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@@ -3,8 +3,10 @@
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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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+t = int("1398ED7F59A62962D5A47DD0D32B71156DD6AF6B46BEA949976331B8E1", 16)
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+
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+# print(len(hex(t)[2:])*4)
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def linear_diophantine_equation(a, b):
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if b > a:
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@@ -26,13 +28,101 @@ 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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+def test_solution(m):
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+ return (m**2) % n == c
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+
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+def is_square_num(n):
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+ if n <= 0:
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+ return False
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+ return math.sqrt(n)**2 == n
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+
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+def is_int(n):
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+ return int(n) == n
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+
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+# m*m - k*n = c
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+# (m*m)/c - (k*n)/c = 1 k' = k * c
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+# m * m * c^-1 - k' * n = 1
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+
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+# c = m*m - k*n
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+# c = 1*x - k*n mit x = m^2
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+
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+# c = gcd(m, n)
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+
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+d, x, y = linear_diophantine_equation(n, c)
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+print(d, x, y)
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+
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+for i in range(-10, 10):
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+ print(i, test_solution(y + i * t))
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+ # h = hex(y)[2:]
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+ # print(''.join([chr(int(h[i:i+2], 16)) for i in range(len(h))]))
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+
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+# print(y * c + x * n)
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+
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+# y1 * c + x1 * n = 1
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+# y2 * m*m + x2 * n = 1
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+
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+# y2 * m*m + x2 * n = y1 * c + x1 * n
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+# y2 * m*m + (x2-x1)*n = y1 * c
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+# -y1*c + (x2-x1)*n = y2*m*m
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+
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+lcm = c * n
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+while not is_square_num(lcm):
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+ lcm += n
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+
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+print(hex(lcm))
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+print(is_square_num(lcm))
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+
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+# tmp = -1 * y * c - x * n
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+#
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+# solution = tmp + n*n
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+# while not is_square_num(solution) and not test_solution(math.sqrt(solution)):
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+# solution += n
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+#
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+# if is_square_num(solution):
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+# print(len(hex(math.sqrt(solution))[2:]), hex(int(math.sqrt(solution))))
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+#
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+
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+#
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+# print(is_square_num(x))
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+# print(test_solution(x))
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+# # print(hex(d))
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+
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+# ggT(m², n) = ggT(c, n)
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+
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+# print(gcd(c,n))
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+
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+# gcd(m**2, n) = 1
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+#
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+# 1 = x*m**2 + y*n
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+# 1 = x*m**2*c + y*n
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+#
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+# x1*m**2 + y1*n = x2*m**2*c + y2*n
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+# 0 = m**2*x2*c-x1*m**2 + (y1-y2)*n
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+#
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+# gcd(m**2*c, n) = gcd(m**2, n)
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+#
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+# print(gcd(c, n))
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+
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+# m = int("c20cd4b471c96cc2eaab1d1c6e33494219679ae97e48506e311ddbba35", 16)
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+# print(m**2 % n - c)
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+# print(test_solution(m))
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+
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+# mult_inverse = multiplicative_inverse(c, n)
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+#
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+# d, x, y = linear_diophantine_equation(mult_inverse, n)
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+# print(d,x,y)
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+#
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+# print(mult_inverse*x - y*n)
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+#
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+# print(is_square_num(x))
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+# print(is_square_num(y))
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+
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+# print(is_square_num(c))
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+
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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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-
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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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@@ -45,11 +135,10 @@ def test_solution(m):
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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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-
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-mult_inverse = multiplicative_inverse(c, n)
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-
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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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+#
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+#
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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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