# Bitwise operation on secret values revealing the result only to the participants

Given the following situation, what sort of cryptographic construction am I looking for?

• Alice has a bitfield (vector, polynomial representation, etc.)
• Bob has a different bitfield of the same length
• Alice and Bob want to know the bitwise AND of their two bitfields without revealing the result to others and without revealing their personal bitfields to each other or anyone else

For example

• Alice has 0101
• Bob has 1100

What would one do for Alice and Bob to know the result 0101 & 1100 = 0100 without revealing anything as stated above?

I imagine this would require some combination of zero-knowledge and homomorphic techniques, but I will be the first to admit that this is probably a bit out of my depth.

• Obviously, given the partially-reversible quality of the AND operation, some data will be revealed to the other participant, but I'm explicitly excluding that weakness in my thinking here. I'm not worried about Mallory sending 1111. – Scott Colby Aug 25 '18 at 2:42