stuff
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anon
parent
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commit
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@ -1,6 +1,7 @@
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from util import Object
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import numpy as np
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# XXX: remove this
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import libnum
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CURVE_LINSPACE_OFFSET = 10
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@ -14,50 +15,63 @@ DEFAULT_CURVES = {
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'secp256k1 (BTC)': (0, 7, 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 - 1),
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}
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# XXX
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def init_arg_getter_righer(f, *args):
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def g(*args):
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return f(args[0], args[1], args[2])
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return g
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def line_slope(x1, y1, x2, y2):
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return (y2 - y1) / (x2 - x1)
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def intersection(x1, y1, x2, y2, x3, y3, x4, y4):
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s1 = line_slope(x1, y1, x2, y2)
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s2 = line_slope(x3, y3, x4, y4)
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if s1 == s2:
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raise Exception("passed lines are paralel")
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c1 = y1 - s1 * x1
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c2 = y3 - s2 * x3
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x = (c2 - c1) / (s1 - s2)
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y = s1 * x + c1
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return x, y
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class EllipticCurve(Object):
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@init_arg_getter_righer
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def __init__(self, a, b):
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self.a = a
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self.b = b
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self._points()
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def _points(self):
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def iterih_squre(x):
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def iterih_square(x):
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return (x**3) + (self.a * x**2) + self.b
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start = -1
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for start in np.linspace(-10, 0, 2000):
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if iterih_squre(start) > 0:
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break
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start = 0
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step = 0.1
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while True:
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if iterih_square(start) < 0: break
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else: start -= step
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self.pp = np.empty((2, CURVE_LINSPACE_NUM))
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self.np = np.empty((2, CURVE_LINSPACE_NUM))
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for i, xi in enumerate(np.linspace(start, start + CURVE_LINSPACE_OFFSET, CURVE_LINSPACE_NUM)):
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t = np.sqrt(iterih_squre(xi))
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t = np.sqrt(iterih_square(xi))
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self.pp[0][i] = xi
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self.pp[1][i] = t
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self.np[0][i] = xi
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self.np[1][i] = -t
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def points(self):
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return np.concatenate((self.pp, self.np), axis=0)
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def add(self, p1, p2):
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p1x, p1y = p1
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p2x, p2y = p2
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s = (p2y - p1y) / (p2x - p1x)
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x = s**2 - p1x - p2x
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y = s * (p1x - x) - p1y
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def _cord_slope(self, x1, y1, x2, y2):
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return (y2 - y1) / (x2 - x1)
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def _tangent_slope(self, x, y):
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return (3 * x**2 + self.a) / (2 * y)
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def _add(self, s, x1, y1, x2, y2):
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x = s**2 - x1 - x2
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y = s * (x1 - x) - y1
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return (x, y)
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def add(self, x1, y1, x2, y2):
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return self._add(self._cord_slope(x1, y1, x2, y2), x1, y1, x2, y2)
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def double(self, x, y):
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return self._add(self._tangent_slope(x, y), x, y, x, y)
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def scalar_multiply(point, n):
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pass
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def yfromx(self, x, is_top = True):
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r = np.sqrt((x**3) + (self.a * x**2) + self.b)
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r = +r if is_top else -r
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return r
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#def yfromx(self, x, is_top = True):
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# r = np.sqrt((x**3) + (self.a * x**2) + self.b)
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# r = +r if is_top else -r
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# return r
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def EllipticCurveOverFiniteField(Object):
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class EllipticCurveOverFiniteField(Object):
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def __init__(self, a, b, mod):
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self.a = a
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self.b = b
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@ -66,13 +80,36 @@ def EllipticCurveOverFiniteField(Object):
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def _points(self):
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self.xs = []
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self.ys = []
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def y_squared(x):
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return (x**a + b) % mod
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for x in range(0, mod):
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if libnum.has_sqrtmod_prime_power(y_squared(x), mod, 1):
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square_roots = libnum.sqrtmod_prime_power(y_squared(x), mod, 1)
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def iterih_square(x):
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return ((x**3) + (self.a * x**2) + self.b) % self.mod
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for x in range(0, self.mod):
