Crypto Update

Co-Authored-By: David Lim <[email protected]>

README.md

@@ -35,6 +35,26 @@ f6a7bea70e44d0ae8f7990f327b7be537e28cf81f3c5df400677c3f8294ed9ec flagchecker
 ```"/root/.cargo/registry/src/github.com-{id}/reqwest"``` gives us a clue about [a library of higher level HTTP client](https://crates.io/crates/reqwest)
 * There are links not only to Rust packages, but also to particular files in those packages.
 
+## Cryptography - RSA Variations
+### Setup 
+Installing Sage
+```
+git clone https://github.com/sagemath/sage.git
+cd sage
+make configure
+./configure
+make
+./sage
+```
+
+Installing Python Libraries
+```
+pip3 install pycryptodome
+```
+
+Troubleshooting
+[Sagemath Installation in DebianOS](https://pikaroot.github.io/blogs/2023-02-06-Sagemath_Installation_without_git_clone_repo)
+
 ## Boot2Root
 ### Setup
 ```

ez-crypto/ez-answer.py

@@ -0,0 +1,24 @@
+#!/usr/bin/env python3
+from Crypto.Util.number import long_to_bytes
+from math import gcd
+
+a = 1870969079253383528901020811919583012674817901777029440472598207624075857424597551104772657070
+b = 2800712810085008927480330812056676117466496566710583328698036063700356794222073134503996127684
+z1 = 1471692015636458855512725282253417591312312305484809984316224137970424905307644060778134345670
+z2 = 792449287882501111272245107538509962076645267685366076350352640742939177817296346333204609371
+s = 31337
+
+f1 = z1 - (a * s + b)
+f2 = z2 - (a * (a * s + b) + b)
+p = gcd(f1, f2)
+print(long_to_bytes(int(p)).decode('latin-1'))
+print(p)
+
+N = 4892859209552999323872659687370348379127745643113821262786525515571537182220986612456469239342928177158573027631641823744589146302682629015019207630171301051593095288921587679376772619467
+e = 65537
+ct = 539412014186375973839103813384645095457567346931432414765860827711741737113352253186058334245660603139758935545076579254418244151719401216900449931898980356125612701132273350239082121055
+q = N // p
+assert N == p * q
+d = pow(e, -1, (p-1)*(q-1))
+m = pow(ct, d, N)
+print(long_to_bytes(m))

ez-crypto/ez-output.txt

@@ -0,0 +1,4 @@
+a = 1870969079253383528901020811919583012674817901777029440472598207624075857424597551104772657070
+b = 2800712810085008927480330812056676117466496566710583328698036063700356794222073134503996127684
+f(31337) = 1471692015636458855512725282253417591312312305484809984316224137970424905307644060778134345670
+f(f(31337)) = 792449287882501111272245107538509962076645267685366076350352640742939177817296346333204609371

ez-crypto/ez.py

@@ -0,0 +1,21 @@
+#!/usr/bin/env python3
+from Crypto.Util.number import bytes_to_long, isPrime
+from sympy import *
+from secrets import randbelow
+
+p = nextprime(bytes_to_long(open("msg.txt", "rb").read()))
+
+a = randbelow(p)
+b = randbelow(p)
+
+def f(s):
+ return (a * s + b) % p
+
+print("a = ", a)
+print("b = ", b)
+print("f(31337) = ", f(31337))
+print("f(f(31337)) = ", f(f(31337)))
+
+N = 4892859209552999323872659687370348379127745643113821262786525515571537182220986612456469239342928177158573027631641823744589146302682629015019207630171301051593095288921587679376772619467
+e = 65537
+ct = 539412014186375973839103813384645095457567346931432414765860827711741737113352253186058334245660603139758935545076579254418244151719401216900449931898980356125612701132273350239082121055

ez-crypto/msg.txt

@@ -0,0 +1 @@
+y0u_d0n3_th3_LCG_p4rt_n0w_RSA_c4n_d0n3_

hard-crypto/hard.py

@@ -0,0 +1,19 @@
+#!/usr/bin/env python3
+from Crypto.Util.number import bytes_to_long
+from sympy import *
+from flag import flag
+
+2*c**5 - a**3 + b*c = 47769864706750161581152919266942014884728504309791272300873440765010405681123224050402253883248571746202060439521835359010439155922618613520747411963822349374260144229698759495359592287331083229572369186844312169397998958687629858407857496154424105344376591742814310010312178029414792153520127354594349356721
+a**4 + b**5 + a*b*c = 89701863794494741579279495149280970802005356650985500935516314994149482802770873012891936617235883383779949043375656934782512958529863426837860653654512392603575042842591799236152988759047643602681210429449595866940656449163014827637584123867198437888098961323599436457342203222948370386342070941174587735051
+b**6 + 2*c**5 + c*b = 47769864706750161581152919266942014884728504309791272300873440765010405681123224050402253883248571746202060439521835359010439155922618613609786612391835856376321085593999733543104760294208916442207908167085574197779179315081994735796390000652436258333943257231020011932605906567086908226693333446521506911058
+
+p = nextprime(a**2 + b**2 + c**2)
+q = nextprime(c**2 + b**3 - b*a*c)
+
+n, e = p*q, 65537
+ct = pow(bytes_to_long(flag), e, n)
+print(f'e: {e}')
+print(f'ct: {ct}')
+
+# e: 65537
+# ct: 4316046906387448694144731583157234766331600819923556808382864614844417971639257794673147161731085742779102934848976456829034944708038808598529507690690451513032765586224752163703954497290838332996612354963795612924889454878868394201322418550671489921060228998345872552588042424260966646662860606264792921680555291338063183367842347

medium-crypto/medium-output.txt

@@ -0,0 +1,15 @@
+# medium.png
+Keep this for tomorrow session.
+n:935630460868988262869902212660181832282331648376251
+11831868785021731849937816047251456242519147772494568
+902491239896968507
+p:115627821762881213688249172714598910374461629460339
+76247489177
+q:809174164664013321352242310374654264478223045966119
+3152834291
+
+# output.png
+(n, e, enc)
+9356304608689882628699022126601818322823316483762518686918002882530118318687850217318499378160472514562425191477724945682522667885125161902491239896968507
+65537
+4687209496413444146495130493217522601571018523545866226865359451376720404640132741523654964453050620508388190793827659151414526611259223984961674830223215