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tl;dr: Forget univariate. Forget FFTs. Multilinear polynomials are the bomb! $ \def\bin{\{0,1\}} \def\eq{\mathsf{eq}} \def\SC{\mathsf{SumCheck}} \def\MLE#1{\mathsf{MLE}(#1)} \def\i{\boldsymbol{i}} \def\j{\boldsymbol{j}} \def\x{\boldsymbol{x}} \def\X{\boldsymbol{X}} \def\y{\boldsymbol{y}} \def\Y{\boldsymbol{Y}} $

tl;dr: Hyrax is polynomial commitment scheme (PCS) with (1) sublinear commitment-and-proof sizes and (2) sublinear opening-and-verification times. Hyrax is constructed from Pedersen vector commitments and Bulletproofs inner product arguments (IPAs). Hyrax has information-theoretic hiding commitments and honest verifier zero-knowledge (HVZK) PCS ...

tl;dr: KZG + Hyrax = KZH[^KZHB25e]. This name makes me happy: not only it stands on its own but it also coincides with the first three authors’ initials!

tl;dr: Motorcycles are drugs. Alin might buy a motorcycle and risk the few, still-functioning limbs in his body. Someone should convince him not to do this. Update (July 2020): Alin purchased a 2017 Honda Rebel 500. He has never been more happy and frightened at the same time. Even after taking basic, intermediate and advanced riding clinics, ...

tl;dr: A quick note on the most commonly-occuring 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.