To all he-experts out there:
I want to implement a matrix-vector multiplication with very large matrices (600000 x 55). Currently I am able to perform he operations like Addition, Multiplication, InnerProduct etc. with small inputs. When I try to apply these operations on larger inputs I get errors like Invalid next size (normal) or I ran out of main memory until the os kills the process (exit code 9).
Do you have any recommendations/examples how to archive an efficient way of implementing a matrix-vector multiplication or something similar? (Using BFV and CKKS).
PS: I am using the PALISADE library but if you have better suggestions like SEAL or Helib I would happily use them as well.
CKKS, which is also available in PALISADE, would be a much better option for your scenario as it supports approximate (floating-point-like) arithmetic and does not require high precision (large plaintext modulus). BFV performs all operations exactly (mod plaintext modulus). You would have to use a really large plaintext modulus to make sure your result does not wrap around the plaintext modulus. This gets much worse as you increase the depth, e.g., two chained multiplications.
For matrix-vector multiplication, you could use the techniques described in https://eprint.iacr.org/2019/223, https://eprint.iacr.org/2018/254, and the supplemental information of https://eprint.iacr.org/2020/563. The main idea is to choose the right encoding and take advantage of SIMD packing. You would work with a power-of-two vector size and could pack the matrix either as 64xY (multiple rows) per ciphertext or a part of each row per ciphertext, depending on which one is more efficient.