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tl;dr: Definition of vector commitment (VC) schemes (e.g., Merkle trees, KZG-based, Pointproofs[^GRWZ20], aSVC[^TABplus20], etc. can all satisfy this definition.)

tl;dr: It’s 2025. Do you know why Schnorr signatures are always better than ECDSA?

tl;dr: Pointcheval-Sanders (PS) is the coolest most versatile signature scheme I know of!

tl;dr: Inspired by a tweet1, we explore whether, given (1) an R1CS and (2) some “powers-of-$\tau$”, we could construct a cryptographic proof that a Groth16 VK was derived from them. This should make it more efficient for folks to ensure that an on-chain VK corresponds to some published ZK circuit code (e.g., circom). Nonetheless, this is not suf...

tl;dr: Everything I wanted to know but was afraid to ask about circom.

tl;dr: Groth16 is one of the most popular general-purpose zkSNARK schemes. Although Groth16 is slower to prove than more recent zkSNARKs, it has the smallest proof size and the fastest verification time. This probably explains why it has seen such wide adoption in the cryptocurrency space. (Recently, WHIR[^ACFY24e] could hope to challenge its ve...

tl;dr: This post describes some useful differentiation tricks when dealing with polynomials in cryptography.

tl;dr: A quadratic arithmetic program (QAP), a Rank-1 Constraint System (R1CS), and an NP relation are equivalent ways of representing a hard problem (or computation) whose solution can be verified in polynomial-time. In particular, R1CS is just a reformulation of QAPs as linear equations and, these days, it is used widely when formalizing compu...