SHF: Small: A New Approach for Hardware Design of High-Precision Discrete Gaussian Sampling

新的密码系统可以提高日常应用的安全水平和隐私保障。然而，这些系统通常需要新的构建块，而这些构建块以前并不存在。来自高斯分布的高精度采样是这样一种耗时且关键的构建块，必须通过定制的硬件解决方案有效地实施。结果解决方案的统计准确性必须得到保证，以遵守加密安全要求。此外，开发的解决方案必须足够灵活，以支持多种当前和潜在的未来应用。现有的硬件设计无法满足这些条件。这个项目将通过硬件设计、算法、统计和密码学方面的交叉方法来解决这个问题。拟议活动的成功完成将是朝着可证明安全的取样器设计的自动化解决方案迈出的重要一步。该项目将与其他几所大学合作，帮助硬件安全领域的劳动力发展。在这个项目中，将开发新的采样器硬件设计来支持基于格子的密码系统，例如后量子密码学和同态加密应用中的那些系统。虽然在密码学和其他应用的背景下已经对均匀分布的采样进行了深入的研究，但对于非均匀分布的采样的工作明显较少，例如高斯分布，这是基于格的密码系统所独有的。为此，该项目将首先探索新的算法方法，以简化高斯抽样技术中使用的随机搜索过程。然后，该项目将探索近似技术，以优化搜索，同时将对统计偏差的影响降至最低。此外，该项目将寻求全面的设计自动化解决方案，可以为给定的参数集创建优化的采样硬件。由此产生的解决方案将被映射到可重新配置的硬件，并以先前的建议为基准，以比较管理费用和节省。该奖项反映了NSF的法定使命，并已通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

New cryptographic systems can improve the security level and privacy assurance of everyday applications. These systems, however, often require new building blocks that did not exist earlier. High-precision sampling from Gaussian distributions is one such time-consuming and critical building block that has to be implemented efficiently with customized hardware solutions. The statistical accuracy of the resulting solutions must be guaranteed to abide by cryptographic security requirements. Moreover, the developed solutions must be flexible enough to support multiple current and potential future applications. Existing hardware designs cannot meet these conditions. This project will address this problem by a cross-cutting approach on hardware design, algorithms, statistics, and cryptography. Successful completion of the proposed activity will be a significant step towards automated solutions for provably-secure sampler designs. The project will help workforce development in the area of hardware security in collaboration with several other universities. The results of the project will be made open-source and will potentially be made available to other agencies, e.g., NIST.In this project, new sampler hardware designs will be developed to support lattice-based cryptographic systems such as those in post-quantum cryptography and homomorphic-encryption applications. Although sampling from uniform distributions has been thoroughly studied in the context of cryptography and other applications, there are significantly fewer works on sampling from non-uniform distributions such as the Gaussian distribution, which is unique to lattice-based cryptosystems. To that end, the project will first explore novel algorithmic approaches that simplify the random-search process used in Gaussian-sampling techniques. The project will then explore the approximation techniques that optimize the search while minimizing the impact on statistical deviations. Furthermore, the project will seek full design-automation solutions that can create optimized sampling hardware for a given set of parameters. The resulting solutions will be mapped to reconfigurable hardware and benchmarked against earlier proposals to compare the overheads and savings.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.