Home

A polynomial $\phi$ of degree $d$ is a vector of $d+1$ coefficients: \begin{align} \phi &= [\phi_0, \phi_1, \phi_2, \dots, \phi_d] \end{align} For example, $\phi = [1, 10, 9]$ is a degree 2 polynomial. Also, $\phi’ = [1, 10, 9, 0, 0, 0]$ is also a degree 2 polynomial, since the zero coefficients at the end do not count. But $\phi’’ = [...

tl;dr: We “authenticate” a polynomial multipoint evaluation using Kate-Zaverucha-Goldberg (KZG) commitments. This gives a new way to precompute $n$ proofs on a degree $t$ polynomial in $\Theta(n\log{t})$ time, rather than $\Theta(nt)$. The key trade-off is that our proofs are logarithmic-sized, rather than constant-sized. Nonetheless, we use ou...

tl;dr: Most people implement threshold BLS naively, using a $O(t^2)$ algorithm to compute Lagrange coefficients. We show how to use a faster $O(t\log^2{t})$-time algorithm for this. This makes aggregating $(t,n)$ BLS threshold signatures much faster, both at small and large scales. The question of scaling threshold signatures came to us at VMw...

This is a re-exposition of a post by Dan Boneh, Ben Fisch, Ariel Gabizon on how to obtain a constant-sized range proof from constant-sized polynomial commitments. This post was moved to Decentralized Thoughts.

This is Ryan Holiday’s “Ego is the enemy” in bullet-point form. These are the ideas I found interesting from the book, without the excellent stories used to back them. For those, you’ll have to buy the book. I changed some of the excerpts from 2nd person to 1st person, so they resonate more. I kept the same table of contents as in the book, exc...

These are my notes from a quick workshop at Stony Brook University given by Professor Michael Bender and Professor Rob Johnson in May 2012. How to make the presentation Prefix competitive If you had one slide, make your presentation. If you had two slides, extend your 1 slide presentation. 1 slide -> 2 slides -> 3 slides. Quick...

This is an updated guide on how to build and install Eucalyptus 3.3.0 on Ubuntu 13.04. I have tested these steps on a freshly installed & updated Ubuntu 13.04 machine on Sunday, July 21st, 2013. There is another guide here for Eucalyptus 3.2 and Ubuntu 12.04. :) Prerequisites A Linux-capable machine with virtualization extensions Spac...

Recently, I’ve been spending my time up in the clouds (i.e. sunt cu capul in nori) messing around with Eucalyptus. Eucalyptus is an open-source cloud platform. In my experience, this means that you can download it from GitHub, compile it and then torture yourself trying to get it to run :) Here, I am presenting a short guide on building, instal...