediction for at least 2x speedup for multiplications with polynomials of degree 512 or more.","PeriodicalId":6576,"journal":{"name":"2018 IEEE 25th Symposium on Computer Arithmetic (ARITH)","volume":"71 1","pages":"115-119"},"PeriodicalIF":0.0000,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction\",\"authors\":\"Nir Drucker, S. Gueron, V. Krasnov\",\"doi\":\"10.1109/ARITH.2018.8464777\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Polynomial multiplication over binary fields $\\\\mathbb{F}_{2^{n}}$ is a common primitive, used for example by current cryptosystems such as AES-GCM (with $n=128)$. It also turns out to be a primitive for other cryptosystems, that are being designed for the Post Quantum era, with values $n\\\\gg 128$. Examples from the recent submissions to the NIST Post-Quantum Cryptography project, are BIKE, LEDAKem, and GeMSS, where the performance of the polynomial multiplications, is significant. Therefore, efficient polynomial multiplication over $\\\\mathbb{F}_{2^{n}}$, with large $n$, is a significant emerging optimization target. Anticipating future applications, Intel has recently announced that its future architecture (codename “Ice Lake”) will introduce a new vectorized way to use the current VPCLMULQDQ instruction. In this paper, we demonstrate how to use this instruction for accelerating polynomial multiplication. Our analysis shows a prediction for at least 2x speedup for multiplications with polynomials of degree 512 or more.\",\"PeriodicalId\":6576,\"journal\":{\"name\":\"2018 IEEE 25th Symposium on Computer Arithmetic (ARITH)\",\"volume\":\"71 1\",\"pages\":\"115-119\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2018 IEEE 25th Symposium on Computer Arithmetic (ARITH)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.2018.8464777\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 IEEE 25th Symposium on Computer Arithmetic (ARITH)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.2018.8464777","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fast multiplication of binary polynomials with the forthcoming vectorized VPCLMULQDQ instruction
Polynomial multiplication over binary fields $\mathbb{F}_{2^{n}}$ is a common primitive, used for example by current cryptosystems such as AES-GCM (with $n=128)$. It also turns out to be a primitive for other cryptosystems, that are being designed for the Post Quantum era, with values $n\gg 128$. Examples from the recent submissions to the NIST Post-Quantum Cryptography project, are BIKE, LEDAKem, and GeMSS, where the performance of the polynomial multiplications, is significant. Therefore, efficient polynomial multiplication over $\mathbb{F}_{2^{n}}$, with large $n$, is a significant emerging optimization target. Anticipating future applications, Intel has recently announced that its future architecture (codename “Ice Lake”) will introduce a new vectorized way to use the current VPCLMULQDQ instruction. In this paper, we demonstrate how to use this instruction for accelerating polynomial multiplication. Our analysis shows a prediction for at least 2x speedup for multiplications with polynomials of degree 512 or more.