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In the paper "Multiparty Computation Secure Against Continual Memory Leakage" on pg. 1239 the footnote at the bottom points out the difference between $joint$ leakage and $disjoint$ leakage. The authors say the weakly leakage resilient protocol of BGG+11 cannot be directly used because it only applies to $joint$ leakage.

My understanding is the adversary has been made more powerful and is able to perform disjoint leakage (i.e. he can make leakage requests on random modules at any time).

I was wondering if somebody could explain this footnote a bit more clearly. Why does a weakly resilient protocol not apply directly?

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