"with this new base-point, Eve now has a new private key d’ that corresponds to the original public key Q, i.e Q = d×G but also Q = d’×G’ = d’×Q/d’=Q. "
Specifically, G' = Q and d' = 1 works
via @tqbf @CasCremershttps://twitter.com/tqbf/status/1217518138885115906?s=20 …
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published a follow up story shedding light on additional elements that enabled the attackhttps://twitter.com/TalBeerySec/status/1219368533425041409?s=20 …
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Also added the degenerate case ( Q=G' and d'=1) example to the original story.
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My read is that Microsoft failed to do much internal auditing of their own crypto implementations. Should they not have been expected to have discovered this on their own?
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hindsight is 20/20
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For a more basic intro, here’s the blog post that introduced the billiards analogy:https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/ …
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I don’t understand how the billiards analogy, or really any discussion of the intuition behind stuff like chord-tangent, is helpful. It’s fundamentally arbitrary. What people need to grok is the equations, which are simple.
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The irony of this is I just started reading about ECC yesterday from a very beginner perspective. Of course a vulnerability would come up
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I remember asking my math teacher “what do we need this for?..”. I now know the answer.
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