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The Vanishing Polynomial for QAPs

My latest post continues exploring how to encode a verification problem inside a SNARK. This time, I explore the role of the Vanishing Polynomial when constructing a Quadratic Arithmetic Program to represent a set of constraints.

ZK Snarks and Their Algebraic Structure – Part 3

ZK-Snarks would not be possible without the use of bilinear pairings. In my series about their algebraic structure for beginners, I cover pairings in this post, after groups, fields and elliptic curves. I give an explanation of what they are and how to operate with them, along with a simple example very famous in cryptography.