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if libnum.has_sqrtmod_prime_power(iterih_square(x), self.mod, 1):
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square_roots = libnum.sqrtmod_prime_power(iterih_square(x), self.mod, 1)
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for sr in square_roots:
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self.ys.append(sr)
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self.xs.append(x)
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def points(self):
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return self.xs, self.ys
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def add(self, x1, y1, x2, y2):
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s = line_slope(x1, y1, x2, y2)
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x = (s**2 - x1 - x2) % self.mod
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y = (s * (x1 - x) - y1) % self.mod
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return (x, y)
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def double(self, x, y):
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return 0, 0
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def scalar_multiply(point, n):
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pass
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def elliptic_curve_factory(is_finite, a, b, mod, curve = None):
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if curve != None:
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a = curve.a
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b = curve.b
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try:
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mod = curve.mod
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except:
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mod = mod
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if is_finite:
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return EllipticCurveOverFiniteField(a, b, mod)
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else:
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return EllipticCurve(a, b)
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@ -2,20 +2,51 @@ from elliptic_curve import *
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plots = []
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def is_too_far_away(x, y):
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return x > 100 or x < -100 or y > 100 or y < -100
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#state.update_points(state.curve.xs[0])
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#state.update_points(state.curve.xs[1], False)
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# XXX this was used for testing displaying points on the curve
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def update_points(x, is_top = True):
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y = state.curve.yfromx(x, is_top)
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if y == y: # False if NaN
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state.points.append((x, y))
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def addition(ax, curve, x1, y1, x2, y2):
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def display_elliptic_curve(ax, curve):
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global plots
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p = curve.add((x1, y1), (x2, y2))
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print((x1, y1), (x2, y2), p)
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plots += ax.plot(*curve.points(), color='red')
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def display_elliptic_curve_over_finite_field(ax, curve):
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global plots
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xs, ys = curve.points()
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plots += [ax.scatter(
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xs,
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ys,
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color='red', s=20, marker='o'
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)]
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def double_elliptic_curve(ax, curve, x, y):
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global plots
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p = curve.double(x, y)
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plots += ax.plot([x], [y], 'o')
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plots += [ax.axline(
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(x, y),
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(p[0], -p[1]),
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linestyle='--'
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)]
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if not is_too_far_away(*p):
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plots += [ax.axline(
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p,
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(p[0], p[1] + 1),
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linestyle='--'
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)]
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plots += ax.plot([p[0]], [p[1]], 'o')
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def double_elliptic_curve_over_finite_field(ax, curve, x, y):
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pass
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def clear():
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global plots
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for i in plots:
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i.remove()
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plots = []
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def addition_elliptic_curve(ax, curve, x1, y1, x2, y2):
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global plots
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p = curve.add(x1, y1, x2, y2)
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plots += [ax.axline(
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(x1, y1),
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(x2, y2),
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@ -23,7 +54,7 @@ def addition(ax, curve, x1, y1, x2, y2):
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)]
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xa = [x1, x2]
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ya = [y1, y2]
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if p[0] < 100 and p[0] > -100 and p[1] < 100 and p[1] > -100:
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if not is_too_far_away(*p):
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xa.append(p[0])
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ya.append(p[1])
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plots += [ax.axline(
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@ -33,23 +64,30 @@ def addition(ax, curve, x1, y1, x2, y2):
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)]
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plots += ax.plot(xa, ya, 'o')
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def clear():
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def addition_elliptic_curve_over_finite_field(ax, curve, x1, y1, x2, y2):
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global plots
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for i in plots:
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i.remove()
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plots = []
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def display_elliptic_curve(ax, curve):
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global plots
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plots += ax.plot(*curve.points(), color='red')
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def display_elliptic_curve_over_finite_field(ax_curve):
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xs, xy = curve.points()
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plots += [ax.scatter(
