Fig. 7
From: Secure tumor classification by shallow neural network using homomorphic encryption
Illustration of data packing and matrix multiplication. To efficiently compute with encrypted data, data packing and matrix multiplication method should be highly concerned. (a) We basically follow the method in [15] which breaks the matrix-matrix multiplication into matrix-vector multiplications with vectors of special form. (b) Naïve packing method with 4 CMults and 8 Rots and (c) ours with 4 CMults and 2 Rots are given as a toy example with s=8 samples, g=4 genes, T=4 tumor types and ciphertext slot-size n=32, when using m=2 duplication of \(\vec {x}_{i}\)s (See Warm-up with Toy Example). If we use imaginary part for message space, we can even reduce the number of CMults to \(\frac {sg}{2n} \cdot m \lceil \frac {T}{m} \rceil = 2\), where the number of Rots remains the same as \(\log \frac {n}{ms} \cdot \lceil \frac {T}{m} \rceil =2\) (See Putting It All Together)