🌲 $\Sigma$-protocols
tl;dr: A quick note on the most commonly-occurring variant of $\Sigma$-protocols, inspired from the Boneh-Shoup textbook!
⭐️ The multivariate sumcheck protocol
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.
🌲 ElGamal encryption
tl;dr: ElGamal public key encrypting $\approx$ Using an ephemeral Diffie-Hellman exchanged key as a one-time pad.
🌲 Univariate sumcheck
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?).
🌲 Cinder: A simple-but-not-so-efficient dense-to-sparse MLE compiler
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.
110 post articles, 14 pages.