Hi

I am trying to understand this article. Can someone explain to me how the ECDSA adaptor signing is work?

From the article:

1.
ECDSA adaptor signing
s' = (H(m) + R t p)r^-1

As I understand this is standard formula where x = t p - is a private key for the signature s'. So public key is P = t p G

2.
Decryption ECDSA adaptor signature:
s = s' t^-1 =  (H(m) + R t p)(rt)^-1

I can't understand this. Because it follows that:
s = s' t^-1 =  (H(m) + R t p)(rt)^-1 = (H(m) t^-1 + R p)r^-1

But this is not standart formula for ECDSA signature ((
I should be
s = (H(m) + R p)r^-1

I don't think the article is wrong. Most likely I'm missing something. Can anyone help with understanding these formulas?