# local collisions in SHA 0

I have found interesting for me paper about constructing collisions in SHA 0. On page 60 the author determines M variable which is a concatenation of 32-bits vectors $M^{(i)}$, but I can't find any explanation about this

$$\forall i,0\leq i\leq 79,M^{(i)}_{0,k}=0\text{ if }k\neq 1$$ $$\forall i,0\leq i\leq 79,M^{(i)}_{0,k}=m_0^{(i)}$$

$M$ with superscript $(i)$ means a 32-bits vector which refers to $i$-th word W.

What does $M$ with two subscripts $0$ and $k$ mean?

It is very important to make it clear because whole process of getting right mask $M$ is based on the first mask $M_0$. Please help me to understand the author's definition.

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

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