diff --git a/src/protocol/2pc/deap.md b/src/protocol/2pc/deap.md index 31bf83d..3a051b1 100644 --- a/src/protocol/2pc/deap.md +++ b/src/protocol/2pc/deap.md @@ -83,12 +83,12 @@ Alice, if honest, has learned the correct output $v$ thanks to the authenticity ### Equality Check -1. Bob opens his garbled circuit and OT by sending $\Delta_B$, $y$ and $\rho$ to Alice. -2. Alice, can now derive the _purported_ input labels to Bob's garbled circuit $([X]^{\\*}_B, [Y]^{\\*}_B)$. -3. Alice uses $\rho$ to open all of Bob's OTs for $[x]_B$ and verifies that they were performed honestly. Otherwise she aborts. -4. Alice verifies that $G_B$ was garbled honestly by checking $\mathsf{Gb}([X]^{\\*}_B, [Y]^{\\*}_B) == G_B$. Otherwise she aborts. -5. Alice now opens $\mathsf{com}_{\mathsf{check}_A}$ by sending $\mathsf{check}_A$ and $r$ to Bob. -6. Bob verifies $\mathsf{com}_{\mathsf{check}_A}$ then asserts $\mathsf{check}_A == \mathsf{check}_B$, aborting otherwise. +17. Bob opens his garbled circuit and OT by sending $\Delta_B$, $y$ and $\rho$ to Alice. +18. Alice, can now derive the _purported_ input labels to Bob's garbled circuit $([X]^{\\*}_B, [Y]^{\\*}_B)$. +19. Alice uses $\rho$ to open all of Bob's OTs for $[x]_B$ and verifies that they were performed honestly. Otherwise she aborts. +20. Alice verifies that $G_B$ was garbled honestly by checking $\mathsf{Gb}([X]^{\\*}_B, [Y]^{\\*}_B) == G_B$. Otherwise she aborts. +21. Alice now opens $\mathsf{com}_{\mathsf{check}_A}$ by sending $\mathsf{check}_A$ and $r$ to Bob. +22. Bob verifies $\mathsf{com}_{\mathsf{check}_A}$ then asserts $\mathsf{check}_A == \mathsf{check}_B$, aborting otherwise. Bob is now convinced that $v^A$ is correct, ie $f(x, y) = v^A$. Bob is also assured that Alice only learned up to k bits of his input prior to revealing, with a probability of $2^{-k}$ of it being undetected.