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October 9, 2018 11:41
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Generate Bitcoin address
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require 'digest' | |
# | |
# secp256k1 domain parameters | |
# | |
G = '0479BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8' | |
Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798 | |
Gy = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8 | |
puts "Base point: #{G}" | |
puts "Base point X coordinate: #{Gx.to_i}" | |
puts "Base point Y coordinate: #{Gy.to_i}" | |
puts | |
p = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 - 1 | |
puts "Prime number (dec): #{p}" | |
puts "Prime number (hex): #{p.to_s(16)}" | |
puts | |
n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 | |
puts "Subgroup order: #{n}" | |
h = 1 | |
puts "Cofactor: #{h}" | |
puts | |
# | |
# 0. Private key | |
# | |
k = 0x18e14a7b6a307f426a94f8114701e7c8e774e7f9a47e2c2035db29a206321725 | |
# k = 0b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010 | |
puts "Private key (bin): #{k.to_s(2)}" | |
puts "Private key (dec): #{k}" | |
puts "Private key (hex): #{k.to_s(16)}" | |
puts | |
# | |
# 1. Public key | |
# | |
# TODO: better understanding of multiplicative inverse, point addition, point doubling | |
def extended_euclidean_algorithm(a, b) | |
s, old_s = 0, 1 | |
t, old_t = 1, 0 | |
r, old_r = b, a | |
while r != 0 | |
quotient = old_r / r | |
old_r, r = r, old_r - quotient * r | |
old_s, s = s, old_s - quotient * s | |
old_t, t = t, old_t - quotient * t | |
end | |
[old_r, old_s, old_t] | |
end | |
def inverse(n, p) | |
gcd, x, y = extended_euclidean_algorithm(n, p) | |
(n * x + p * y) % p == gcd || raise('invalid gcd') | |
gcd == 1 || raise('no multiplicative inverse') | |
x % p | |
end | |
def ec_double(px, py, pn) | |
i_2y = inverse(2 * py, pn) | |
slope = (3 * px**2 * i_2y) % pn | |
x = (slope**2 - 2 * px) % pn | |
y = (slope*(px - x) - py) % pn | |
[x, y] | |
end | |
def ec_add(ax, ay, bx, by, pn) | |
return [ax, ay] if bx == 0 && by == 0 | |
return [bx, by] if ax == 0 && ay == 0 | |
return ec_double(ax, ay, pn) if ax == bx && ay == by | |
i_bax = inverse(ax - bx, pn) | |
slope = ((ay - by) * i_bax) % pn | |
x = (slope**2 - ax - bx) % pn | |
y = (slope*(ax - x) - ay) % pn | |
[x, y] | |
end | |
def ec_multiply(m, px, py, pn) | |
nx, ny = px, py | |
qx, qy = 0, 0 | |
while m > 0 | |
qx, qy = ec_add qx, qy, nx, ny, pn if m&1 == 1 | |
nx, ny = ec_double nx, ny, pn | |
m >>= 1 | |
end | |
[qx, qy] | |
end | |
# PDx, PDy = ec_double(Gx, Gy, p) | |
# PAx, PAy = ec_add(Gx, Gy, Px, Py, p) | |
Px, Py = ec_multiply(k, Gx, Gy, p) | |
puts "Px: #{Px.to_s(16)}" | |
puts "Py: #{Py.to_s(16)}" | |
# raise "Not Equal: #{ PAx.to_s(16) } != #{ PMx.to_s(16) }" if PAx != PMx | |
P = "#{Py > 0 ? '02' : '03'}#{Px.to_s(16)}" | |
puts "Public key (P): #{P}" | |
((Px**3 + 7 - Py**2) % p == 0) || raise('ERROR: public key point is not on the curve') | |
puts | |
# | |
# 2. Generating SHA256 | |
# | |
sha256=Digest::SHA256.hexdigest([P].pack('H*')) | |
puts "SHA256: #{sha256}" | |
puts | |
# | |
# 3. Generating RIPEMD160 | |
# | |
ripemd160=Digest::RMD160.hexdigest([sha256].pack('H*')) | |
puts "RIPEMD160: #{ripemd160}" | |
puts | |
# | |
# 4.5.6.7.8. Wrap version byte and checksum | |
# | |
network='00' | |
with_version="#{network}#{ripemd160}" | |
# puts "WITH VERSION: #{with_version}" | |
checksum=Digest::SHA256.hexdigest(Digest::SHA256.digest([with_version].pack('H*')))[0, 8] | |
# puts "CHECKSUM: #{checksum}" | |
wrap_encode="#{with_version}#{checksum}" | |
puts "WRAP ENCODE: #{wrap_encode}" | |
puts | |
# | |
# 9. Bitcoin address | |
# | |
def base58(binary_hash) | |
alphabet = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz' | |
value = binary_hash.unpack('H*')[0].to_i 16 | |
output = '' | |
while value > 0 | |
remainder = value % 58 | |
value /= 58 | |
output += alphabet[remainder] | |
end | |
output += alphabet[0] * binary_hash.bytes.find_index{|b| b != 0} | |
output.reverse | |
end | |
A = base58([wrap_encode].pack('H*')) | |
puts "Bitcoin Address: #{A}" | |
puts |
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