Faster elliptic-curve discrete logarithms on FPGAs
Faster elliptic-curve discrete logarithms on FPGAs
复制标题
FPGA 上更快的椭圆曲线离散对数
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Ralf Zimmermann
中科院分区：
文献类型：
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作者：
D. Bernstein;Susanne Engels;T. Lange;R. Niederhagen;C. Paar;P. Schwabe;Ralf Zimmermann
本文在FPGA上加速了二元域上椭圆曲线上的离散多项式的计算。作为一个例子，本文成功地攻击了SECG标准曲线sect 113 r2，这是一种二进制椭圆曲线，直到2010年才从SECG标准中删除，直到2015年6月才在OpenSSL中禁用。此外，本文成功地攻击了一个117.35位的ECDL在椭圆曲线上的F2127。这是完成的ECDL计算的新大小记录，使用的素数阶比之前的记录保持器大40倍以上。更重要的是，本文更有效地使用FPGA，每个高速ECDL内核的大小节省了近3/2。本文将3个内核压缩到低成本的Spartan-6 FPGA中，并将更多的内核压缩到更大的FPGA中。公共领域的论文。这项工作得到了NSF（美国）的支持。根据资助1018836; NWO（荷兰）根据赠款639.073.005、613.001.011和Veni 2013项目13114;以及欧盟委员会根据合同INFSO-ICT-284833（PUFFIN）和ICT-645421 ECRYPT-CSA通过ICT计划。此文件的永久ID：01 ac 92080664 fb 3a 778 a430 e028 e55 c8。丹尼尔J.伯恩斯坦伊利诺伊大学芝加哥分校，美国电子邮件：djb@cr.yp.to丹尼尔J.伯恩斯坦·塔尼娅兰格埃因霍温理工大学，荷兰电子邮件：tanja@hyperelliptic.org鲁本尼德奥尔弗劳恩霍夫安全信息技术研究所，德国？电子邮件：ruben@polycephaly.org？这项工作是作者在埃因霍温理工大学工作时完成的。Susanne Engels · Christof帕尔· Ralf Zimmermann Ruhr-University波鸿，德国电子邮件：susanne. rub.de电子邮件：ralf. zimmermann@www.example.com电子邮件：ralf. zimmermann@www.example.com Peter施瓦贝Radboud University，The Netherlands电子邮件：peter@cryptojedi.org还对许多较小规模的攻击进行了基准测试，以证明估计的可靠性。rub.de rub.de
This paper accelerates computations of discrete logarithms on elliptic curves over binary fields on FPGAs. As toy example, this paper successfully attacks the SECG standard curve sect113r2, a binary elliptic curve that was not removed from the SECG standard until 2010 and was not disabled in OpenSSL until June 2015. Furthermore, this paper successfully attacks a 117.35-bit ECDL on an elliptic curve over F2127 . This is a new size record for completed ECDL computations, using a prime order that is more than 40 times larger than the previous record holder. More importantly, this paper uses FPGAs much more efficiently, saving a factor close to 3/2 in the size of each high-speed ECDL core. This paper squeezes 3 cores into a low-cost Spartan-6 FPGA and many more cores into larger FPGAs. The paper Public domain. This work was supported by NSF (U.S.) under grant 1018836; by NWO (Netherlands) under grants 639.073.005, 613.001.011, and Veni 2013 project 13114; and by the European Commission through the ICT program under contracts INFSO-ICT-284833 (PUFFIN) and ICT-645421 ECRYPT-CSA. Permanent ID of this document: 01ac92080664fb3a778a430e028e55c8. Daniel J. Bernstein University of Illinois at Chicago, USA E-mail: djb@cr.yp.to Daniel J. Bernstein · Tanja Lange Eindhoven University of Technology, The Netherlands E-mail: tanja@hyperelliptic.org Ruben Niederhagen Fraunhofer Institute for Secure Information Technology, Germany? E-mail: ruben@polycephaly.org ?The work was done while the author was with Eindhoven University of Technology. Susanne Engels · Christof Paar · Ralf Zimmermann Ruhr-University Bochum, Germany E-mail: susanne.engels@rub.de E-mail: christof.paar@rub.de E-mail: ralf.zimmermann@rub.de Peter Schwabe Radboud University, The Netherlands E-mail: peter@cryptojedi.org also benchmarks many smaller-size attacks to demonstrate reliability of the estimates.