Construction of Post-quantum Signature Schemes based on Lattices

提出的研究将重点放在后量子密码学（PQC）上。当大规模量子计算机可用时，现代公钥加密将受到威胁。因此，为了防止未来的网络安全空间受到量子攻击，我们需要不受量子攻击影响的加密算法。后量子密码学（PQC）依赖于量子机器没有已知优势的难题。这类难题有几种选择，每个类在性能开销方面都有一些优缺点。NIST最近宣布了密钥封装机制（KEM）和签名方案[1]的后量子标准。业界也在准备迁移到量子安全解决方案，用它们的后量子变体取代经典的加密解决方案。数字签名方案在认证机制中扮演着重要的角色。还有一些特殊类型的签名方案，例如用于英特尔SGX可信计算系统和物联网（IoT）应用的增强隐私ID （EPID）签名方案[2]。因此，有强烈的动机保护EPID签名方案免受未来的量子攻击，因此我们需要EPID签名的后量子变体。我和我的合作者Dutta已经研究出了一种EPID签名方案的后量子变体，然而，该签名方案受到签名大小过大的影响。在与Dutta的拟议合作中，我们有以下目标：1。基于格理论的难点问题提高EPID签名方案的有效性研究了基于点阵的通用后量子签名方案，以及如何使其在签名和验证时间方面更有效。我希望这次会议能有一个有意义的结果。[0]李建军，李建军，李建军，李建军，李建军：增强隐私ID：一种具有增强撤销能力的直接匿名认证方案。2007年ACM研讨会论文集中关于电子社会中的隐私。21 - 30页。

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