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BBS+ signatures

tl;dr: BBS+ is a transformation[^ASM08e] of the the Boneh-Boyen-Shacham (BBS) group signature scheme[^BBS04] into a standalone signature scheme. This blog post describes BBS+ as well as a recent improvement over it dubbed standalone BBS[^TZ23e]. Why BBS+? The BBS+ and standalone BBS schemes have some really nice properties: Can sign a vect...

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Bulletproofs IPA for multiexp

$ \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...

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Keyless blockchain accounts on Aptos

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...

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What in the Smurf is a silent-setup multiverse unpredictable function?

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...

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How to reshare a secret

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. $H$) ...

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