Homomorphic Encryption
Contents
Outsourcing computation, privately
Homomorphic evaluation function:
Eval: f, Enc(x) -> Enc(f(x))
Fully homomorphic encryption
Fully homomorphic = correctness for any efficient f = correctness for universal set
Approximate eigenvector method
基于GSW13的特征向量的构造,我们可以在ciphertext上计算加法和乘法,然后可以通过secret key恢复出message的计算结果。但是这个方法不安全,因为特征向量很容易被找到。
**idea:**使用approximate eigenvectors,在secret key右乘cipher text
Learning with errors (LWE) R05
Rearranging notation
**basic idea: ** we have a matrix A, we can generate a matrix s, such that sA=$\eta$
Encryption scheme from LWE
Encryption
Decryption
it can be generalized to matrices.