Quote from: NytHawk on January 26, 2018, 09:31:00 AM

Considering that (correct me if I am wrong) there are around 160 possible private keys that can map to one single address,

That is NOT correct. Where did you get that number from?

Quote from: NytHawk on January 26, 2018, 09:31:00 AM

my question is, is it possible that a single private key could map to this multi signature address?

Addresses that start with 3 are a P2SH address. This means that you need 2 things to spend the value that is "sent to that address".

1. You need a script that hashes to the value associated with the address

2. You need to supply the necessary data for that script to evaluate successfully.

Note, that there is no requirement for a signature or private key at all unless required by the script that hashes to the value associated with the address.

You have created a multi-sig script and then used the hash value of that script to build the transaction. Therefore, you know of exactly 1 script that definitely hashes to the value needed. If anyone else has that script, then they can use it, however they then need to satisfy the requirements of that script if they want to spend the value. So, if your script requires signatures from more than one private key, then they will need access to more than one private key to use that script.

If they can create a different script that hashes to the same value as your script, then they won't need to satisfy the requirements of your script. Instead they'll need to satisfy the requirements of THEIR script. The good news is that any script that they create has on average a 1 in 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 chance of hashing to the same value as your script. As such, they could spend the entire rest of the existence of the universe creating and hashing scripts, and they still wouldn't have a reasonable chance of accessing your bitcoins.