Just as a note but a "rolling code" could be as simple as an XOR and I would wager that the receiver has a stack of forward and reverse codes, probably five in each direction for each key or something similar and will accept any and use that to synchronize the next stack. Could also have a time factor involved. This is how digital access cards with rolling displays and some challenge-response cards work. One of the first things you consider is loss of sync and recovery. (Crypto is fun).

Just my opinion but the transponder/RFID part of the SKREEM should just be a simple, bypassable subroutine. For me just having the right key should be enough.

ps Mercedes started using the SKREEM in the last century.

BTW, just finished rebuilding/refurbishing a key fob that had a broken key. Works fine.