Valid private keys on curve25519 Given that valid private keys on curve25519 must be less than the order of the curve which is (as I understand) already smaller than 2^256, AND a valid key must be clamped to be divisible by 8 and have its high bit set, what is the actual 2^X number of valid private keys approx?
The private keys are integers $x$ with $2^{254} \leq x &lt; 2^{255}$ and $x \equiv 0 \pmod 8$, or just $x \in 2^{254} + 8\{0,1,2,\dots,2^{251} - 1\}$, so there are exactly $2^{254}/8 = 2^{251}$ of them.