  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.
