Day 14?

Day 14/decode.py

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

Day 14/power.ps1

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+. "$PSScriptRoot\flag.ps1" #thumbprint 1398ED7F59A62962D5A47DD0D32B71156DD6AF6B46BEA949976331B8E1
+
+if ($PSVersionTable.PSVersion.Major -gt 2)
+{
+    $m = [System.Numerics.BigInteger]::Parse($flag, 'AllowHexSpecifier');
+    $n = [System.Numerics.BigInteger]::Parse("0D8A7A45D9BE42BB3F03F710CF105628E8080F6105224612481908DC721", 'AllowHexSpecifier');
+    $c = [System.Numerics.BigInteger]::ModPow($m, 1+1, $n)
+    write-host "encrypted flag:" $c.ToString("X");
+}