I am given 5 different encryption modulus, $N$, each ranging from 78 to 88 numbers long. Then for the encryption exponent, each has the same which is 5. Then I am given 5 different encrypted messages, $E$, which also ranges from 76 to 88 numbers long. I am trying to decrypt the message without having to discover the private key.
One way is to use the Chinese Remainder Theorem where we follow the procedure as follows: $x=E_i \mod R_i$ for $i=1,2,3,4,5$. So for $x$, I took all the combination for i and tried to decrypt it by taking the 5-th root of the solution I get for all the $x^\prime$s. However, this is not really working for me as for every solution I get for $x$, it is not possible to take the 5-th root without having decimal fraction.
Anyone who is familiar with the procedure I am taking about, could you tell me what I am doing wrong and possibly help me through this? Thanks in advance. The method I am using by the way is known as the common encryption exponent.