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shunyaCTF-2024/crypto/RivestSaltedAdelman/README.md

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+# Rivest Salted Adleman
+
+### Domain: Crypto
+
+### Points: 100
+
+### Solves: 24
+
+## Given information 
+
+```
+"Bob told me original q was eksored with some secret value 1 2 9 or 1 thru 9 something like that.... ughhh I am so confused...."
+```
+
+## Solution 
+
+Since it was mentioned that q was XORed with the number 123456789, so we XORed the salted_q with 123456789 since XORing any number twice gives the same number. Saved the number obtained as q.   
+To find n, we multiplied p with q.   
+Since p,q and e are given, we found d using the formula `e.d ≡ 1 mod (p-1)(q-1)`.   
+Since c,d and n are given, we found m using the formul `m = c^d mod n`.   
+We get the message m which we convert to bytes.   
+
+```
+from sympy import *
+from Crypto.Util.number import * 
+p = 95224848836921243754124073456831190902097637702298493988505946669357481749059
+
+salted_q = 62480590829144807189161429469255353976579455660965599518063804867866301233320
+
+# q = salted_q ^ 123456789
+
+q = 62480590829144807189161429469255353976579455660965599518063804867866211464637
+
+salted_n = 5949704816946842021797594696485093255706996345339732550774644373410311670577880550185915164563052783086742129032939489765553432953432924892778486382904377417840
+
+# n =p*q
+
+n = 5949704816946842021797594696485093255706996345339732550774644373410310233934264553505213393677159246237065515948410918285615690359863993103739392886526583
+
+e = 65537
+
+c = 332390996033761218977578960091058900061139210257883065481008023465866203213646838419152404854307189904898248026722555965488045307811040811040694129009535565921
+
+# phi =(p-1)*(q-1)
+
+# d= inverse(e,phi) 
+
+d = 546700679122539674615333556040606551808406426776261797469595929271661629747336488381383432365916543563803464361628868524035950851824227587881066617058001
+
+# m = pow (c,d,n)
+
+m = 16423049470388721486924294439704034947965
+
+flag = long_to_bytes(m)
+
+print (flag)
+```
+