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.

翻译：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，除了对此新方法的一种新颖实现外，还引入了黎曼本原。Chrysalis本身是首个依赖全纯学习误差（Holomorphic Learning with Errors）的密码方案，这是学习误差的一种复数形式。用于安全性归约的拟议NP难问题是不可交换格罗滕迪克问题（non-commutative Grothendieck problem）。该问题的归约通过应用双线性矩阵来实现，这些矩阵以全纯向量丛的形式存在，使得每个全纯表达式之间的坐标系统通过满射函数相互关联。结果是在双线性矩阵不等式的约束下任意选取的一组点，近似于该不可交换问题。这是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的。