Usage of sign circuit in CKKS

[ProgrammingFlorian]

Hello,

I'm currently in need of the sign(x) operator and I've tried to implement it using the CKKS circuit. I've looked at the documentation from the function itself and initialized all parameters using the CKKS general and bootstrapping tutorial.

Unfortunately, I've not been able to get the function running, I keep getting this error:

panic: cannot Conjugate: cannot apply Automorphism: GaloisKey[32767] is nil: key for galEl 32767 = 5^{4096} key is missing

I've tried adding a GaloisKey for 5^4096 to the comparison evaluator, but to no luck.
I'd appreciate any help on how to use the circuit and I've provided a (self-contained) snippet with my code below.

// Init
var err error
var params ckks.Parameters

LogN := 14
if params, err = ckks.NewParametersFromLiteral(
ckks.ParametersLiteral{
	LogN:            LogN,
	LogQ:            []int{38, 28, 28, 28, 28, 28, 28, 28, 28},
	LogP:            []int{61},
	LogDefaultScale: 28,
}); err != nil {
panic(err)
}

keyGen := rlwe.NewKeyGenerator(params)

secretKey := keyGen.GenSecretKeyNew()
publicKey := keyGen.GenPublicKeyNew(secretKey)

relinearizationKey := keyGen.GenRelinearizationKeyNew(secretKey)

galEls := make([]uint64, 1)
galEls[0] = params.GaloisElement(int(math.Pow(5, 4096)))

evaluationKey := rlwe.NewMemEvaluationKeySet(relinearizationKey, keyGen.GenGaloisKeysNew(galEls, secretKey)...)

encoder := ckks.NewEncoder(params)

encryptor := rlwe.NewEncryptor(params, publicKey)
decryptor := rlwe.NewDecryptor(params, secretKey)

evaluator := ckks.NewEvaluator(params, evaluationKey)

// https://github.com/tuneinsight/lattigo/blob/945cdf37938c253a48d76e29be461c2401cff730/examples/singleparty/ckks_bootstrapping/basics/main.go#L56
btpParametersLit := bootstrapping.ParametersLiteral{
LogN: utils.Pointy(LogN),
LogP: []int{61, 61, 61, 61},
Xs:   params.Xs(),
}
btpParameters, _ := bootstrapping.NewParametersFromLiteral(params, btpParametersLit)
btpEvKeys, _, _ := btpParameters.GenEvaluationKeys(secretKey)
bootstrapper, _ := bootstrapping.NewEvaluator(btpParameters, btpEvKeys)
minimaxEvaluator := minimax.NewEvaluator(params, evaluator, bootstrapper)
comparisonEvaluator := comparison.NewEvaluator(params, minimaxEvaluator)
comparisonEvaluator.WithKey(rlwe.NewMemEvaluationKeySet(relinearizationKey, keyGen.GenGaloisKeysNew(galEls, secretKey)...))

// Sign operator test

m1 := []float64{2, -3, 4}

p1 := ckks.NewPlaintext(params, params.MaxLevel())

if err := encoder.Encode(m1, p1); err != nil {
panic(err)
}

ct1, err := encryptor.EncryptNew(p1)
if err != nil {
panic(err)
}

ct2, err := comparisonEvaluator.Sign(ct1)
if err != nil {
panic(err)
}

pt2 := decryptor.DecryptNew(ct2)
r1 := make([]float64, params.MaxSlots())
if err := encoder.Decode(pt2, r1); err != nil {
panic(err)
}

fmt.Println(r1[:3])

[Pro7ech]

You need to use params.GaloisElementForComplexConjugation() (which is cyclotomic order - 1). By the way, params.GaloisElements already computes 5^k mod cyclotomic order.

[ProgrammingFlorian]

I've changed line 24 to

galEls[0] = params.GaloisElementForComplexConjugation()

Unfortunately, my code still isn't working properly, I'm getting results now but they are too large:

[8.094343902355059e+21 2.185781316952097e+23 1.5929979549916332e+19]

Is there anything I've configured wrongly oder should the sign operation be followed by another operation?

[Pro7ech]

This is another unrelated issue, and I'm not able to provide help without having access to a concise main that reproduces the error. What I can tell is that most likely you are giving as input values that are not in the expected interval (expects values in the range [-1, 1]). I recommend you read the documentation of the comparison.Evaluator.