Public key cryptography lies among the most important bases of security protocols. The classic instances of these cryptosystems are no longer secure when a large-scale quantum computer emerges. These cryptosystems must be replaced by post-quantum ones, such as isogeny-based cryptographic schemes. Supersingular isogeny Diffie-Hellman (SIDH) and key encapsulation (SIKE) are two of the most important such schemes. To improve the performance of these protocols, we have designed several modular multipliers. These multipliers have been implemented for all the prime fields used in SIKE round 3, on a Virtex-7 FPGA, showing a time and area-time product improvement of up to 60.1% and 64.5%, respectively. These multipliers are also suitable for applications such as RSA, as shown by implementations for 512-bit, 1024-bit, and 2048-bit generic moduli on a Virtex-7 FPGA. Our fastest multiplier has been used in the implementation of SIDH and SIKE round 3. Employing six instances of this multiplier, SIDH completes after 7.33, 8.93, 13.39, and 18.67 milliseconds and the encapsulation and the decapsulation of SIKE is performed in 7.13, 8.68, 13.08, and 18.16 milliseconds over $p_{434}$ , $p_{503}$ , $p_{610}$ , $p_{751}$ , respectively, which yields a least improvement factor of 1.23.

中文翻译：

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超奇异质同构Diffie-Hellman的硬件体系结构和使用快速蒙哥马利乘法器的密钥封装

公钥密码术是安全协议最重要的基础之一。当大规模量子计算机出现时，这些密码系统的经典实例不再安全。这些密码系统必须替换为后量子密码系统，例如基于等位基因的密码方案。超奇异同构Diffie-Hellman（SIDH）和密钥封装（SIKE）是最重要的此类方案中的两个。为了提高这些协议的性能，我们设计了几个模块化乘法器。这些乘法器已在Virtex-7 FPGA上针对SIKE第3轮中使用的所有主要字段实现，显示时间和面积时间乘积分别提高了60.1％和64.5％。这些乘法器也适用于RSA等应用，如512位，1024位，Virtex-7 FPGA上的2048位通用模数。我们最快的乘数已用于实施SIDH和SIKE第3轮。利用此乘数的六个实例，SIDH在7.33、8.93、13.39和18.67毫秒后完成，SIKE的封装和解封装在7.13、8.68， 13.08和18.16毫秒 $ p_ {434} $ ， $ p_ {503} $ ， $ p_ {610} $ ， $ p_ {751} $ 分别产生至少1.23的改善因子。