Cryptographic computations: algorithms, architectures, and assurances

为了提供通信和计算机的安全性，可以使用各种加密方案。这些方案中的许多需要特殊类型的计算，例如，椭圆曲线上的点加法，它处理非常大和抽象的操作数，例如有限域的元素。主流处理器不直接支持这种计算，需要特殊的表示、算法和硬件架构。在实际应用中，这些算法和架构是为了满足各种限制条件下的性能要求，如有限的面积、窄带宽和低功耗。更重要的是，它们需要以一种不通过各种侧通道（如功耗信号、电磁辐射、恶意攻击者故意诱导的故障导致的错误输出）泄露与密码系统密钥相关的信息的方式运行。研究的主要目的是研究密码计算的各个方面，从椭圆曲线点加法到基本域算法的数字签名生成，并且是通信和计算机中使用的许多安全方案的核心。根据提议的研究，我们计划为这种计算开发新的算法和硬件架构。该算法的开发被认为是相当具有挑战性的，预计将在很大程度上受到底层数学结构的性质的影响，并且对于场算法来说可能是相当抽象的。将算法映射到硬件的工作将考虑到实现平台、目标应用程序，更重要的是，由于密码学中使用了非常大的操作数，各种架构挑战非常重要。此外，还需要付出相当大的努力，以使关键的加密计算能够抵抗各种侧信道攻击。

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.