Home

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: 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.

tl;dr: A $t$-out-of-$n$ sharing of $s$ can be reshared as a $t’$-out-of-$n’$. How? Each old player $t’$-out-of-$n’$ reshares their share with the new players. Let $H$ denote an agreed-upon set of $\ge t$ old players who (re)shared correctly. Then, each new player’s $t’$-out-of-$n’$ share of $s$ will be the Lagrange interpolation (w.r.t. $H$) ...

tl;dr: “If you thought before that science is certain, well, that’s just an error on your part.” – Richard Feynman

tl;dr: …because (1) they are only secure when the tree is correctly-computed (e.g., secure with BFT consensus, but insecure in single-server transparency logs), (2) you cannot efficiently insert or delete leaves, and (3) they have worse proof sizes. What does that mean? Never implement one. Stick to Merkle tries (a.k.a., Merkle prefix trees). Or...

tl;dr: Pointcheval-Sanders (PS) signatures[^PS16] are incredibly powerful: (1) they can sign Pedersen commitments directly and (2) they can be re-randomized together with the signed commitment. This enables very simple schemes for proving yourself anonymously. For example, an authority can give you a PS signature on a commitment of your age and ...