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tl;dr: A quick note on the most commonly-occurring variant of $\Sigma$-protocols, inspired from the Boneh-Shoup textbook!

tl;dr: The sumcheck protocol is an extremely-powerful technique for (zero-knowledge) argument systems. In this short blog post, I will try to summarize it for my own benefit and, hopefully, yours too.

tl;dr: I got nothing, except Karthik Inbasekar’s write-up1. Marlin & Me, by Karthik Inbasekar, 2022 [PDF] ↩

tl;dr: ElGamal public key encrypting $\approx$ Using an ephemeral Diffie-Hellman exchanged key as a one-time pad.

tl;dr: Notes on the [BG12] verifiable shuffle.

tl;dr: Who said you can only sumcheck your multivariate polynomials? $\sum_{i\in[n]} a(\omega^i)b(\omega^i)$ can be proved with two size-$n$ multiexps and 6 FFTs! And verified with a size-4 multipairing (and a bit more?).

tl;dr: Spartan is a versatile zkSNARK framework that requires a sparse MLE PCS to be instantiated. This blog post explains a simple (and likely well-known) compiler to get such a PCS given a weaker dense PCS as input.

tl;dr: What a beautiful construction!