Cryptographic computations: algorithms, architectures, and assurances

为了为通信和计算机提供安全，可以使用各种密码方案。其中许多方案需要特殊类型的计算，例如椭圆曲线上的点加法，这处理非常大和抽象的操作数，例如有限域的元素。这种计算不被主流处理器直接支持，并且需要特殊的表示、算法和硬件结构。对于实际应用，这些算法和体系结构都是为了满足有限面积、窄带宽、低功耗等各种约束下的性能要求。更重要的是，它们需要以一种方式运行，以便它们不会通过各种旁路泄露与密码系统密钥相关的信息，例如功耗信号、电磁辐射和由恶意攻击者故意诱导的故障导致的错误输出。这项研究的主要目的是研究密码计算的各个方面，这些方面从通过椭圆曲线点生成数字签名到基本的域运算，并且是通信和计算机中使用的许多安全方案的核心。根据拟议的研究，我们计划致力于为此类计算开发新的算法和硬件架构。算法的开发被认为是非常具有挑战性的，预计将在很大程度上受到基础数学结构的属性的影响，并且对于域算术来说可能是相当抽象的。将算法映射到硬件上的努力将考虑实现平台、目标应用，以及更重要的是，由于密码学中使用的非常大的操作数，各种体系结构挑战是相当重要的。此外，还需要付出相当大的努力才能使关键的密码计算能够抵抗各种旁路攻击。

In order to provide security for communications and computers, various cryptographic schemes can be used.  Many of these schemes require special type of computations, e.g., point addition on elliptic curves, which deal with very large and abstract operands, such as elements of finite fields. Such computations are not directly supported by main stream processors, and require special representations, algorithms and hardware architectures. For practical applications, these algorithms and architectures are to meet performance requirements under various constraints, such as limited area, narrow bandwidth, and low power. More importantly, they need to operate in a way so that they do not leak information related to the secret key of the cryptosystem through various side channels, such as power consumption signals, electromagnetic emanations, and erroneous outputs caused by faults induced deliberately by a malicious attacker. The main objective of the research is to investigate various aspects of cryptographic computations that extent from digital signature generation by elliptic curve point addition to basic field arithmetic, and are at the heart of many security schemes used in communications and computers. Under the proposed research, we plan to work towards the development of novel algorithms and hardware architectures for such computations. The algorithm development is envisioned to be quite challenging and is expected to be largely influenced by properties of the underlying mathematical structures and can be quite abstract for field arithmetic. Efforts for mapping of algorithms onto hardware will take into account implementation platforms, target applications, and more importantly, various architectural challenges that are quite significant owing to very large size operands used in cryptography. In addition, considerable efforts will be required so that critical cryptographic computations are resistant against various side-channel attacks.