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[i[0] for i in xs],
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[i[1] for i in xy],
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color='red', s=20, marker='o'
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p = curve.add(x1, y1, x2, y2)
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x_axis_intersection = intersection(x1, y1, x2, y2, 0, 0, 1, 0)
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limit_intersection = intersection(x1, y1, x2, y2, 0, curve.mod-1, 1, curve.mod-1)
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print(x_axis_intersection, limit_intersection)
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plots += [ax.plot(
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(x_axis_intersection[0], limit_intersection[0]),
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(x_axis_intersection[1], limit_intersection[1]),
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linestyle='--'
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)]
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plots += ax.plot([p[0], p[1]], 'x')
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def addition(ax, curve, x1, y1, x2, y2):
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if isinstance(curve, EllipticCurve):
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addition_elliptic_curve(ax, curve, x1, y1, x2, y2)
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elif isinstance(curve, EllipticCurveOverFiniteField):
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addition_elliptic_curve_over_finite_field(ax, curve, x1, y1, x2, y2)
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def double(ax, curve, x, y):
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if isinstance(curve, EllipticCurve):
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double_elliptic_curve(ax, curve, x, y)
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elif isinstance(curve, EllipticCurveOverFiniteField):
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double_elliptic_curve_over_finite_field(ax, curve, x, y)
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def display(ax, curve):
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if isinstance(curve, EllipticCurve):
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37
gui.py
37
gui.py
@ -16,20 +16,21 @@ def display():
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elliptic_curve_display.display(state.ax, state.curve)
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ps = state.curve.points()
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elliptic_curve_display.addition(state.ax, state.curve, ps[0][3], ps[1][3], ps[0][6], ps[1][6])
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elliptic_curve_display.double(state.ax, state.curve, ps[0][6], ps[1][6])
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state.canvas.draw()
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def update_curve(curve=None):
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global state
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if curve != None:
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a, b, mod = curve
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else:
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a = int(state.a_input.get())
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b = int(state.b_input.get())
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mod = int(state.mod_input.get())
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state.a_strvar.set(a)
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state.b_strvar.set(b)
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state.mod_strvar.set(mod)
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state.curve = EllipticCurve(a, b, mod)
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a = int(state.a_input.get())
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b = int(state.b_input.get())
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mod = int(state.mod_input.get())
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state.curve = elliptic_curve_factory(state.is_finite, a, b, mod, curve)
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state.a_strvar.set(state.curve.a)
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state.b_strvar.set(state.curve.b)
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try:
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state.b_strvar.set(state.curve.mod)
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except:
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pass
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def rerender(curve=None):
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if curve != None:
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@ -44,7 +45,7 @@ def init(curve):
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state.points = list()
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tk_init()
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update_curve(DEFAULT_CURVES['Default'])
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state.curve = elliptic_curve_factory(state.is_finite, *DEFAULT_CURVES['Default'])
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tk_fill()
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def tk_init():
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@ -57,12 +58,17 @@ def tk_init():
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state.controls = ttk.Frame(root)
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state.toolbar = NavigationToolbar2Tk(state.canvas, root, pack_toolbar=False)
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state.toolbar.update()
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state.a_strvar = tk.StringVar()
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state.b_strvar = tk.StringVar()
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state.mod_strvar = tk.StringVar()
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state.a_strvar = tk.StringVar(value=str(0))
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state.b_strvar = tk.StringVar(value=str(0))
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state.mod_strvar = tk.StringVar(value=str(0))
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state.is_finite = tk.IntVar(value=0)
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def tk_fill():
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global state
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# Finite field view toggle
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tk.Checkbutton(state.controls, text="Finite field view",
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variable=state.is_finite, command=lambda: rerender(state.curve),
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).pack()
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# Equation -- y^2 = x^3 + a * x^2 + b
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state.curve_equation = ttk.Frame(state.controls)
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equation = [
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@ -85,8 +91,7 @@ def tk_fill():
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("b", "red", state.b_strvar.get(), "b_input"),
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("modulos", "magenta", state.mod_strvar.get(), "mod_input"),
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]
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f = ttk.Frame(state.controls)
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f.pack()
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(f := ttk.Frame(state.controls)).pack()
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for i, d in enumerate([{k:v for k,v in zip(entry_keys, t)} for t in entry_values]):
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ttk.Label(f, text=d["name"], foreground=d["color"]).grid(row=i, column=0)
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w = state[d["label_name"]] = tk.Scale(f, from_=0, to=100, orient=tk.HORIZONTAL, length=200)
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