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arXiv 1801.07702cs.CR
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后量子密码学:Riemann原语与Chrysalis

Post-Quantum Cryptography: Riemann Primitives and Chrysalis

Ian Malloy

AI总结:

本研究提出基于黎曼球面的后量子密码方案Chrysalis,引入Riemann原语,以非交换Grothendieck问题为NP难安全归约基础,通过双线性矩阵等技术实现安全归约,是首个基于全纯容错学习的密码方案。

摘要:

Chrysalis项目是一种利用黎曼球面实现后量子密码学的拟议方法。为此,除了这种新方法的全新实现外,还引入了Riemann原语。Chrysalis本身是首个依赖全纯容错学习(Holomorphic Learning with Errors,一种复杂的容错学习形式)的密码方案。用于安全性归约的NP难问题是非交换Grothendieck问题。该问题的归约通过在全纯向量丛上应用双线性矩阵实现,使得坐标系通过各全纯表达式之间的满射函数相交。结果是在双线性矩阵不等式约束下得到一组任意选取的点,可逼近该非交换问题。这一结果通过将双线性矩阵的二次型应用于线性矩阵不等式来实现。

英文摘要:

The Chrysalis project is a proposed method for post-quantum cryptography using the Riemann sphere. To this end, Riemann primitives are introduced in addition to a novel implementation of this new method. Chrysalis itself is the first cryptographic scheme to rely on Holomorphic Learning with Errors, which is a complex form of Learning with Errors. The proposed NP-Hard problem for security reduction is the non-commutative Grothendieck problem. The reduction of this problem is achieved by applying bilinear matrices in terms of the holomorphic vector bundle such that coordinate systems are intersected via surjective functions between each holomorphic expression. The result is an arbitrarily selected set of points within constraints of bilinear matrix inequalities approximate to the non-commutative problem. This is achieved by applying the quadratic form of bilinear matrices to a linear matrix inequality.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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