PyBitmessage/pyelliptic/arithmetic.py

104 lines
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import hashlib, re
P = 2**256-2**32-2**9-2**8-2**7-2**6-2**4-1
A = 0
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424
G = (Gx,Gy)
def inv(a,n):
lm, hm = 1,0
low, high = a%n,n
while low > 1:
r = high/low
nm, new = hm-lm*r, high-low*r
lm, low, hm, high = nm, new, lm, low
return lm % n
def get_code_string(base):
if base == 2: return '01'
elif base == 10: return '0123456789'
elif base == 16: return "0123456789abcdef"
elif base == 58: return "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"
elif base == 256: return ''.join([chr(x) for x in range(256)])
else: raise ValueError("Invalid base!")
def encode(val,base,minlen=0):
code_string = get_code_string(base)
result = ""
while val > 0:
result = code_string[val % base] + result
val /= base
if len(result) < minlen:
result = code_string[0]*(minlen-len(result))+result
return result
def decode(string,base):
code_string = get_code_string(base)
result = 0
if base == 16: string = string.lower()
while len(string) > 0:
result *= base
result += code_string.find(string[0])
string = string[1:]
return result
def changebase(string,frm,to,minlen=0):
return encode(decode(string,frm),to,minlen)
def base10_add(a,b):
if a == None: return b[0],b[1]
if b == None: return a[0],a[1]
if a[0] == b[0]:
if a[1] == b[1]: return base10_double(a[0],a[1])
else: return None
m = ((b[1]-a[1]) * inv(b[0]-a[0],P)) % P
x = (m*m-a[0]-b[0]) % P
y = (m*(a[0]-x)-a[1]) % P
return (x,y)
def base10_double(a):
if a == None: return None
m = ((3*a[0]*a[0]+A)*inv(2*a[1],P)) % P
x = (m*m-2*a[0]) % P
y = (m*(a[0]-x)-a[1]) % P
return (x,y)
def base10_multiply(a,n):
if n == 0: return G
if n == 1: return a
if (n%2) == 0: return base10_double(base10_multiply(a,n/2))
if (n%2) == 1: return base10_add(base10_double(base10_multiply(a,n/2)),a)
def hex_to_point(h): return (decode(h[2:34],16),decode(h[34:],16))
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def point_to_hex(p): return '04'+encode(p[0],16,64)+encode(p[1],16,64)
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def multiply(privkey,pubkey):
return point_to_hex(base10_multiply(hex_to_point(pubkey),decode(privkey,16)))
def privtopub(privkey):
return point_to_hex(base10_multiply(G,decode(privkey,16)))
def add(p1,p2):
if (len(p1)==32):
return encode(decode(p1,16) + decode(p2,16) % P,16,32)
else:
return point_to_hex(base10_add(hex_to_point(p1),hex_to_point(p2)))
def hash160(string):
intermed = hashlib.sha256(string).digest()
return hashlib.new('ripemd160').update(intermed).digest()
def dbl_sha256(string):
return hashlib.sha256(hashlib.sha256(string).digest()).digest()
def bin_to_b58check(inp):
inp_fmtd = '\x00' + inp
leadingzbytes = len(re.match('^\x00*',inp_fmtd).group(0))
checksum = dbl_sha256(inp_fmtd)[:4]
return '1' * leadingzbytes + changebase(inp_fmtd+checksum,256,58)
def pubkey_to_address(pubkey):
return bin_to_b58check(hash_160(changebase(pubkey,16,256)))