Add Twin Primes.

Author: ytoku

Twin Primes/solver/solve.py

@@ -0,0 +1,28 @@
+from Crypto.Util.number import *
+import Crypto.PublicKey.RSA as RSA
+
+with open("key1", "r") as f:
+    n1 = long(f.readline())
+    e1 = long(f.readline())
+with open("key2", "r") as f:
+    n2 = long(f.readline())
+    e2 = long(f.readline())
+with open("encrypted", "r") as f:
+    c = long(f.readline())
+
+# {(p+2)(q+2) - pq - 4}/2 = p+q
+s = (n2 - n1 - 4)/2
+
+# phi(pq) = pq - (p+q) + 1
+phi1 = n1 - s + 1
+d1 = inverse(e1, phi1)
+
+# phi((p+2)(q+2)) = pq + (p+q) + 1
+phi2 = n1 + s + 1
+d2 = inverse(e2, phi2)
+
+rsa1 = RSA.construct((n1, e1, d1))
+rsa2 = RSA.construct((n2, e2, d2))
+
+m = long_to_bytes(rsa1.decrypt(rsa2.decrypt(c)))
+print m[:m.find("\0")]

Twin Primes/workspace/encrypt.py

@@ -0,0 +1,46 @@
+from Crypto.Util.number import *
+import Crypto.PublicKey.RSA as RSA
+import os
+
+N = 1024
+
+def getTwinPrime(N):
+    while True:
+        p = getPrime(N)
+        if isPrime(p+2):
+            return p
+
+def genkey(N = 1024):
+    p = getTwinPrime(N)
+    q = getTwinPrime(N)
+    n1 = p*q
+    n2 = (p+2)*(q+2)
+    e = long(65537)
+    d1 = inverse(e, (p-1)*(q-1))
+    d2 = inverse(e, (p+1)*(q+1))
+    key1 = RSA.construct((n1, e, d1))
+    key2 = RSA.construct((n2, e, d2))
+    if n1 < n2:
+        return (key1, key2)
+    else:
+        return (key2, key1)
+
+rsa1, rsa2 = genkey(N)
+
+with open("flag", "r") as f:
+    flag = f.read()
+padded_flag = flag + "\0" + os.urandom(N/8 - 1 - len(flag))
+
+c = bytes_to_long(padded_flag)
+c = rsa1.encrypt(c, 0)[0]
+c = rsa2.encrypt(c, 0)[0]
+
+with open("key1", "w") as f:
+    f.write("%d\n" % rsa1.n)
+    f.write("%d\n" % rsa1.e)
+with open("key2", "w") as f:
+    f.write("%d\n" % rsa2.n)
+    f.write("%d\n" % rsa2.e)
+
+with open("encrypted", "w") as f:
+    f.write("%d\n" % c)

Twin Primes/workspace/encrypted

@@ -0,0 +1 @@
+7991219189591014572196623817385737879027208108469800802629706564258508626010674513875496029177290575819650366802730803283761137036255380767766538866086463895539973594615882321974738140931689333873106124459849322556754579010062541988138211176574621668101228531769828358289973150393343109948611583609219420213530834364837438730411379305046156670015024547263019932288989808228091601206948741304222197779808592738075111024678982273856922586615415238555211148847427589678238745186253649783665607928382002868111278077054871294837923189536714235044041993541158402943372188779797996711792610439969105993917373651847337638929

Twin Primes/workspace/flag

@@ -0,0 +1 @@
+TWCTF{3102628d7059fa267365f8c37a0e56cf7e0797ef}

Twin Primes/workspace/key1

@@ -0,0 +1,2 @@
+19402643768027967294480695361037227649637514561280461352708420192197328993512710852087871986349184383442031544945263966477446685587168025154775060178782897097993949800845903218890975275725416699258462920097986424936088541112790958875211336188249107280753661467619511079649070248659536282267267928669265252935184448638997877593781930103866416949585686541509642494048554242004100863315220430074997145531929128200885758274037875349539018669336263469803277281048657198114844413236754680549874472753528866434686048799833381542018876362229842605213500869709361657000044182573308825550237999139442040422107931857506897810951
+65537

Twin Primes/workspace/key2

@@ -0,0 +1,2 @@
+19402643768027967294480695361037227649637514561280461352708420192197328993512710852087871986349184383442031544945263966477446685587168025154775060178782897097993949800845903218890975275725416699258462920097986424936088541112790958875211336188249107280753661467619511079649070248659536282267267928669265252935757418867172314593546678104100129027339256068940987412816779744339994971665109555680401467324487397541852486805770300895063315083965445098467966738905392320963293379345531703349669197397492241574949069875012089172754014231783160960425531160246267389657034543342990940680603153790486530477470655757947009682859
+65537