Add 4 reproducible solved examples (ps_and_qs, lost_modulus, a2s, russian_threesome) + examples README

examples/lost_modulus/prob.py

@@ -0,0 +1,42 @@
+from Crypto.Util.number import *
+
+
+class Key:
+    def __init__(self, bits):
+        assert bits >= 512
+        self.p = getPrime(bits)
+        self.q = getPrime(bits)
+        self.n = self.p * self.q
+        self.e = 0x100007
+        self.d = inverse(self.e, (self.p-1)*(self.q-1))
+        self.dmp1 = self.d%(self.p-1)
+        self.dmq1 = self.d%(self.q-1)
+        self.iqmp = inverse(self.q, self.p)
+        self.ipmq = inverse(self.p, self.q)
+
+    def encrypt(self, data):
+        num = bytes_to_long(data)
+        result = pow(num, self.e, self.n)
+        return long_to_bytes(result)
+
+    def decrypt(self, data):
+        num = bytes_to_long(data)
+        v1 = pow(num, self.dmp1, self.p)
+        v2 = pow(num, self.dmq1, self.q)
+        result = (v2*self.p*self.ipmq+v1*self.q*self.iqmp) % self.n
+        return long_to_bytes(result)
+
+    def __str__(self):
+        return "Key([e = {0}, n = {1}, x = {2}, y = {3}])".format(self.e, self.d, self.iqmp, self.ipmq)
+
+def main():
+    key = Key(1024)
+    flag = open('flag').read()
+    encrypt_flag = key.encrypt(flag)
+    assert key.decrypt(encrypt_flag) == flag
+    print key
+    print encrypt_flag.encode('hex')
+
+
+if __name__ == '__main__':
+    main()