80 lines
2.0 KiB
Python
Executable File
80 lines
2.0 KiB
Python
Executable File
#!/usr/bin/env python3
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try:
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from PIL import Image, ImageDraw
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IMG_OUT = True
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except ModuleNotFoundError:
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IMG_OUT = False
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def power(x, y, p):
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res = 1
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x %= p
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while (y > 0):
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if (y & 1):
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res = (res * x) % p
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y = y >> 1
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x = (x * x) % p
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return res
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# Assumption: p is of the form 3*i + 4 where i >= 1
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def sqrtFast(n, p):
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if (p % 4 != 3):
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raise ValueError('Invalid Input')
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# Try "+(n ^ ((p + 1)/4))"
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n = n % p
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x = power(n, (p + 1) // 4, p)
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if ((x * x) % p == n):
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return x
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# Try "-(n ^ ((p + 1)/4))"
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x = p - x
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if ((x * x) % p == n):
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return x
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return None
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def sqrtNormal(n, p):
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n %= p
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for x in range(2, p):
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if ((x * x) % p == n):
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return x
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return None
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def elliptic_curve(a, b, r):
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print(f'generate curve: a={a}, b={b}, r={r}')
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if IMG_OUT:
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image1 = Image.new('RGB', (r, r))
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draw1 = ImageDraw.Draw(image1)
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draw1.rectangle((0, 0, r, r), fill='white')
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image2 = Image.new('RGB', (r, r))
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draw2 = ImageDraw.Draw(image2)
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draw2.rectangle((0, 0, r, r), fill='white')
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sqrtFn = sqrtNormal if (r % 4 != 3) else sqrtFast
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txt = ''
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for x in range(r):
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y2 = (x ** 3 + a * x + b) % r
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u2 = sqrtFn(y2, r) if y2 > 0 else 0
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if u2 is not None:
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z1 = r - 1 - u2
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z2 = r - 1 - (-u2 % r)
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print(x, y2, -y2 % r)
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txt += f'{x} {y2} {-y2 % r}\n'
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if IMG_OUT:
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draw1.rectangle((x, z1, x, z1), fill='black')
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draw1.rectangle((x, z2, x, z2), fill='black')
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draw2.rectangle((x - 2, z1 - 2, x + 2, z1 + 2), fill='black')
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draw2.rectangle((x - 2, z2 - 2, x + 2, z2 + 2), fill='black')
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with open(f'ec-a{a}-b{b}-r{r}.txt', 'w') as f:
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f.write(txt)
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if IMG_OUT:
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print('writing image output')
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image1.save(f'ec-a{a}-b{b}-r{r}-pp.png', 'PNG')
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image2.save(f'ec-a{a}-b{b}-r{r}-lg.png', 'PNG')
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print()
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elliptic_curve(a=149, b=263, r=3299)
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