Speeding Up Fully Homomorphic Encryption

Like machine learning, much of our existing Fully Homomorphic Encryption (FHE) methods use vector and matrix operations. Unfortunately, our generalised CPUs are not well set up for these operations, especially in the way that registers are setup. With a GPU, we support complex operations within minimal clock operations, such as for matrix multiplication, rotation and addition.

Within FHE, use lattices, and where our binary values are represented as polynomials, such as where a point at (9,5,16) is represented by:

16x²+5x+9

We can then define a finite field for the polynomial with a (mod p) operation:

16x²+5x+9 (mod p)

Overall, FHE uses a LWE (Learning With Errors) approach [video]:

We thus need processors that can compute with matrices in an efficient way. For this, we can understand the performance of GPUs and CPUs from this paper [here][1]: