Please explain how does this formula $(aG + bG) = (a + b) G$ work in ECDSA?
$a$ and $b$ are different private keys
Suppose
$a = 3$
$b = 4$
then the public key is $Q = aG$ and $W = bG$ (secp256k1)
Q = F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9
W = E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13
Now we take the formula $(a + b)G$
$(3 + 4)G$
$7g$
$c = 7$
public key $P = cG$
P = 5CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC
Now take the formula $(aG + bG)$
$(Q + W)$
And the amount of public keys $(Q + W)$ will be
DDC465F353664403A152988A8BA8662FC6EEFEEEE3076EF93B2A2732D56EC2CB
Why it turns out:
DDC465F353664403A152988A8BA8662FC6EEFEEEE3076EF93B2A2732D56EC2CB
Why is the answer of this sum not this value:
5CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC