Is there a way to sign a transaction with BTC or any Altcoin without a computer using only pen and paper?

Question

Was wondering if this is possible to do. Lets say Satoshi Nakamoto ended up prison in a foreign country and he was only able to communicate with the outside world by writing letters using only a pen and paper and being able to send it anywhere in the world. How can he sign a Bitcoin/Altcoin transaction using only pen and paper when he has memorized the following:

1. A brain wallet address.
2. Private Key

Now he would have to create a transaction and then sign it. And for him to broadcast the transaction, he would send it to someone while keeping his coins safe aswell. How can this be done using only pencil and paper?

Answer 1

He cannot for a bunch of reasons:

1. He has no idea what the unspent transaction hashes are (not memorized).
2. He does not have a good way to know where he's sending the coins.
3. In order to actually sign the transaction, Satoshi would need to do ECC math on the SECP256K1 curve, which he hasn't memorized.

Supposing that he's given an unsigned transaction to sign and he somehow has memorized the parameters of the SECP256K1 curve, it would be possible, but it's likely to take him a very long time to sign a single transaction. Point doubling alone is 14 operations of 256 bit numbers using Jacobian coordinates. For signing anything, you usually need to double the generator point 256 times.

Basically, he can if given all these numbers, but it's likely not (A) secure since he'll leave have the paper around which has evidence of his private key which he needs in order to sign and (B) efficient in any sense of the word since it's very likely he'll make mistakes and a single mistake will render the signature invalid.