How to re-secure a multisignature wallet if private key is stolen

Question

Here are two attack scenarios on bitcoin private keys:

1) Assume that, BitCorp has just noticed that a Mallory has just compromised one of their servers holding their Bitcoin Private keys. Luckily, they are using a 2-out-3 multi-signature wallet, so Mallory has learnt only one of the 3 sets of keys. The other two sets are on different servers that Mallory cannot access. How do that re-secure their wallet and effectively revoke the information that Mallory has learned?

2) If BitCorp uses 2-out-,2 instead of 2-out-3 wallet, what steps can they take 'in advance' so that they can recover, even in the event of one of their servers getting broken into(and Mallory not just learning but also potentially 'deleting' the key material on that server)?

Answer 1

How do that re-secure their wallet and effectively revoke the information that Mallory has learned?

They would have to generate new keys and send the Bitcoin to the multisig address that uses those new keys. If Mallory has/had access to one wallet, she could record any and all keys in that wallet. Thus all keys in that wallet must be considered compromised and never used again. Any Bitcoin associated with those keys should be moved to a newly generated wallet that is not compromised.

2) If BitCorp uses 2-out-,2 instead of 2-out-3 wallet, what steps can they take 'in advance' so that they can recover, even in the event of one of their servers getting broken into(and Mallory not just learning but also potentially 'deleting' the key material on that server)?

They can create pre-signed timelocked transactions that send the coins to another address that they control where those private keys are stored on separate servers. In the event that Mallory compromises and deletes the private key for one key in the 2-of-2, that transaction can be broadcast after the timelock and the coins moved to a new address where the private keys exist.