量子计算环境下具有特殊性质的格基签名体制

As the best candidate of post-quantum cryptography, the value of lattice-based cryptography has been approved by the public. However, with the popularity of e-commerce and Internet banking, the lattice-based signature also has disadvantages of large space size and the insufficient cryptography notions. And they have been the biggest obstacle on the way to putting lattice-based digital signature schemes into use. In this project, we devote ourselves to STFS (simpler, tighter, faster and smaller) trapdoor generation technique and the construction of signatures with special feature. The major research contents of this project is as follow: (1) further exploring mechanism of lattice-based trapdoor generation algorithm, combing the special properties of the ideal lattice and the cycle lattice to conduct research on more simple and efficient lattice-based trapdoor generation algorithm; (2) further studying the mechanism of the pre-image sampling algorithm and the lattice-based delegation algorithm, based on the new lattice-based trapdoor generation algorithm to construct the more efficient key extraction algorithm and lattice-based delegation algorithm; (3) to explore the possibility and security of the new lattice-based trapdoor’s application in hierarchical identity-based/proxy/group/ ring /aggregate/certificateless/forward secure digital signature, and construct the corresponding lattice-based signature schemes. To sum up, this project is to expand and deepen the theory of lattice-based digital signature, and provide a more sufficient theory for the practical application of lattice-based signature schemes.

作为后量子密码的典型代表，格公钥密码的普识价值早已被认知。然而，随着电子商务和网上银行的日渐普及，庞大的空间尺寸以及不够完善的密码原型俨然已成为格基签名走向实用化的最大障碍。本项目旨在研究格上STFS（simpler、tighter、faster and smaller）陷门生成技术和具有特殊性质的签名构造技术。拟就以下内容开展研究：（1）进一步发掘格基陷门生成算法的机理，结合循环格和理想格的特殊性质，研究可证明安全前提下更简单、高效的陷门生成算法；（2）进一步研究原像采样算法和格基委派算法的机理，利用新型陷门构造更高效的密钥提取算法和格基委派算法；（3）探讨新型陷门应用于分级/代理/群组/环组/聚合/无证书/前向安全签名的可能性、安全性，并构造相应的签名方案。综上所述，本课题预期将拓展和深化格基签名的理论，并为格基签名方案走向实用化提供更加充分的理论储备。

格公钥密码的普识价值早已被认知。然而，随着电子商务的日渐普及，庞大的空间尺寸以及不够完善的密码原型俨然已成为格基签名走向实用化的最大障碍。本项目研究格上陷门生成技术和具有特殊性质的签名构造技术。重要结果具体如下：.无证书有序聚合签名：将陷门采样技术引入到NTRU格上，从而构造抗碰撞陷门函数，利用该陷门函数构造了NTRU格上的无证书有序聚合签名方案。该方案在随机预言机模型下是可证明安全的。.基于证书的有序聚合签名：基于NTRU格上的原像采样算法和抛弃采样技术构造基于证书的有序聚合签名方案。在随机预言机模型下，方案的安全性可规约至问题。.前向安全代理签名：在格上引入前向安全的代理签名这一概念并给出其安全性模型，基于格上已知NP困难的小整数解问题提出了随机预言机模型下和标准模型下前向安全的格基代理签名。.前向安全有序聚合签名：从前向安全性等方面入手，基于格上的小整数解问题，首次构造了随机预言机模型下和标准模型下前向安全的格基有序聚合签名方案。.以上构造的各种具有特殊性质的格基签名不仅丰富了格基数字签名的应用场景，还将为其在区块链、物联网等高级别服务功能上的应用打下理论基础。