As a follow-up, let me recommend Püschel & Moura (2006) “Algebraic Signal Processing Theory”, https://arxiv.org/pdf/cs/0612077.pdf and Püschel’s other papers about similar topics.
Or in a different direction, DJB (2008), “Fast multiplication and its applications”, http://cr.yp.to/lineartime/multapps-20080515.pdf
As a follow-up, let me recommend Püschel & Moura (2006) “Algebraic Signal Processing Theory”, https://arxiv.org/pdf/cs/0612077.pdf and Püschel’s other papers about similar topics.
Or in a different direction, DJB (2008), “Fast multiplication and its applications”, http://cr.yp.to/lineartime/multapps-20080515.pdf