Degree-D Reverse Multiplication-Friendly Embeddings: Constructions and Applications

Daniel Escudero, Cheng Hong, Hongqing Liu, Chaoping Xing, Chen Yuan

Abstract: In the recent work of (Cheon & Lee, Eurocrypt’22), the concept of a degree-D packing method was formally introduced, which captures the idea of embedding multiple elements of a smaller ring into a larger ring, so that element-wise multiplication in the former is somewhat “compatible” with the product in the latter. Then, several optimal bounds and results are presented, and furthermore, the concept is generalized from one multiplication to degrees larger than two. These packing methods encompass several constructions seen in the literature in contexts like secure multiparty computation and fully homomorphic encryption.