# Why AND gate is * on Fully Homomorphic Encryption, BFV scheme?

According to Representing a function as FHE circuit, the AND gate for FHE encrypted data is just A*B, in the case that the plaintext has only 0 or 1 coefficients.

Remember that on the BFV FHE scheme, it encrypts polynomials, and we can set the maximum value of the coefficients of the polynomial. So, if we set the max value to 1, then we can do binary gates easily. For example:

  1 + 0x^1 + 1x^2 + 0x^3
+ 0 + 1x^1 + 1x^2 + 0x^3
______________________
1 + 1x^1 + 0x^2 + 0x^3


So + is essentially the OR gate for the polynomials. But I'm strugling to understand * as being the AND, specially because the multiplication of these polynomials are mod x^n +1, where n is the degree of the polynomials. So it's not a simple multiplication.

Why AND = *?

• It really depends on the FHE scheme. If you use constant polynomials, then it will be equal. Who claimed that it is a multiplication? The answer you linked talks about specific ones that are a single bit encrypted. Jan 14 at 15:24
• @kelalaka what would be a constant polynomial? And the scheme should be BFV. If not a multiplication, what is it? 2 days ago