Relation between ring dimension, batch size, num slots and length

Library Questions
1

Hi!
I use OpenFHE to perform some simple numerical simulations. And I have questions to the naming and meaning of several parameters used in OpenFHE. It would be great if someone could clarify it me.

Is a batch size used to configure a CryptoContext in parameters.SetBatchSize(batchSize); the same as num slots used to create Plaintext in cryptoContext->MakeCKKSPackedPlaintext(x, 1, depth - 1, nullptr, numSlots);? Are their interchangeable or have to be the same?

Which relation do batch size and num slots have to ring dimension and length of data vector. ( length of data vector could be not a power of two, unlike three other parameters)

Thank you in advance!

2

In the CKKS scheme, slots * 2 = dimension. The maximum value of batch size is slots. (Only in CKKS scheme, BGV/BFV is different from CKKS)
I think the remainder is filled with 0 when the length of vector is less than batch size.

3

When the number of slots is specified during MakeCKKSPackedPlaintext, that number of slots is set for a specific plaintext/ciphertext. The batch size is the global (default) setting for all ciphertexts in the cryptocontext.

4

Thank you very much!
Could you also take look at following questions? Just to ensure, that I’m configure num_slots and batch_size in effective way.

  • Can num_slots be greater than the originally specified batch_size?
  • What is the motivation is to create Plaintexts with different num_slots from a single CryptoContext (CC)? Are there performance benefits?
  • Is it possible to do arithmetic with plaintext/ciphertests of different num_slots?
  • If the previous question was answered with “yes”, and the one before that with “better performance”, is there any reason to not always set num_slots to the smallest power-of-two such that the data fits?

Example for the last question: If batchSize == 128 , but my data is either length == 30 or length == 50 , should I just always set num_slots to 32 and 64 respectively?

5
  • Can num_slots be greater than the originally specified batch_size?

Yes

  • What is the motivation is to create Plaintexts with different num_slots from a single CryptoContext (CC)? Are there performance benefits?

Primarily for CKKS bootstrapping (it gets slightly cheaper for a smaller number of slots). Also the approximation error is smaller in some operations when working with more sparse ciphertexts.

  • Is it possible to do arithmetic with plaintext/ciphertests of different num_slots?

No, it does not make sense (in the same binary operation)

6

OK, so just to confirm I understood it correctly:

  • The technical maximum number of slots for CKKS-based encoding is GetRingDimension()/2 (inherent in CKKS)
  • When specifying batchSize for CCParams, …
    • it is used as one of the factors to determine the required ring dimension
    • it is used to set the default number of slots for newly created Plaintexts/Ciphertexts
  • Using GetSlots on a plaintext (or its derived ciphertext) created without specifying slots in MakeCKKSPackedPlaintext, results in the number of slots equal to the batch size
  • Using SetSlots on a plaintext or before creating a ciphertext allows one to dynamically reduce the number of slots.
  • Using SetSlots after a ciphertext was created to change the number of slots generally leads to a broken ciphertext unless manually.

At least this is what I have found from experimentation…