Addressees with publick key Y coordinate = 0 ?

[COBRAS]

Hi

Can someone remember sach addresses ?

Br.

[pooya87]

If in y² = x³ + 7 you set y to 0 then there is no solution to x³ = -7 (mod p) as far as I can tell*. Which means no point on secp256k1 curve can have zero y coordinate.

* x = ModPow(-7, p+2/9, p)

[garlonicon]

Which means no point on secp256k1 curve can have zero y coordinate.

True, but the question is about address. So, you can of course use "020000000000000000000000000000000000000000000000000000000000000000" as your point, that means x=0 and gives 15wJjXvfQzo3SXqoWGbWZmNYND1Si4siqV address, there are even some real Bitcoins on it. In the same way, you can use any invalid public key, outside elliptic curve, and make any address out of it. In the same way you can use uncompressed public key with x=0, y=0, completely outside curve and by hashing "0400000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000" you can reach 16QaFeudRUt8NYy2yzjm3BMvG4xBbAsBFM.

So yes, you can make any address by choosing any point in this way, you can even send coins as P2PK to such point, you can also P2TR to invalid x-value, but it will be unspendable.

[alexeyneu]

all checks on address will be ok without leading 04h