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I sent maidsafecoin to a segwit Bitcoin address generated by my Ledger Nano S. My understanding is the coin is safe at the address and the Nano recorded the transaction as a very small amount of btc. I have the bitcoin address. Can I extract the private key from the Nano S that corresponds to the bitcoin address and so move the maidsafe coin?

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The whole point of using a hardware wallet is that private keys can never leave the device, so no, there is no 'extract private key' function on the ledger.

The only way to gain access to individual keys is by using the recovery seed, but doing that is extremely unsafe. The scheme used to derive child keys on a hardware wallet is incompatible with private key export as a single private key leaking could compromise the entire wallet.

Relevant BIP32 section

Note however that the following properties does not exist:

  • Given a parent extended public key (Kpar,cpar) and a child public key (Ki), it is hard to find i.
  • Given a parent extended public key (Kpar,cpar) and a non-hardened child private key (ki), it is hard to find kpar.

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