  This article describes a lightweight additive homomorphic algorithm with the
same encryption and decryption keys. Compared to standard additive homomorphic
algorithms like Paillier, this algorithm reduces the computational cost of
encryption and decryption from modular exponentiation to modular
multiplication, and reduces the computational cost of ciphertext addition from
modular multiplication to modular addition. This algorithm is based on a new
mathematical problem: in two division operations, whether it is possible to
infer the remainder or divisor based on the dividend when two remainders are
related. Currently, it is not obvious how to break this problem, but further
exploration is needed to determine if it is sufficiently difficult. In addition
to this mathematical problem, we have also designed two interesting
mathematical structures for decryption, which are used in the two algorithms
mentioned in the main text. It is possible that the decryption structure of
Algorithm 2 introduces new security vulnerabilities, but we have not
investigated this issue thoroughly.
