**Cryptographie 200 - Poor RSA**

Énoncé :
<code>
This time Fady decided to go for modern cryptography implementations, He is fascinated with choosing his own prime numbers, so he picked up RSA once more. Yet he was unlucky again!
</code>

A notre disposition nous avons :

- Un message chiffré 
<code>
Ni45iH4UnXSttNuf0Oy80+G5J7tm8sBJuDNN7qfTIdEKJow4siF2cpSbP/qIWDjSi+w=
</code>

- Une clé publique

Résolution :

Récupération des infos de la clé publique :

<code>openssl rsa -in key.pub -pubin -text -modulus > info_key</code>

<code>
Public-Key: (399 bit)
Modulus:
    52:a9:9e:24:9e:e7:cf:3c:0c:bf:96:3a:00:96:61:
    77:2b:c9:cd:f6:e1:e3:fb:fc:6e:44:a0:7a:5e:0f:
    89:44:57:a9:f8:1c:3a:e1:32:ac:56:83:d3:5b:28:
    ba:5c:32:42:43
Exponent: 65537 (0x10001)
Modulus=52A99E249EE7CF3C0CBF963A009661772BC9CDF6E1E3FBFC6E44A07A5E0F894457A9F81C3AE132AC5683D35B28BA5C324243
writing RSA key
-----BEGIN PUBLIC KEY-----
ME0wDQYJKoZIhvcNAQEBBQADPAAwOQIyUqmeJJ7nzzwMv5Y6AJZhdyvJzfbh4/v8
bkSgel4PiURXqfgcOuEyrFaD01soulwyQkMCAwEAAQ==
-----END PUBLIC KEY-----
</code>

Il faut maintenant convertir le modulo de l'hexadécimal à l'int.

On utilise le site : [[http://www.mobilefish.com/services/big_number/big_number.php]]

On factorise sur factor-db :
<code>
http://factordb.com/index.php?query=833810193564967701912362955539789451139872863794534923259743419423089229206473091408403560311191545764221310666338878019
</code>

On obtient les deux facteurs premiers.

Du coup on a :

modulo=833810193564967701912362955539789451139872863794534923259743419423089229206473091408403560311191545764221310666338878019

exponent=65537

p=863653476616376575308866344984576466644942572246900013156919

q=965445304326998194798282228842484732438457170595999523426901

On va recréer notre clé privé avec le code get_priv_key.c (voir article RSA) :

On compile le code
<code>
gcc -o get_priv_key get_priv_key.c -lssl -lcrypto
</code>

On créer la clé privé :
<code>
./get_priv_key 863653476616376575308866344984576466644942572246900013156919 965445304326998194798282228842484732438457170595999523426901 65537 > priv.key
</code>

On déchiffre le fichier :
<code>
openssl rsautl -decrypt -inkey priv.key -in <(base64 -d flag.b64 )

ALEXCTF{SMALL_PRIMES_ARE_BAD}
</code>