一种针对全同态加密体制的密钥恢复攻击

摘要

Fully Homomorphic Encryption (FHE) makes it possible to perform all sorts of calculation in cipher domain, and own great value in cloud computing. However, the security of existing FHE schemes under the non-adaptive chosen-ciphertext attacks remains an issue to be studied. In this paper the construction of the Learning With Errors-based FHE scheme is analyzed, and it is pointed out that this cryptosystem has a potential security flaw, which creates the risk of private key leakage when confronting non-adaptive chosen cipher attacks. According to this, a key recovery attack is proposed, which is capable of recovering the private keys of such cryptosystem with the help of decryption oracle, through blending the dichotomy approximation in cipher domain and the solution of linear congruent equations.%全同态加密能够实现密文域上的各种运算，在云计算环境下具有重要的应用价值。然而，现有全同态加密体制在非适应性选择密文攻击下的安全性仍然是一个有待研究的问题。该文通过对基于容错学习(LWE)问题构造的全同态加密体制结构进行分析，指出其中存在的一个安全隐患，使其在遭受此类攻击时存在私钥泄露的风险。据此提出一种密钥恢复攻击方法，能够在拥有解密喻示的条件下，利用密文域二分逼近和求解线性同余方程组相结合的手段，对此类密码体制的私钥实施有效还原。