Computing coefficient modulus BGV scheme.

[tarakaramg]

I am trying to compute the ciphertext coefficient modulus (q) of the BGV scheme. But, I am a bit confused about how this is represented in Seal.

This is related to coeff_modulus (parms().coeff_modulus()). However, it is not a single integer but a list of integers. I am wondering whether

1. Is the ciphertext coefficient modulus (q) the product of all the elements of context_data.parms().coeff_modulus()?
2. How is this number related to total_coeff_modulus?
3. It seems to me that total_coeff_modulus = product of elements of parms().coeff_modulus(), but when I look at the values both are different. For example in the context below total_coeff_modulus is a 20-digit integer but total_coeff_modulus_bit_count is 218 bits. Why are they different?

Scheme: BFV | | Encryption parameters : | scheme: BFV | poly_modulus_degree: 8192 | coeff_modulus size: 218 (43 + 43 + 44 + 44 + 44) bits | plain_modulus: 1024 | total_coefficient_modulus: 10537575945477046273

Thank you.

[kimlaine]

1. Yes, the ciphertext modulus is the product of all individual modulus factors in context_data.parms().coeff_modulus().
2. They are the same thing.
3. The bit count 218 is correct. I'm guessing you are only printing the lowest 64 bits in your example above. Note that the total_coeff_modulus() function returns a pointer to uint64_t: that's where you'll need to read the 4 64-bit words of the 218-bit integer.