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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 the Boneh-Boyen-Shacham (BBS) group signature scheme[^BBS04] into a standalone...

tl;dr: I was at the Next-Generation Secure Distributed Computing seminar at Schloss Dagstuhl and spoke about how a blockchain should keep a secret.

$ \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: What is a keyless blockchain account? Put simply, “Your blockchain account = Your Google account”. In other words, this keyless approach allows you to derive a blockchain account from any of your existing OpenID Connect (OIDC) account (e.g., Google, Apple), rather than from a traditional secret key or mnemonic. There are no long-term se...

tl;dr: ECDSA is one of the most widely-deployed signature schemes (for better or worse). ECDSA is efficient, offers versatility via its pubkey recovery feature and is widely adopted due to Bitcoin’s success. Its history is fascinating, as is its security analysis. Nonetheless: you should stay away from it, as I argue here.

tl;dr: Signs $m$ as $\sigma = (R, s)$, where $s = r - H(R, m) \cdot \sk$, $R = g^r$ and $r\randget \Zp$. Verifies this signature against $\pk = g^\sk$ as $R \equals g^s \cdot \pk^{H(R, m)}$.

tl;dr: This blog post investigates whether threshold verifiable unpredictable functions (VUFs) can be efficiently instantiated in the silent setup setting, which avoids the need for an interactive, expensive and often complex distributed key generation (DKG) phase. We show that (1) silent setup threshold VUFs are possible from multilinear maps a...

In this post, we describe a strawman threshold signature construction by Baird et al.[^BGJplus23] which produces unique signatures. In their paper, Baird et al. modify this construction into a (non-unique) multiverse threshold signature scheme.