local collisions in SHA 0
In the referenced paper, $M^{(i)}_{j,k}$ is bit $k$ of the 32-bit $M^{(i)}_j$, with $-5\le i&lt;80$, $j$ the same index as in $m_j$ with $0\le j&lt;6$, and bit index $k$ is with $0\le k&lt;32$.

The question's two statements are thus equivalent to
$$\forall i,0\leq i\leq79,\quad M^{(i)}_0=\begin{cases}
\mathtt{00000000_h}&amp;\text{if }m_0^{(i)}=0\\
\mathtt{00000002_h}&amp;\text{if }m_0^{(i)}=1
\end{cases}$$