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Update proof_of_space.md (#220)
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kernel1983 authored Jul 4, 2021
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Expand Up @@ -818,7 +818,7 @@ The problem with the above construction is that the verifier can perform a Hellm

The new idea in the paper is to construct a function $[N] \to [N]$ that can resist such attacks, by making the function hard to compute in the forward direction for a chosen input.

The function that has to be inverted is $f(x_1) = f_2(x_1, x_2)$, where $f_2(x_1, x_2) = H(x_1 || x_2)$, but with the requirement that $f_1(x_1) = f_1(x_2) + 1$, where $f_1(x)$ can be another hash function.
The function that has to be inverted is $f(x_1) = f_2(x_1, x_2)$, where $f_2(x_1, x_2) = H(x_1 || x_2)$, but with the requirement that $f_1(x_1) = f_1(x_2)$, where $f_1(x)$ can be another hash function.
Given a challenge $Chall$, the prover must find $x_1$ and $x_2$.
Since we cannot efficiently compute $f(x_1)$ for any $x_1$ (without storing the $f_1$ table), Hellman attacks can be mitigated.
However, the entire $f$ function table can still be computed in quasilinear time.
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