Faster matrix approximate homomorphic encryption

Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen's algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from ??????(??????3) to ??????????????????????????????log 7, where ????????????????????????is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme.