Lecture 4: Pairings

Repository containing Lecture 4 demonstration material

🎯 Goal

Alice wants to verify to Bob that she knows such $x,y$ satisfying $y = x^2$ without revealing $x$ or $y$. Given pairing $e: \mathbb{G}_1 \times \mathbb{G}_2 \to \mathbb{G}_T$, she does that by doing the following:

• Alice calculates $P_1 = [x]G_1$, $P_2 = [x]G_2$, $Q = [y]G_1$.
• Alice sends $(P_1, P_2, Q)$ to Bob.
• Bob verifies that $e(P_1,P_2) = e(Q, G_2)$.

📚 Table of Contents

#	File	Description
1	pairings.py	Contains all the low-level implementation of pairing.
2	demo.sage	Demo itself.