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I am nearly new in Code-based cryptography and I am trying to understand the soft Stern attack in [GJMS17] which the authors used to break the soft McEliece cryptosystem [BSC16]. The description of attack in the paper is not clear and I couldn't even find any other resources to figure out the details. My questions are as follows:

1- In Step 1 (1a) of the algorithm, the third condition on the column permutation is that $$ \Pi_{i=1,2,...,\frac{k+l}{2}} p_i \approx \Pi_{\frac{k+l}{2}+1,...,(k+l)} p_i $$

Why this is necessary?

2- In Step (1b), a transformation is used to ensure that the reliability value for each variable in the information set is positive. The reason for doing this, is also unclear for me.

Can anyone give some hint?

Thanks in advance.

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    $\begingroup$ You need to describe what you don't understand so we can see your technical skills. I mean the papers already try to explain the attack, so otherwise you might end up with another description you don't understand (if we somebody takes the time to answer at all). PS I don't know anything about this myself. $\endgroup$ – Maarten Bodewes May 30 '18 at 23:00

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