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Basics of Polynomials for Cryptography

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’’ = [...

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Towards Scalable Verifiable Secret Sharing and Distributed Key Generation

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...

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"Ego is the enemy", by Ryan Holiday

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...

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How to give (and make) a presentation

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...

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