5

Is it possible for Carol to find Bobs key in $S_{pks}$ This is a decisional Diffie-Hellman problem. We can summary this problem as: "we're given the values $G, aG, abG$, and a series of values $c_1G, c_2G, ... c_nG$, can we recognize $c_iG = bG$" We can reword the problem as "assuming $H = aG$, we're given the values $H, (a^{-1})H, bH$, can ...


3

Lets say I have $g^x \bmod p$ and $g^{xy} \bmod p$. How can I efficiently obtain $g^y \bmod p$? We hope that there is no efficient method (without using knowledge of $x$ or $y$) Here's why: if you can solve that problem, you can solve the (computational) Diffie-Hellman problem; here's how: Suppose that you did have an Oracle that, given $g, g^x, g^{xy}$, ...


2

As X3DH uses elliptic curve Diffie-Hellman, I'll write things in elliptic curve notation thus if we have a curve $E$ with $q$ points and a base point $G$ we might see Alice choose a private key $a\pmod q$ and create a public key $A=aG$. It should be easy to convert to multiplicative notation if you need to. Regular Diffie-Hellman In the regular form of the ...


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