Into the symmetry

tl;dr Mozilla Firefox prior to version 72 suffers from Small Subgroups Key Recovery Attack on DH in the WebCrypto 's API. The Firefox's team fixed the issue r emoving completely support for DH over finite fields (that is not in the WebCrypto standard). If you find this interesting read further below. Premise In this blog post I assume you are already knowledgeable about Diffie-Hellman over finite fields and related attacks. If not I recommend to read any cryptography book that covers public key cryptography. Here is a really cool simple explanation by David Wong : I found a cooler way to explain Diffie-Hellman :D pic.twitter.com/DlPvGwZbto — David Wong (@cryptodavidw) January 4, 2020 If you want more details about Small Subgroups Key Recovery Attack on DH I covered some background in one of my previous post ( OpenSSL Key Recovery Attack on DH small subgroups (CVE-2016-0701) ). There is also an academic pape r where we examine the issue with some more rigors. ...

This continues the post from part 1 . In the previous post we discussed about Verifiable Delay Functions . Here is a quick summary of what we discussed in the first part: We covered the definition of  Verifiable Delay Functions (VDF). We have seen a short history of how this idea slowly developed. We hinted the existence of some constructions. We described some application with an eye on the blockchain World. In this post we will switch gear and we will focus on a particular construction: the isogenies VDF (a construction defined by Luca De Feo , Simon Masson , Christophe Petit and myself ). We try to keep the description as easy as possible simplifying many things, without trying not to worry too much about mathematical rigor (that risks to become mathematical rigor mortis :)), so mathematicians out there I beg your pardon! . Isoge WHAT?   Isogeny based cryptography is last baby in the (cryptography) family .   Below you can see a short history of isog...