# Really Secure Algorithm (Crypto 324 points)
![](ReallySecureAlgorithm.png)
Similar to [Reverse Search Algorithm](../ReallySecureAlgorithm) Challenge, we are given the public key and the ciphertext.
```n = 263267198123727104271550205341958556303174876064032565857792727663848160746900434003334094378461840454433227578735680279553650400052510227283214433685655389241738968354222022240447121539162931116186488081274412377377863765060659624492965287622808692749117314129201849562443565726131685574812838404826685772784018356022327187718875291322282817197153362298286311745185044256353269081114504160345675620425507611498834298188117790948858958927324322729589237022927318641658527526339949064156992164883005731437748282518738478979873117409239854040895815331355928887403604759009882738848259473325879750260720986636810762489517585226347851473734040531823667025962249586099400648241100437388872231055432689235806576775408121773865595903729724074502829922897576209606754695074134609e = 65537c = 63730750663034420186054203696069279764587723426304400672168802689236894414173435574483861036285304923175308990970626739416195244195549995430401827434818046984872271300851807150225874311165602381589988405416304964847452307525883351225541615576599793984531868515708574409281711313769662949003103013799762173274319885217020434609677019589956037159254692138098542595148862209162217974360672409463898048108702225525424962923062427384889851578644031591358064552906800570492514371562100724091169894418230725012261656940082835040737854122792213175137748786146901908965502442703781479786905292956846018910885453170712237452652785768243138215686333746130607279614237568018186440315574405008206846139370637386144872550749882260458201528561992116159466686768832642982965722508678847```
Lets try FactorDB.
![](FactorDB.png)
It turns out the given public exponent is a square of a prime.
Just because we found the primes, we cannot directly decrypt the ciphertext using normal RSA because in normal RSA, the primes are distinct. But over here, the primes are equal. So the value of phi(n) (Eulers totient function) would be p\*(p-1) instead of (p-1)\*(q-1).
Using that knowledge, we can decrypt the ciphertext.
```vagrant@ubuntu-xenial:~$ pythonPython 2.7.12 (default, Nov 12 2018, 14:36:49)[GCC 5.4.0 20160609] on linux2Type "help", "copyright", "credits" or "license" for more information.>>> import gmpy>>> import libnum>>> n = 263267198123727104271550205341958556303174876064032565857792727663848160746900434003334094378461840454433227578735680279553650400052510227283214433685655389241738968354222022240447121539162931116186488081274412377377863765060659624492965287622808692749117314129201849562443565726131685574812838404826685772784018356022327187718875291322282817197153362298286311745185044256353269081114504160345675620425507611498834298188117790948858958927324322729589237022927318641658527526339949064156992164883005731437748282518738478979873117409239854040895815331355928887403604759009882738848259473325879750260720986636810762489517585226347851473734040531823667025962249586099400648241100437388872231055432689235806576775408121773865595903729724074502829922897576209606754695074134609>>> e = 65537>>> c = 63730750663034420186054203696069279764587723426304400672168802689236894414173435574483861036285304923175308990970626739416195244195549995430401827434818046984872271300851807150225874311165602381589988405416304964847452307525883351225541615576599793984531868515708574409281711313769662949003103013799762173274319885217020434609677019589956037159254692138098542595148862209162217974360672409463898048108702225525424962923062427384889851578644031591358064552906800570492514371562100724091169894418230725012261656940082835040737854122792213175137748786146901908965502442703781479786905292956846018910885453170712237452652785768243138215686333746130607279614237568018186440315574405008206846139370637386144872550749882260458201528561992116159466686768832642982965722508678847>>> p = 16225510719965861964299051658340559066224635411075742500953901749924501886090804067406052688894869028683583501052917637552385089084807531319036985272636554557876754514524927502408114799014949174520357440885167280739363628642463479075654764698947461583766215118582826142179234382923872619079721726020446020581078274482268162477580369246821166693123724514271177264591824616458410293414647>>> assert n == p * p>>> phi = p * (p-1)>>> d= int(gmpy.invert(e,phi))>>> libnum.n2s(pow(c,d,n))'hsctf{square_number_time}'```