Hypercomplex: abstract & fast header-only C++ template library for lattice-based cryptosystems in high-dimensional algebras

The following work presents a C++ library which is dedicated to performing arbitrary-precise calculations on hypercomplex numbers from the Cayley-Dickson algebras. Basic arithmetical operations as well as a few miscellaneous functions are implemented. Its most important feature is the support for encryption/decryption procedures for public-key lattice-based cryptosystems in high-dimensional algebras over truncated polynomial rings.