Keyspace and Bitcoin Addresses

[ecdsa123]

If we are talking about space .. first we need understand , there are no 2**256 public key.

there are a lot of less than we think.

Code:

import random
import sys

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f

n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141

E = EllipticCurve(GF(p), [0, 7])

G = E.point( (0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8))   # Base point


for i in range(1,256):
    try:
        
        d=E.lift_x((2**i))
        print("found point",d)
    except:
        print("sorry, there is no point on curve with x=",2**i)

[ymgve2]

There are exactly 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140 public keys, as per the definition of the curve.

There are therefore 2**256 - 0x14551231950b75fc4402da1732fc9bec0 keys, and while the second number seems large, it's insignificantly small compared to the full keyspace.