I have five encryption mods ($n_1$ through $n_5$) with the same encryption exponent ($e$) and the same message encrypted using the five public keys giving $E_1$ through $E_5$ that were not given in a particular order. I am trying to use the Chinese remainder theorem attack (common encryption exponent attack). My question is as follows:

1) How can I match each encrypted message with the public key used to encrypt them? Do I just have to try all possible combinations until I get readable output? Since I have five pairs it would be a lot of permutations to try...

UPDATE: It seems that CRT_list might help me do what I need, but it doesn't fully answer the question. http://doc.sagemath.org/html/en/reference/rings_standard/sage/arith/misc.html#sage.arith.misc.CRT_list


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