Homomorphic Encryption

2022-09-20 76 words One minute

Contents

Outsourcing computation, privately

Homomorphic evaluation function:

Eval: f, Enc(x) -> Enc(f(x))

Fully homomorphic = correctness for any efficient f = correctness for universal set

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

**basic idea: ** we have a matrix A, we can generate a matrix s, such that sA=$\eta$

it can be generalized to matrices.