# Alex Kampa

## Fast Consensus in Weakly Byzantine Asynchronous Environments

We explore conditions for achieving binary consensus in a single communication step when conditions are favourable. With leader-based protocols and known block producers this is possible with only a slight weakening of fault tolerance assumptions.

Posted 2023-05-29 by Alex Kampa ‐ **7 min read**

## Simple Soundness Proofs

Soundness proofs tend to be quite long and technical. We describe a general method to significantly simplify such proofs if some specific conditions are met.

Posted 2022-10-14 by Alex Kampa ‐ **8 min read**

## Weil reciprocity on the projective line

What is this lead??

Posted 2022-10-07 by Alex Kampa ‐ **11 min read**

## The Bellare-Micali Oblivious Transfer

Oblivious transfer (OT) is a cryptographical primitive that is fundamental for secure multiparty computation. We give a brief introduction to the Bellare-Micali OT protocol, which is particularly simple and elegant.

Posted 2022-05-03 by Alex Kampa ‐ **4 min read**

## Lagrange bases in subgroups of $F_p^*$

Our first Maths Seminar note is about Lagrange bases in subgroups of $F_p^*$ which happen to have a simple and explicit formula. Numerous examples as well as detailed proofs of the main results are provied. We note that these particular Langrange bases have been used in the construction of the well-known PLONK zk scheme.

Posted 2022-05-02 by Alex Kampa ‐ **3 min read**