Decryption fails after relinearization (CKKS)

[andreea-anghel]

I am using the following SealContext:

  seal::EncryptionParameters params(seal::scheme_type::ckks);
  size_t poly_modulus_degree = 32768;
  params.set_poly_modulus_degree(poly_modulus_degree);
  std::vector<int> coefs{ 40, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 40 };
  params.set_coeff_modulus(seal::CoeffModulus::Create(poly_modulus_degree, coefs));
  seal::SEALContext context(params);

to compute the following set of operations

    float a = -0.119982;
    float b = -0.119981;
    double scale = pow(2, 30);

    seal::Plaintext plain_a, plain_b;
    seal::Ciphertext enc_a, enc_b;

    seal::CKKSEncoder ckks_encoder(context);
    seal::Encryptor ckks_encryptor(context, public_key);

    ckks_encoder.encode(a, scale, plain_a);
    ckks_encoder.encode(b, scale, plain_b);

    ckks_encryptor.encrypt(plain_a, enc_a);
    ckks_encryptor.encrypt(plain_b, enc_b);

    seal::Evaluator evaluator(context);
    evaluator.sub_inplace(enc_a, enc_b);
    decrypt_print(enc_a, context, secret_key);
    
    evaluator.multiply_inplace(enc_a, enc_a);
    decrypt_print(enc_a, context, secret_key);
    
    seal::RelinKeys relin_keys;
    keygen_ckks.create_relin_keys(relin_keys);
    evaluator.relinearize_inplace(enc_a, relin_keys);
    decrypt_print(enc_a, context, secret_key);

where the decrypt_print function is defined as

void decrypt_print(seal::Ciphertext& encrypted, seal::SEALContext& context, seal::SecretKey& key) {
    seal::Decryptor decryptor(context, key);
    seal::Plaintext plain;
    decryptor.decrypt(encrypted, plain);
    std::vector<double> result;
    seal::CKKSEncoder encoder(context);
    encoder.decode(plain, result);
    std::cout << "decrypted value " << result[0] << std::endl;
}

When I run the operations above, I get the following output:

(after sub_inplace)          decrypted value 3.77205e-10
(after multiply in place)  decrypted value -1.36176e-16
(after relinearize)            decrypted value -6.51654e+115

My question is what could be the reason for the failed decryption after relinearization? The scale is stable across the operations above.

Thank you for any insight or comment.

[WeiDaiWD]

Have you tried decryption right after encoding and encryption? They should give different values from a or b. scale sets an upper-bound on the amount of precision preserved after the decimal point. When scale == pow(2, 30), you cannot preserve more than 3 digits.

[andreea-anghel]

thanks @WeiDaiWD yes, indeed the values are slightly different even after decryption. Could you please expand on your last statement, regarding the 3 digits (why only 3 digits)? How could one preserve more digits?

[WeiDaiWD]

Sorry, my bad, I meant to say 9 digits -- 2^30 is close to 10^9. Anyway, precision preserved after decimal point is upper bounded by scale; it's always equal to or less than scale because noise exists in ciphertexts. Increasing scale is the easiest way to preserve more digits.