Attacking or tampering with sensitive data continues to increase risks to economic processes or human activities. These risks are significant key factors to improve the development and implementation of security systems. Therefore, improving cryptography is essentially needed to enhance the security of critical data. For example, elliptic curve cryptography (ECC) over the Galois field $GF(2^{163})$ is one of the public-key (asymmetric) cryptographic techniques, in which demands mapping a message (163-bit) to a point in the prime subgroup of the elliptic curve. To the best of our knowledge, mapping methods are not yet available on Field-Programmable Gate Arrays (FPGAs). Also, asymmetric encryption schemes often do not consider encrypting/decrypting data packets because of their computation complexity and performance limitations. In this letter, we propose and develop a concurrent reconfigurable cryptosystem to encrypt and decrypt stream of data using ECC on FPGA. First, we present hardware design and implementation to map a plain message on the elliptic curve based on isomorphic transformation, then second, we architect the elliptic curve ElGamal public-key encryption method by using point addition and multiplication on Koblitz elliptic curve on FPGA. Our proposed cryptosystem is synthesized and implemented on Intel Cyclone 10 GX and Xilinx Kintex-7 FPGAs to evaluate throughput, and it achieves 25.73-57.1 Mbps.

中文翻译：

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用于同构变换和 EC ElGamal 加密的椭圆曲线密码系统 (ECC) 的 FPGA 设计

攻击或篡改敏感数据继续增加经济过程或人类活动的风险。这些风险是改进安全系统开发和实施的重要关键因素。因此，本质上需要改进密码学来增强关键数据的安全性。例如，伽罗瓦域上的椭圆曲线密码术 (ECC) $GF(2^{163})$ 是一种公钥（非对称）加密技术，其中要求将消息（163 位）映射到椭圆曲线素数子群中的一个点。据我们所知，现场可编程门阵列 (FPGA) 上还没有映射方法。此外，由于其计算复杂性和性能限制，非对称加密方案通常不考虑加密/解密数据包。在这封信中，我们提出并开发了一种并发可重构密码系统，以在 FPGA 上使用 ECC 对数据流进行加密和解密。首先，我们介绍了基于同构变换将普通消息映射到椭圆曲线上的硬件设计和实现，然后，我们通过在FPGA上的Koblitz椭圆曲线上使用点加法和乘法来构建椭圆曲线ElGamal公钥加密方法。我们提出的密码系统在 Intel Cyclone 10 GX 和 Xilinx Kintex-7 FPGA 上综合和实现，以评估吞吐量，达到 25.73-57.1 Mbps。