Construction of Post-quantum Signature Schemes based on Lattices

拟议的研究将集中在后量子密码学（PQC）。当大规模量子计算机出现时，现代公钥密码学将受到威胁。因此，为了使未来的网络安全空间免受量子攻击，我们需要不受量子攻击的加密算法。后量子密码学（PQC）依赖于量子机器没有已知优势的难题。有几个选择这样的困难的问题，每一类都有一些优点和缺点的性能开销。NIST最近宣布了密钥封装机制（KEM）和签名方案的后量子标准[1]。业界也在准备迁移到量子安全的解决方案，用后量子的变体取代经典的密码解决方案。数字签名方案在认证机制中发挥着重要作用。还有一些特殊类型的签名方案，如增强隐私ID（EPID）签名方案[2]，用于英特尔SGX可信计算系统和物联网（IoT）应用。因此，我们需要一个后量子变形的EPID签名方案，我和我的合作者Dutta已经提出了一个后量子变形的EPID签名方案，但是该签名方案的签名长度太大。在与Dutta的合作中，我们有以下目标：1。基于格理论提出的困难问题，使EPID签名方案更加高效.研究基于格的通用后量子签名方案，以及如何使它们在签名和验证时间方面更有效。我希望从中获得有意义的成果。[1]后量子密码学：精选算法2022，https：//csrc.nist.gov/Projects/post-quantum-cryptography/selected-algorithms-2022 [2] Brickell，E.，Li，J.：Enhanced Privacy ID：一种具有增强撤销功能的直接匿名证明方案。2007年ACM电子社会隐私研讨会论文集。pp. 21-30

The proposed research will focus on post-quantum cryptography (PQC). Modern public key cryptography will be under threat when large scale quantum computers will be available. Thus to keep the future cybersecurity space from quantum attack we need cryptographic algorithms that do not fall for quantum attack. Post-quantum cryptography (PQC) relies on hard problems for which there is no known advantage of quantum machines. There are several choices of such hard problems, and each class has some pros and cons in performace overheads. NIST has recently announced the post-quantum standards for Key Encapsulation Mechanism (KEM) and signature schemes [1]. The industry is also preparing for the migration to the quantum safe solutions by replacing the classical cryptographic solutions by their post-quantum variants.Digital signature schemes play an important role in authentication mechanisms. There are also some special types of signature schemes such as Enhanced privacy ID (EPID) signature scheme [2] that is used in Intel SGX trusted computing systems and also in Internet of Technology (IoT) applications. So, there is a strong motivation to secure EPID signature scheme from future quantum attacks, thus we need a post-quantum variant of EPID signatures.My collaborator Dutta and I already have worked out one post-quantum variant of EPID signature scheme, however, that signature scheme suffers from the large signature size. In this proposed collaboration with Dutta, we have the following objectives:1. Making EPID signature scheme more efficient based on hard problems drawn from lattice theory.2. Studying the general purpose post-quantum signature schemes based on lattice and how they can be made more efficient in terms of signing and verification time.I hope for a meaningful outcome from it. [1] Post-Quantum Cryptography: Selected Algorithms 2022, https://csrc.nist.gov/Projects/post-quantum-cryptography/selected-algorithms-2022[2] Brickell, E., Li, J.: Enhanced Privacy ID: A direct anonymous attestation scheme with enhanced revocation capabilities. In Proceedings of the 2007 ACM workshop on Privacy in electronic society. pp. 21-30