Question about the result of two-time encryption

[Ten000hours]

Hi,

I have a question about the result after the encryption for ciphertext two times using CKKS scheme. The whole process of what I did is: encrypt an numpy array --> ciphertext multi_plain with plaintext(numpy array) --> decrypt the result ciphertext --> re-encrypt the result --> ciphertext multi_plain plaintext --> decrypt for getting result. The reason for two times encryption is to refresh the noise budget. Everything works well until I get the result after the second multi_plain. Here is the question:

if I choose a relatively small value, like 400, for the plaintext part(the variable kenel in the following code), it will produce the correct result after two-time multiplication. But when I choose a value like 4000 for plaintext, it outputs the wrong result. Why it happens?

result for choosing 4000 for b ( wrong for 001 : should equal to 4000 4000 1)

result for choosing 400 for b( correct for 001 : 400 400 1 )

The main code is following ( sorry for using python version of SEAL for demo, I think it works just as SEAL since it using backbone of SEAL):

input_message = np.arange(0, 64).reshape(8, 8)
slot_count, scale, encryptor, evaluator, decryptor, galois_keys, ckks_encoder,relin_key,context = Setup()
a =  encryptor.encrypt(ckks_encoder.encode(input_message.flatten(), scale)
kenel = np.full((3,3),483)
b=ckks_encoder.encode(kenel.flatten(), scale)    
---------first multi-------------
evaluator.multiply_plain_inplace(a, b)

-------re-encrypt--------------
input = ckks_encoder.decode(decryptor.decrypt(a))
slot_count, scale, encryptor, evaluator, decryptor, galois_keys, ckks_encoder, relin_key, context = Setup()
plain_matrix1 = ckks_encoder.encode(input, scale)
a = encryptor.encrypt(plain_matrix1)    
b=ckks_encoder.encode(kenel.flatten(), scale)
--------------second multi-----------------
evaluator.multiply_plain_inplace(a, b)
--------decrypt--------    
check_res = ckks_encoder.decode(decryptor.decrypt(a))

The CKKS setup code:

parms = EncryptionParameters(scheme_type.ckks)
poly_modulus_degree = 4096
parms.set_poly_modulus_degree(poly_modulus_degree)
parms.set_coeff_modulus(CoeffModulus.Create(
    poly_modulus_degree, [36,37,36])) #36,36,37
scale = 2.0**30
context = SEALContext(parms)
print_parameters(context)

[WeiDaiWD]

The encrypted values have an upper-bound defined by coeff_modulus. One of your results grows too close to 2.0**(36+37-30), for example, 63 4000 4000 has 30 bits. We can confirm whether this is the cause by setting all input messages to 1. Would you please give it a try?

[Ten000hours]

The encrypted values have an upper-bound defined by coeff_modulus. One of your results grows too close to 2.0**(36+37-30), for example, 63 4000 4000 has 30 bits. We can confirm whether this is the cause by setting all input messages to 1. Would you please give it a try?

Thanks for your reply. I have given a go for setting all input message to 1, which means 1 4000 4000 for all values in the component-wise matrix multiplication, but still produces wrong result. Also, how close do you think it would be "dangerous" to produce an incorrect result? What is the range for "too close"?

[WeiDaiWD]

Would you please simply and share your code so that I can reproduce the error and debug it?

[Ten000hours]

Sorry for late reply. Please check the link below for my code. https://codecollab.io/@proj/GrayCartGray It imported the Python lib of SEAL, please check the link for installation: https://github.com/Huelse/SEAL-Python

[WeiDaiWD]

When encoding integers into a plaintext-only object, you can choose scale = 1.0; this applies to b.