How propagate the error delta in backpropagation in convolutional neural networks (CNN)?
So you are correct that the principle of backpropagation is to do the reverse of the operations. The same is true about the convolutional layer.
The forward pass of the convolutional layer can be expressed by
$x_{i, j}^l = \sum_m \sum_n w_{m,n}^l o_{i+m, j+n}^{l-1} + b_{i, j}^l$.
Where $m$ and $n$ is the shape of the convolutional kernel that you will pass over your input image and $w$ is the associated weight for that kernel. $o$ is the input features and $x$ is the resulting value represented by their respective layers $l-1$ and $l$.
For backpropagation we will want to compute $\frac{\partial x}{\partial w}$.
$\frac{\partial x^l_{i, j}}{\partial w^l_{m', n'}} = \frac{\partial}{\partial w^l_{m', n'}} (\sum_m \sum_n w_{m,n}^l o_{i+m, j+n}^{l-1} + b_{i, j}^l)$.
By expanding the summation we end up observing that the derivative will only be non-zero when $m=m'$ and $n=n'$. We then get
$\frac{\partial x^l_{i, j}}{\partial w^l_{m', n'}} = o^{l-1}_{i+m', j+n'}$.
We can then put this result into the overall error term we have calculated.