From 000e7195289f5166d959601cce428aceee0c9f3d Mon Sep 17 00:00:00 2001
From: Maxime Vorwerk <Maxime Vorwerk>
Date: Wed, 31 Jul 2024 17:34:09 +0200
Subject: [PATCH] triple-secure

---
 triple_secure/encrypt.py     | 29 ++++++++++++++++++++++++
 triple_secure/public-key.txt |  5 +++++
 triple_secure/sol.py         | 43 ++++++++++++++++++++++++++++++++++++
 3 files changed, 77 insertions(+)
 create mode 100755 triple_secure/encrypt.py
 create mode 100755 triple_secure/public-key.txt
 create mode 100755 triple_secure/sol.py

diff --git a/triple_secure/encrypt.py b/triple_secure/encrypt.py
new file mode 100755
index 0000000..f46c7c0
--- /dev/null
+++ b/triple_secure/encrypt.py
@@ -0,0 +1,29 @@
+#!python3
+
+from Crypto.Util.number import getPrime, bytes_to_long
+
+with open('flag.txt', 'rb') as f:
+    flag = f.read()
+
+p = getPrime(1024)
+q = getPrime(1024)
+r = getPrime(1024)
+
+n1 = p * q
+n2 = p * r
+n3 = q * r
+
+moduli = [n1, n2, n3]
+
+e = 65537
+c = bytes_to_long(flag)
+
+for n in moduli:
+    c = pow(c, e, n)
+
+with open('public-key.txt', 'w') as f:
+    f.write(f'n1: {n1}\n')
+    f.write(f'n2: {n2}\n')
+    f.write(f'n3: {n3}\n')
+    f.write(f'e: {e}\n')
+    f.write(f'c: {c}\n')
diff --git a/triple_secure/public-key.txt b/triple_secure/public-key.txt
new file mode 100755
index 0000000..05b5602
--- /dev/null
+++ b/triple_secure/public-key.txt
@@ -0,0 +1,5 @@
+n1: 15192492059814175574941055248891268822162533520576381643453916855435310880285336743521199057138647926712835561752909538944229702432795423884081992987060760867003375755338557996965825324749221386675061886921763747311599846248565297387814717840084998677273427776535730840343260681623323972936404815862969684384733188827100528542007213405382537935243645704237369770300643318878176739181891072725262069278646319502747718264711249767568106460533935904219027313131270918072460753061248221785076571054217566164086518459844527639082962818865640864990672033657423448004651989761933295878220596871163544315057550871764431562609
+n2: 15896482259608901559307142941940447232781986632502572991096358742354276347180855512281737388865155342941898447990281534875563129451327818848218781669275420292448483501384399236235069545630630803245125324540747189305877026874280373084005881976783826855683894679886076284892158862128016644725623200756074647449586448311069649515124968073653962156220351541159266665209363921681260367806445996085898841723209546021525012849575330252109081102034217511126192041193752164593519033112893785698509908066978411804133407757110693612926897693360335062446358344787945536573595254027237186626524339635916646549827668224103778645691
+n3: 16866741024290909515057727275216398505732182398866918550484373905882517578053919415558082579015872872951000794941027637288054371559194213756955947899010737036612882434425333227722062177363502202508368233645194979635011153509966453453939567651558628538264913958577698775210185802686516291658717434986786180150155217870273053289491069438118831268852205061142773994943387097417127660301519478434586738321776681183207796708047183864564628638795241493797850819727510884955449295504241048877759144706319821139891894102191791380663609673212846473456961724455481378829090944739778647230176360232323776623751623188480059886131
+e: 65537
+c: 5527557130549486626868355638343164556636640645975070563878791684872084568660950949839392805902757480207470630636669246237037694811318758082850684387745430679902248681495009593699928689084754915870981630249821819243308794164014262751330197659053593094226287631278905866187610594268602850237495796773397013150811502709453828013939726304717253858072813654392558403246468440154864433527550991691477685788311857169847773031859714215539719699781912119479668386111728900692806809163838659848295346731226661208367992168348253106720454566346143578242135426677554444162371330348888185625323879290902076363791018691228620744490
diff --git a/triple_secure/sol.py b/triple_secure/sol.py
new file mode 100755
index 0000000..b2b05d1
--- /dev/null
+++ b/triple_secure/sol.py
@@ -0,0 +1,43 @@
+#!python3
+from sage.all import *
+import pwn
+
+pwn.log.info("reading file")
+with open("public-key.txt", 'r') as f:
+    lines = f.readlines()
+    n1 = Integer(lines[0][4:].strip())
+    n2 = Integer(lines[1][4:].strip())
+    n3 = Integer(lines[2][4:].strip())
+    e = Integer(lines[3][3:].strip())
+    c = Integer(lines[4][3:].strip())
+
+pwn.log.info("calculating p, q, r")
+p = gcd(n1, n2)
+q = gcd(n1, n3)
+r = gcd(n2, n3)
+assert p*q == n1
+assert p*r == n2
+assert q*r == n3
+pwn.success("p: {:x}".format(p))
+pwn.success("q: {:x}".format(q))
+pwn.success("r: {:x}".format(r))
+
+pwn.log.info("calculating d1, d2, d3")
+_p = p-1
+_q = q-1
+_r = r-1
+d1 = pow(e, -1, _p*_q).lift()
+d2 = pow(e, -1, _p*_r).lift()
+d3 = pow(e, -1, _q*_r).lift()
+pwn.log.success("d1: {:x}".format(d1))
+pwn.log.success("d2: {:x}".format(d2))
+pwn.log.success("d3: {:x}".format(d3))
+
+pwn.log.info("decrypting message...")
+m2 = pow(c, d3, n3).lift()
+m1 = pow(m2, d2, n2).lift()
+m = pow(m1, d1, n1).lift()
+pwn.log.info("decrypted message!")
+m_literal = pwn.pack(int(m), 'all', 'big', False)
+pwn.log.success("flag: {}".format(m_literal.decode()))
+