feat(core_crypto): add glwe tensor product, relinearization, glwe keyswitch and lwe trace packing keyswitch

[Carl-Zama]

PR content/description

Adds the following:

1. Slice decomposers to decompose polynomials.
2. Glwe Keyswitch Keys and the Glwe Keyswitch operation to go from Glwe Ciphertexts encrypted under one Glwe Secret Key to one encrypted under a second Glwe Secret Key while keeping the same message.
3. Glwe tensor product operation to multiply two polynomial plaintexts.
4. Glwe Relinearization Keys and the Glwe Relinearization operation which converts the format of the Glwe tensor product operation output back to be format of the inputs.
5. Ability to apply an automorphism to a polynomial.
6. Lwe Trace Packing Keyswitch Keys and the Lwe trace packing keyswitch operation which can pack a list of LWE ciphertexts into a single GLWE ciphertext at specified coefficients.
7. Operations to perform a dot product between two LWE lists and to perform a number of LWE multiplications in parallel, i.e. a component-wise product of two LWE lists.

Check-list:

• Tests for the changes have been added (for bug fixes / features)
• Docs have been added / updated (for bug fixes / features)
• Relevant issues are marked as resolved/closed, related issues are linked in the description
• Check for breaking changes (including serialization changes) and add them to commit message following the conventional commit specification

[IceTDrinker]

Hey thanks for the PR, I'll try to take some time to read it, but I won't have time before next week, in the mean time if pcc is failing you can fix the errors it sends back :)

[Carl-Zama]

Hey thanks for the PR, I'll try to take some time to read it, but I won't have time before next week, in the mean time if pcc is failing you can fix the errors it sends back :)

No problem, I should have hopefully fixed the pcc issues.

[IceTDrinker]

I think a potential first step would be to prep the glwe keyswitch stuff, for a first standalone PR

[Carl-Zama]

I think a potential first step would be to prep the glwe keyswitch stuff, for a first standalone PR

Okay, yes I would agree. Do you want me to do that?

[IceTDrinker]

I think a potential first step would be to prep the glwe keyswitch stuff, for a first standalone PR

Okay, yes I would agree. Do you want me to do that?

I’ll check with Sam as he knows better what your current tasks are 🙂