What are Zero Knowledge Proofs?
Suyash Bagad
Proof of Knowledge
Coke from Bottle
Coke from Can
Victor
Peter
\(x\)
\(V\)
\(P\)
Coke from Can
Victor
Peter
Guess?
Bottle!
\langle P, V \rangle (x) = \begin{cases}
1 & \text{if } V \text{ accepts} \\
0 & \text{if } V \text{ rejects}
\end{cases}
Proof of Knowledge
Coke from Bottle
Coke from Can
Victor
Peter
Try again!
Proof of Knowledge
Coke from Bottle
Victor
Peter
Can!
If \(P\) actually knows the taste, \( \Pr[ \langle P,V \rangle(x) = 1 ]\) = 1
If \(P\)'s claim is wrong, \( \Pr[ \langle P,V \rangle(x) = 1 ] = \left(\frac{1}{2}\right)^2 \)
\(\implies\) Completeness!
\(\implies\) Soundness!
Proof of Knowledge
Zero Knowledge Proofs
Zero Knowledge Proofs
Reveal!
Zero Knowledge Proofs
Zero Knowledge Proofs
Zero Knowledge Proofs
Zero Knowledge Proofs
Reveal!
Zero Knowledge Proofs
Zero Knowledge Proofs
On repeating the experiment a number of times,
- If the prover is honest, verifier accepts!
- If the prover is cheating, verifier will catch it!
- No information about 3-colouring is revealed!
\(\text{Completeness,}\)
\(\text{Soundness,}\)
\(\text{Zero-Knowledge!}\)
