Notation question for hash functions Let $H(-)$ be a cryptographic hash function with values in $\{0,1\}^k$.

What do we mean when we say that $H(x) &lt; D$ for some $D\in \mathbb N$? Are we summing the elements of $H(x)$?
$H(x) &lt; D$ likely mean that $D$ is greater than the integer in range $[0,2^k-1]$ represented by the $k$-bit bitstring $H(x)$ in binary, per some convention. If we note the bits of that bitstring $b_0$ for the first/left one, and $b_{k-1}$ for the last/right one:

$\displaystyle\ \ \ D&gt;\sum_{i=0}^{k-1}b_i\,2^{k-1-i}\ $ for big-endian, which thends to be the default convention; or

$\displaystyle\ \ \ D&gt;\sum_{i=0}^{k-1}b_i\,2^k\ \ $ for little-endian.

If $H$ is secure in the random oracle model, and $x$ chosen without knowledge of $H$, then (for either convention) $H(x) &lt; D$ holds with probability $\displaystyle{\max\left({D\over2^k},1\right)}$.