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## I used the following program to benchmark ECDSA multiply vs. ECDSA
## multiply-then-add.
##
## Originally from http://bitcoin.stackexchange.com/a/25039
##
## Sample output (where I get my 2% figure from.)
## =======================================================================
## 7.90899729849
## 8.05856181495
## pubkey 0x50863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352L 0x2cd470243453a299fa9e77237716103abc11a1df38855ed6f2ee187e9c582ba6L
## =======================================================================
import timeit
import random
class CurveFp( object ):
def __init__( self, p, a, b ):
self.__p = p
self.__a = a
self.__b = b
def p( self ):
return self.__p
def a( self ):
return self.__a
def b( self ):
return self.__b
def contains_point( self, x, y ):
return ( y * y - ( x * x * x + self.__a * x + self.__b ) ) % self.__p == 0
class Point( object ):
def __init__( self, curve, x, y, order = None ):
self.__curve = curve
self.__x = x
self.__y = y
self.__order = order
if self.__curve: assert self.__curve.contains_point( x, y )
if order: assert self * order == INFINITY
def __add__( self, other ):
if other == INFINITY: return self
if self == INFINITY: return other
assert self.__curve == other.__curve
if self.__x == other.__x:
if ( self.__y + other.__y ) % self.__curve.p() == 0:
return INFINITY
else:
return self.double()
p = self.__curve.p()
l = ( ( other.__y - self.__y ) * \
inverse_mod( other.__x - self.__x, p ) ) % p
x3 = ( l * l - self.__x - other.__x ) % p
y3 = ( l * ( self.__x - x3 ) - self.__y ) % p
return Point( self.__curve, x3, y3 )
def __mul__( self, other ):
def leftmost_bit( x ):
assert x > 0
result = 1L
while result <= x: result = 2 * result
return result / 2
e = other
if self.__order: e = e % self.__order
if e == 0: return INFINITY
if self == INFINITY: return INFINITY
assert e > 0
e3 = 3 * e
negative_self = Point( self.__curve, self.__x, -self.__y, self.__order )
i = leftmost_bit( e3 ) / 2
result = self
while i > 1:
result = result.double()
if ( e3 & i ) != 0 and ( e & i ) == 0: result = result + self
if ( e3 & i ) == 0 and ( e & i ) != 0: result = result + negative_self
i = i / 2
return result
def __rmul__( self, other ):
return self * other
def __str__( self ):
if self == INFINITY: return "infinity"
return "(%d,%d)" % ( self.__x, self.__y )
def double( self ):
if self == INFINITY:
return INFINITY
p = self.__curve.p()
a = self.__curve.a()
l = ( ( 3 * self.__x * self.__x + a ) * \
inverse_mod( 2 * self.__y, p ) ) % p
x3 = ( l * l - 2 * self.__x ) % p
y3 = ( l * ( self.__x - x3 ) - self.__y ) % p
return Point( self.__curve, x3, y3 )
def x( self ):
return self.__x
def y( self ):
return self.__y
def curve( self ):
return self.__curve
def order( self ):
return self.__order
INFINITY = Point( None, None, None )
def inverse_mod( a, m ):
if a < 0 or m <= a: a = a % m
c, d = a, m
uc, vc, ud, vd = 1, 0, 0, 1
while c != 0:
q, c, d = divmod( d, c ) + ( c, )
uc, vc, ud, vd = ud - q*uc, vd - q*vc, uc, vc
assert d == 1
if ud > 0: return ud
else: return ud + m
# secp256k1
_p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2FL
_r = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141L
_b = 0x0000000000000000000000000000000000000000000000000000000000000007L
_a = 0x0000000000000000000000000000000000000000000000000000000000000000L
_Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798L
_Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L
class Public_key( object ):
def __init__( self, generator, point ):
self.curve = generator.curve()
self.generator = generator
self.point = point
n = generator.order()
if not n:
raise RuntimeError, "Generator point must have order."
if not n * point == INFINITY:
raise RuntimeError, "Generator point order is bad."
if point.x() < 0 or n <= point.x() or point.y() < 0 or n <= point.y():
raise RuntimeError, "Generator point has x or y out of range."
curve_256 = CurveFp( _p, _a, _b )
generator_256 = Point( curve_256, _Gx, _Gy, _r )
g = generator_256
if __name__ == "__main__":
print '======================================================================='
### set privkey
# wiki
#secret = 0xE9873D79C6D87DC0FB6A5778633389F4453213303DA61F20BD67FC233AA33262L
# question
secret = 0x18E14A7B6A307F426A94F8114701E7C8E774E7F9A47E2C2035DB29A206321725L
rand = random.randint(0, 2**256)
### print privkey
#print 'secret', hex(secret)
### generate pubkey
pubkey = Public_key( g, g * secret )
import __builtin__
__builtin__.__dict__.update(locals())
print timeit.timeit('pubkey.point * rand', number = 100)
print timeit.timeit('pubkey.point + rand * g', number = 100)
### print pubkey
print 'pubkey', hex(pubkey.point.x()), hex(pubkey.point.y())
print '======================================================================='
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