RSA Decipher oracle

RootMe Challenge: Darkness cannot drive out darkness; only light can do that: You have sucessfully intercepted a C text, encrypted with a RSA keypair which you know the (n, e) public component.

Luckily, your victim has made a mistake by using a server that allows you to decrypt any ciphered text with his public key, except for those including a secret that must stay encrypted.

Your job is to handle it in order to decrypt this weird message!

n = 456378902858290907415273676326459758501863587455889046415299414290812776158851091008643992243505529957417209835882169153356466939122622249355759661863573516345589069208441886191855002128064647429111920432377907516007825359999
e = 65537
c = 41662410494900335978865720133929900027297481493143223026704112339997247425350599249812554512606167456298217619549359408254657263874918458518753744624966096201608819511858664268685529336163181156329400702800322067190861310616

1. Calculate the ciphertext

2. Encrypt a message

3. Enter the resulting ciphertext to be decrypted

4. Copy the resulting plaintext and use it to decrypt \(n\)

Resources

• Chosen ciphertext attacks against protocols based on the RSA encryption standard - Daniel Bleichenbacher

• A new and optimal chosen-message attack on RSA-type cryptosystems