But we can use this blockchain for our 'signature transactions' and solve Satoshi's problem.
That's the reason why 'signature chain' works.
Do you mean that the "signature chain" can prevent double spending?
Can a "signature chain" prevent a 51% attack? I doubt it?
To create a "signature chain" you must start with a transaction that carries the "first signature" on the network and this transaction needs to be confirmed by the miners, in the event that someone had 51% of the network hash, what prevents him from repeating this transaction and performing the "double spending", Since he will be the owner of the "first signature" and can repeat the signature?
Isn't it possible for this person to create the same signature on the same transaction before this is discovered?