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DPF-ECC: A Framework for Efficient ECC With Double Precision Floating-Point Computing Power
IEEE Transactions on Information Forensics and Security ( IF 6.8 ) Pub Date : 2021-07-21 , DOI: 10.1109/tifs.2021.3098987
Lili Gao , Fangyu Zheng , Rong Wei , Jiankuo Dong , Niall Emmart , Yuan Ma , Jingqiang Lin , Charles Weems

Used ubiquitously in a huge amount of security protocols or applications, elliptic curve cryptography (ECC) is one of the most important cryptographic primitives, featuring efficiency and short key size compared with other public-key cryptosystems such as DSA and RSA. However, as a computation-intensive public-key cryptographic primitive, ECC arithmetic is still the bottleneck that restrains the overall performance of the end applications. In this paper, instead of the conventional and straightforward integer-based methods, we present a general framework to accelerate ECC schemes over prime field, called DPF-ECC, that deeply exploits double precision floating-point (DPF) computing power. The DPF-ECC framework finely manages each bit of the DPF numbers and minimizes the overhead brought by additional data format conversion, by making use of the DPF representation, the rounding operations, and fused multiply-add instruction supported by the IEEE 754 floating point standard. We also conduct two comprehensive case studies on Crandall primes and Solinas primes to demonstrate how the DPF-ECC framework is applied to the prevailing ECC schemes. To evaluate the proposed DPF-ECC framework in the real world, leveraging the floating-point computing power of GPUs, we implement Curve25519/448 and Edwards25519/448, the popular ECC schemes widely used in TLS 1.3, SSH, etc. The experimental result in Tesla P100 achieves a record-setting performance that outperforms the existing fastest integer work with 2x to 3x throughput. With dependency only on the very commonly supported IEEE 754 floating point standard, DPF-ECC framework can be a very competent and promising candidate for ECC implementation in most of general-purpose platforms.

中文翻译:

DPF-ECC:具有双精度浮点计算能力的高效 ECC 框架

椭圆曲线密码术 (ECC) 在大量安全协议或应用中无处不在,是最重要的密码学原语之一,与其他公钥密码系统(如 DSA 和 RSA)相比,它具有效率高和密钥大小短的特点。然而,作为计算密集型的公钥密码原语,ECC算法仍然是制约终端应用整体性能的瓶颈。在本文中,我们提出了一个通用框架来加速质数域上的 ECC 方案,而不是传统且直接的基于整数的方法,称为 DPF-ECC,它深入利用了双精度浮点 (DPF) 计算能力。DPF-ECC 框架精细地管理 DPF 编号的每一位,并最大限度地减少额外数据格式转换带来的开销,通过使用 IEEE 754 浮点标准支持的 DPF 表示、舍入运算和融合乘加指令。我们还对 Crandall 素数和 Solinas 素数进行了两个综合案例研究,以展示 DPF-ECC 框架如何应用于流行的 ECC 方案。为了在现实世界中评估提议的 DPF-ECC 框架,利用 GPU 的浮点计算能力,我们实现了 Curve25519/448 和 Edwards25519/448,这是在 TLS 1.3、SSH 等中广泛使用的流行 ECC 方案。 实验结果在 Tesla P100 中实现了创纪录的性能,以 2 到 3 倍的吞吐量超越了现有的最快整数工作。仅依赖于非常普遍支持的 IEEE 754 浮点标准,
更新日期:2021-08-20
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