Collaborative Research: EMT/QIS: Quantum Algorithms and Post-Quantum Cryptography

合作研究：EMT/QIS：量子算法和后量子密码学项目摘要密码学是实现电子交易隐私和安全的基本基础设施元素。然而，当大规模量子计算机最终建成时，它将迫使我们放弃现有的加密方法，如RSA和Diffie-Hellman，这些方法目前被广泛使用。拟议的研究将进一步推进这一颠覆性的量子算法研究；但它也旨在建立一个安全的后量子密码学的新框架，以维持这种对社会至关重要的基础设施。拯救现代密码学的最有吸引力的方法是开发经典的密码系统，即使面对量子对手，我们也有令人信服的安全性证据。pi和他们的合作者最近的工作表明，某些代数问题甚至具有与量子算法相关的硬度特性。我们建议加强和利用这些结果来开发加密方案，这些方案可以由今天的计算机执行，但即使在未来的量子攻击中也会保持安全。在此基础上，我们建议开发新的量子算法，用于基于辫群中的共轭性破解密码系统。这是少数几个尚未被证明易受量子攻击的经典密码系统之一。我们的研究项目也直接与四所大学的研究生培训、本科教育创新、教育推广和广泛的科学传播相结合。

Collaborative Research: EMT/QIS:Quantum Algorithms and Post-Quantum CryptographyProject SummaryCryptography is the basic infrastructural element enabling privacy and security for electronic transactions. However, when a large-scale quantum computer is finally built, it will force us to abandon established methods of cryptography, such as RSA and Diffie-Hellman, which are in common use today. The proposed research will further this line of disruptive quantum algorithmic research; but it also aims to erect a new framework of secure post-quantum cryptography, in order to maintain this societally critical infrastructure.The most attractive approach for salvaging modern cryptography would be to develop classical cryptosystems for which we have compelling evidence of security even in the face of quantum adversaries. Recent work by the PIs and their collaborators has shown that certain algebraic problems possess hardness properties relevant even for quantum algorithms. We propose to strengthen and leverage these results in order to develop cryptographic schemes which can be carried out by today's computers, but which will remain secure even against quantum attack in the future.In tandem with this effort, we propose to develop new quantum algorithms for breaking cryptosystems based on conjugacy in the braid group. This is one of the few remaining classical cryptosystems which has not already been shown to be vulnerable to quantum attack.Our research program is also directly integrated with graduate student training at all four institutions, undergraduate educational innovation, educational outreach, and broad scientific dissemination.