Add PlainMatrix and SecureMatrix

[ArseniyKholod]

I was wondering about 2D simulations and thought, that it should not be so difficult to add PlainMatrix and SecureMatrix based on currently existing PlainVector and SecureVector, this is my try.
I pinned OpenFHE_jll to v1.1.2 to let tests run.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Files with missing lines	Coverage Δ
examples/simple_ckks_bootstrapping_matrix.jl	100.00% <100.00%> (ø)
examples/simple_real_numbers_matrix.jl	100.00% <100.00%> (ø)
src/SecureArithmetic.jl	100.00% <ø> (ø)
src/arithmetic.jl	100.00% <100.00%> (ø)
src/openfhe.jl	100.00% <100.00%> (ø)
src/operations.jl	100.00% <100.00%> (ø)
src/types.jl	100.00% <100.00%> (ø)
src/unencrypted.jl	100.00% <100.00%> (ø)

[ArseniyKholod]

Unfortunately, the concept used in the previous commits is not useful, because of the extremely bad efficiency. I tried to build a secure matrix simply combining many secure vectors as rows of the matrix, but e.g. for 40 * 40 Matrix it's necessary to use 40 SecureVector. 40 * 40 matrix could be fit in a single SecureVector with dimension of the ring more than 3200. In case of using 40 such vectors to hold a single matrix, that could fit in a single, all computations become 40 times slower. The solution could be to decrease a ring dimension for these vectors used in a matrix, but due to the security reason it's almost impossible. So as a next step I will try to find a way to fit a matrix in a single vector, simply fusing all rows together and define all necessary arithmetical operations on it.

[sloede]

Unfortunately, the concept used in the previous commits is not useful, because of the extremely bad efficiency. I tried to build a secure matrix simply combining many secure vectors as rows of the matrix, but e.g. for 40 * 40 Matrix it's necessary to use 40 SecureVector. 40 * 40 matrix could be fit in a single SecureVector with dimension of the ring more than 3200. In case of using 40 such vectors to hold a single matrix, that could fit in a single, all computations become 40 times slower. The solution could be to decrease a ring dimension for these vectors used in a matrix, but due to the security reason it's almost impossible. So as a next step I will try to find a way to fit a matrix in a single vector, simply fusing all rows together and define all necessary arithmetical operations on it.

Thanks, very interesting findings. Please make sure that you record your measurements such that we can use them in a publication or talk.

[sloede]

It might be worthwhile to search the Discourse for terms related to matrix: https://openfhe.discourse.group/search?q=matrix

The first few results seem interesting, but also indicate that it might be a non-trivial goal to achieve (at least if trying to do it efficiently).

[ArseniyKholod]

It might be worthwhile to search the Discourse for terms related to matrix: https://openfhe.discourse.group/search?q=matrix

The first few results seem interesting, but also indicate that it might be a non-trivial goal to achieve (at least if trying to do it efficiently).

Thanks for the idea! I will record all results!

[sloede]

Is this still relevant? I lost track whether this is already implemented in SA.jl or not...