Hi all, What is the maximum number of elements a CKKS Plaintext can contain in general and in OpenFHE ? Does it depend only on the security model? Thanks

This is an enormous ring dimension. As @narger mentioned, I would not go beyond N=2^{17} on general-purpose CPU implementations. The limits imposed by ultra-large ring dimensions are mostly computational in terms of runtime and space. Security should not be an issue.

It strictly depends on N, in particular the maximum number of elements is equal to N/2. AFAIK the space is halved because of the default encoding process of CKKS (i.e. Slots encoding), performed in order to make the polynomial multiplication in the ciphertext space reflected as a point-wise multipl…

But can we set N to 2^32 or 2^64 for example ? How much it will impact the performances ?

I do not think it is feasible. N=2^{17} is already a very large value. In your case I would split my data in multiple ciphertexts.

Note in the Conjugate-Invariant CKKS, you can encrypt up to N real numbers.

@sofianeazgh When you need a larger number of slots, you can simply use multiple plaintexts, i.e., encode the large vector into a vector of plaintexts, each with N/2 elements.

Thank you guys for the answers. The multi-vector split method appears to be the most intuitive. However, are you familiar with any methods for matrix multiplication when dealing with large vectors that are split into multiple “sub-vectors”?

Maximum number of slots

FHE Questions

Caesar January 15, 2024, 2:22pm 9

Check this thread, it claims an implementation of matrix multiplication in OpenFHE. Not sure if it supports multiple ciphertexts though.

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Maximum number of slots

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