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.

翻译：本文介绍了一种加密密钥与解密密钥相同的轻量级加法同态算法。与Paillier等标准加法同态算法相比，该算法将加密和解密的计算开销从模指数运算降低为模乘法运算，并将密文加法的计算开销从模乘法运算降低为模加法运算。该算法基于一个新的数学问题：在两个除法运算中，当两个余数相关时，能否根据被除数推断出余数或除数？目前，破解该问题的方法尚不明确，但需进一步探讨其难度是否足够高。除该数学问题外，我们还为解密设计了两类有趣的结构，分别用于正文中提到的两种算法。算法2的解密结构可能引入新的安全漏洞，但我们未对此问题进行深入探究。