Here, for us, are the nut grafs:
In early 2011, Nohl’s team started toying with the OTA protocol and noticed that when they used it to send commands to several SIM cards, some would refuse the command due to an incorrect cryptographic signature, while a few of those would also put a cryptographic signature on this error message.
With that signature and using a well known cryptographic method called rainbow tables, Nohl was able to crack the encryption key on the SIM card in about one minute. Carriers use this key to remotely program a SIM, and it is unique to each card.
This is a little vague and I don't understand the OTA protocol like, at all, but what it sounds like is that there is a case in some implementations of SIM OTA where (a) errors for improperly signed messages are noisy, (b) those errors include some of the plaintext of the improperly signed message, and (c) the error message itself has a signature that is intended to be valid only for the error.
Possible next steps: (i) you can table-solve for the signature (presumably this is a MAC, not a signature) for your intended message due to the way plaintext hits the error message, or (ii) you can table-solve for the plaintext of a previously unknown ciphertext by taking that ciphertext, flipping a bit to invalidate the signature, and collecting the error signature.