Digital signature algorithms take a “message” they’re committing to as an enter. Within the case of Bitcoin transactions, this message is a digest of the transaction knowledge particular to every enter known as signed hash. Moreover, a random secret nonce okay is used to create a signature (though some signing implementations decide this nonce deterministically).

So, when signing

• inputs of various transactions with the identical key
• totally different inputs of the identical transaction with the identical key
• the identical enter of the identical transaction a second time

you’ll nonetheless at all times produce a brand new distinctive signature (aside from the final case which can produce precisely the identical signature when carried out with a deterministic nonce).

IIRC HTLCs at all times use a brand new key taken from a hierarchical deterministic chain of keys derived from a basepoint shared with their channel companion on channel opening. This development permits for efficient reconstruction of the related keys from a minimal backup whereas utilizing distinct keys for every output ever added to the channel’s dedication transactions. I believe that at all times utilizing the identical key would nonetheless be safe however a foul privateness leak, however haven’t verified this principle.