LWE: add evaluation key type and technique

[ZenithalHourlyRate]

Related to #1057.

I roughly prototyped it from openfhe/pke/keyswitch (BGV/CKKS), yet I do not know if this is accurate for binfhe schemes (CGGI).

Example:

#generator = #polynomial.int_polynomial<1 + x**1024>
#ring = #polynomial.ring<coefficientType = i32, coefficientModulus = 65537 : i32, polynomialModulus=#generator>

#key = #lwe.key<id = "s", size = 1>
#key_mult = #lwe.key<id = "s", size = 1, basis = 2>
#key_rotate = #lwe.key<id = "s", size = 1, rotate = 2>

#keyswitch_bv_base = #lwe.bv_keyswitch_technique<base = 65536, dnum = 0>
#keyswitch_bv = #lwe.bv_keyswitch_technique<base = 0, dnum = 3>
#keyswitch_ghs = #lwe.ghs_keyswitch_technique<extra_modulus=<elements = <65537 : i32>, current = 0>>

!evaluation_key_mult = !lwe.new_lwe_evaluation_key<from_key=#key_mult, to_key=#key, ring=#ring, keyswitch_techniques= #keyswitch_bv, #keyswitch_ghs>
!evaluation_key_rotate = !lwe.new_lwe_evaluation_key<from_key=#key_rotate, to_key=#key, ring=#ring, keyswitch_techniques= #keyswitch_bv_base>

[asraa]

Hey! Sorry for the delay - I'm finally back online for development now.

[asraa]

Thanks for starting this!

I will explore replacing the BGV / CKKS dialects with the new lwe types in a PR EOW

[asraa]

nit: just remove the _technique here and below

[asraa]

Suggested change

	`base` is the radix base used in decomposition of the coefficient modulus
	`base` is the radix base used in the digit decomposition of the coefficient modulus

[asraa]

thank you for considering the RNS variants! I understand it's important to know the dnums so that the type converter knows the type / shape of the key switching key. For the lowering, we'll need the actual RNS moduli, which we'll pull from the RNS modulus of the ring in the keyswitching key, right?

[asraa]

we could implement the type constraint here.

[asraa]

OptionalParameter? (can also update the assembly format for an optional print)

[asraa]

Why is this an array ref parameter? Wouldn't only a sinlgle technique apply to a given key?

[ZenithalHourlyRate]

I intentionally left the HYBRID keyswitching technique as a combination of BV attr and GHS attr, so that we do not have to define another LWE_HYBRIDKeySwitchAttr where all base/dnum/extra_modulus will be included. If we accept such elaboration, then we can define it and here can be a single technique.

[j2kun]

Please take a moment to let me know the current state of this PR. Is it blocked, or obsolete/closeable? If blocked, please briefly say what needs to be done to unblock it.

[ZenithalHourlyRate]

Please take a moment to let me know the current state of this PR. Is it blocked, or obsolete/closeable? If blocked, please briefly say what needs to be done to unblock it.

I was thinking of coming back to this when we are going to do some serious thing for the lwe-to-poly pipeline, but did not get the time.

Also I think this is somewhat related to #1274, namely how should we design a lwe-level interface for eval keys. If we has lwe types and ops describing eval key related stuff, we do not need that relin/rotate op interface.

[j2kun]

There is a Googler who wants to do some 20% project on lowering some schemes to polynomial, so I will ensure he's aware of this work.