111 lines
2.1 KiB
Python
111 lines
2.1 KiB
Python
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#!/usr/bin/python
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import math
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c = int("2A4C9AA52257B56837369D5DD7019451C0EC04427EB95EB741D0273D55", 16)
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t = int("1398ED7F59A62962D5A47DD0D32B71156DD6AF6B46BEA949976331B8E1", 16)
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n = int("0D8A7A45D9BE42BB3F03F710CF105628E8080F6105224612481908DC721", 16)
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def linear_diophantine_equation(a, b):
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if b > a:
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return linear_diophantine_equation(b, a)
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if b == 0:
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return a, 1, 0
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d, x, y = linear_diophantine_equation(b, a % b)
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return (d, y, x - (a // b) * y)
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def multiplicative_inverse(a, b):
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d, x, y = linear_diophantine_equation(a, b)
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if y < 0:
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y = (b if b > a else a) + y
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return y
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def gcd(a, b):
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d, x, y = linear_diophantine_equation(a, b)
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return d
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# n > t > c
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# m = flag
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def test_solution(m):
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return m**2 % n == c
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# m**2 % n = x**2
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# m**2 + k*n = c
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# m % n = x
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# m - k*n = x
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# m = x + k * n
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# x = int(math.sqrt(c))
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#
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# while not test_solution(x):
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# x += n
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# print(hex(x), hex(((x**2)%n)-c))
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# print(x)
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mult_inverse = multiplicative_inverse(c, n)
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d, x, y = linear_diophantine_equation(mult_inverse, mult_inverse*n)
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print(hex(d + 6*t - 2*c), test_solution(d + 6*t - 2*c))
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# x = math.sqrt(n)
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# print(x)
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#
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# print(test_solution(c * math.sqrt()))
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# print(test_solution(math.floor(math.sqrt(c * n))))
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# c = (m**2) % n
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# c = m*m - k*n
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# 1 = (m**2)/c - (k*n)/c
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# 1 = (m**2)/c - k*(n/c)
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# k = 1
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# test = k * n / c
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# while test != math.floor(test):
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# k += 1
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# test = k * n / c
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#
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# print(k, test)
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# x = m*m
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# c = x % n
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# c = x - k*n
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# c = k*n+x
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# x ~ (48 56 31 38 2d) ^ 2
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# m_guess = int("485631382d616161612d616161612d616161612d616161612d61616161", 16)
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# x_guess = m_guess ** 2
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# k_guess = (c - x_guess) / n
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#
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# i = 0
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# while not test_solution(m_guess):
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# m_guess += 1
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# i += 1
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#
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# print(i, m_guess)
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# print(test_solution(math.sqrt(c + n)))
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# print(math.sqrt(c))
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# c = x**2
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# m**2 % n = x**2
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# m % n = x
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# i = 0
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# solutioni = 0
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# while i < 100:
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# i += 1
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# if test_solution(i):
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# print(i, i**2%n)
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# 4**2 % 13 = 3
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# 9**2 % 13 = 3
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# 17**2 % 13 = 3
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# 22**2 % 13 = 3
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# 30**2 % 13 = 3
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