一种改进的R-LWE同态掩码方案

Improved R-LWE homomorphic masking scheme

针对格上加密方案的差分能量攻击,Reparaz等人在PQC 2016上提出一种具有加法同态的R-LWE掩码方案。该方案能够有效地抵抗差分能量攻击,但由于密文的同态加法造成密文中噪声尺寸增大,降低解密正确率。针对这一问题,提出一个改进的R-LWE同态掩码方案。引入模转换技术,对同态加密之后的密文进行模归约,在保证明密文对应的前提下,降低密文中的噪声尺寸,提高方案的解密正确率。为了保护子密钥,引入随机矩阵对子密钥进行掩码保护,并给出正确性分析及安全性证明。分析表明,相对于原方案,新方案从安全性和效率上都有较大的提升。

Aiming at the differential power attack of the encryption scheme based on lattice,Reparaz proposed an additively homomorphic R-LWE masking scheme in PQC 2016. This scheme could against the differential power attack effectively,but the additively homomorphic algorithm between the ciphertexts made the size of noise increase. It declined the rate of decryption correctness. In view of this problem,this paper proposed an improved R-LWE homomorphic masking scheme. By introducing the modular switching technology,it made a modular reduction with the cipher text of additively homomorphic. Under the premising that plaintext and the ciphertext were corresponding,it declined the size of noise in the ciphertext. And it could improve the decryption correctness of the scheme. In order to protect the sub keys,it introduced a random matrix to mask the sub key. And it made the correctness analysis and the safety proof. The proposed scheme has better security and efficiency compared to the original scheme.