标题： gECC：基于GPU的椭圆曲线密码学高吞吐量框架 显示英文标题

标题： gECC: A GPU-based high-throughput framework for Elliptic Curve Cryptography

摘要： 椭圆曲线密码学（ECC）是一种加密方法，其安全性与传统的如Rivest-Shamir-Adleman（RSA）技术相当，但计算复杂度更低且密钥尺寸更小，使其成为区块链、安全多方计算和数据库安全等应用中的有竞争力的选择。然而，ECC的吞吐量仍然受到与椭圆曲线（EC）操作相关的显著性能开销的阻碍。本文提出了gECC，一个针对GPU架构优化的ECC通用框架，专门设计以在EC操作中实现高吞吐量性能。gECC结合了基于批处理的EC操作执行和模算术的微体系结构级优化。它利用Montgomery技巧来实现批处理EC计算，并结合了新颖的计算并行化和内存管理技术，以最大化计算并行性并最小化GPU全局内存的访问开销。此外，我们通过研究模乘法的用户代码如何编译为硬件指令以及这些指令的发出率，分析了模乘法的主要瓶颈。我们发现模乘法的效率高度依赖于整数乘加（IMAD）指令的数量。为了消除这一瓶颈，我们提出了一种技术，通过利用谓词寄存器传递进位信息，并使用加法和减法指令（IADD3）来替代IMAD指令，从而最小化IMAD指令的数量。我们的结果表明，与最先进的基于GPU的系统相比，gECC在ECDSA和ECDH上分别实现了5.56倍和4.94倍的性能提升。在一个实际的区块链应用中，与最先进的基于CPU的系统相比，我们可以实现1.56倍的性能提升。 显示英文摘要

摘要： Elliptic Curve Cryptography (ECC) is an encryption method that provides security comparable to traditional techniques like Rivest-Shamir-Adleman (RSA) but with lower computational complexity and smaller key sizes, making it a competitive option for applications such as blockchain, secure multi-party computation, and database security. However, the throughput of ECC is still hindered by the significant performance overhead associated with elliptic curve (EC) operations. This paper presents gECC, a versatile framework for ECC optimized for GPU architectures, specifically engineered to achieve high-throughput performance in EC operations. gECC incorporates batch-based execution of EC operations and microarchitecture-level optimization of modular arithmetic. It employs Montgomery's trick to enable batch EC computation and incorporates novel computation parallelization and memory management techniques to maximize the computation parallelism and minimize the access overhead of GPU global memory. Also, we analyze the primary bottleneck in modular multiplication by investigating how the user codes of modular multiplication are compiled into hardware instructions and what these instructions' issuance rates are. We identify that the efficiency of modular multiplication is highly dependent on the number of Integer Multiply-Add (IMAD) instructions. To eliminate this bottleneck, we propose techniques to minimize the number of IMAD instructions by leveraging predicate registers to pass the carry information and using addition and subtraction instructions (IADD3) to replace IMAD instructions. Our results show that, for ECDSA and ECDH, gECC can achieve performance improvements of 5.56x and 4.94x, respectively, compared to the state-of-the-art GPU-based system. In a real-world blockchain application, we can achieve performance improvements of 1.56x, compared to the state-of-the-art CPU-based system.