Verify the discrete log of ECDSA is in range Is it possible to verify the discrete log in elliptic curve is within range without uncovering it? I need to verify that $x$ is within $1$, $2^{64}$ for $xG=P$.
If you give an attacker $G$ and $P := xG$ with $0&lt;x&lt;2^{64}$ then she can calculate a table with $2^{32}$ entries $yG$ for $0\le y&lt;2^{32}$. Finding for any $0\le z&lt;2^{32}$ the value $P-(z\cdot 2^{32}\cdot G)$ in the table yields $x = y + z\cdot 2^{32}$. Space complexity is $2^{32}$ entries and time complexity $\le\log_2(2^{32})\cdot 2^{32}$.

That's why user679128 uses a blinding scalar $b$.