Alin Tomescu - page 10

tl;dr: A zero-knowledge proof (ZKP) system for an NP relation $R$ allows a prover, who has a statement $\mathbf{x}$ and a witness $\mathbf{w}$ to convince a verifier, who only has the statement $\mathbf{x}$, that $R(\mathbf{x}; \mathbf{w}) = 1$. Importantly, the proof leaks nothing about the secret witness $\mathbf{w}$. (e.g., a ZKP can be used...

tl;dr: An NP relation $R(\mathbf{x}; \mathbf{w})$ is a formalization of an algorithm $R$ that verifies a solution $\mathbf{w}$ to a problem $\mathbf{x}$ (in time $\poly(|\mathbf{x}|+|\mathbf{w}|)$. For example, $\mathsf{Sudoku}(\mathbf{x}; \mathbf{w})$ verifies if $\mathbf{w}$ is a valid solution to the Sudoku puzzle $\mathbf{x}$. NP relations a...

tl;dr: We cover a few basic linear algebra concepts: vectors, matrices, matrix-vector products, vector dot products, Haddamard products, etc.

tl;dr: Do you want to sign (committed) field elements without relying on random oracles? Do you want to efficiently prove (in zero-knowledge) relations over your signed messages? BBS+ is here to help you! The BBS+ signature scheme is a transformation[^ASM08e] of the Boneh-Boyen-Shacham (BBS) group signature scheme[^BBS04] into a standalone sig...

This is some of the stuff I (plan to) read and think others could find useful. Blogroll Oded Goldreich’s essays blog.cr.yp.to David Wong’s Cryptologie Dcentralized thoughts Scott Aaronson Michael Nielsen Filippo Valsorda Craig Gidney Jeremy Kun Cryptography and (zero-knowledge) proof systems Cryptography 101, Alfred ...

tl;dr: We spoke about how a blockchain should keep a secret at the Next-Generation Secure Distributed Computing seminar at Schloss Dagstuhl. We sketched an approach based on trusted execution environments (TEEs) that could be practical, yet could still present interesting research challenges.

$ \def\prove{\mathsf{Prove}} \def\ver{\mathsf{Ver}} \def\A{\mathbf{A}} \def\B{\mathbf{B}} \def\bb{\mathbf{b}} $ tl;dr: This is a post-mortem write-up on how I failed to use the Bulletproofs IPA to convince a verifier that a multi-exponentiation $\A^\bb = \prod_i (A_i)^{b_i}$ was done correctly. The problem is that the Bulletproof verifier has t...

tl;dr: Everything I wanted to know, but was afraid to ask about elliptic curves.