Stefan,
As a TSA Security Screener in the baggage area, I can offer a little advice:
Assume your case will be opened and the contents removed.
Regardless of the case you choose/make, be sure that it has more capacity than you need. You're going to take great care in stowing your rods, but don't fit them together so tightly/intricately that the screener will be required to assemble your puzzle... he simply doesn't have time to do so.
If your case is roomy enough (that capacity thing again), pad/wrap your rods with cloth (wash towels, t-shirts, underwear, whatever).
If your case locks, either stay with it when it is screened so that you can unlock it (you have the right to do this) and make sure it is locked after being screened ( the Screener must do this for you... you can't touch the bag after screening).
In lieu of a lock I use a sturdy tie-wrap and also tape several to my case and draw an arrow to the lock hasp. The Screener will appreciate the fact that she/he doesn't have to root around the station for a tie-wrap and will have a friendly attitude towards your thoughtfully packaged rods
FWIW, I use a "Rod Safe" made in the good ol' U S of A by B&L Sport Products. It's the "Zoom Lock model 1-396, 3" diameter, 53" - 96" length. It's not too pricey and works great.
Have a nice trip,
Rick