Question

Suppose Alice has a and Bob has b. Alice and Bob also share a secure communication channel. Chris wants to compute S = a ⊕ b. Alice does not want Chris or Bob to learn a and Bob does not want Chris or Alice to learn b. How can this be done?

Answer 1

This can be done by sharing some number b/w Alice and Bob.

Let a number c is shared b/w Alice and Bob.

c should not be shared with Chris.

Now, Alice can share (a xor c) with Chris but not to Bob.

Similarly, Bob can share (b xor c) with Chris but not to Alice.

So, Now Chris know (a xor c) and (b xor c).

Chris can calculate (a xor b) = (a xor c) xor ( b xor c).....

So Chris can calculate (a xor b) with satisfying all constraints.

xor = $\bigoplus$