Abstract: A blueprint that produces a family of FHE schemes given any homomorphic monoidal encryption scheme. The ciphertext space is a subspace of the monoid algebra over F2 generated by the initial encryption monoid. The method can be generally applied to any monoid encryption schemes. Advantageously, monoid encryption schemes produce efficient FHE schemes with the inventive blueprint. Furthermore, the corresponding FHE scheme can correctly decrypt and efficiently compute circuits with low (polynomial in the security parameter) additive depth, a feature not realized by prior encryption methods.