I came across this post on Symantec's Blog regarding *most* SIM cards today use the weaker 56-bit DES private key. It can be cracked within a few minutes using rainbow tables.
It says to check with your provider asking if they filter OTA messages on their network, and/or using stronger encryption. Both of my phones use SIM cards.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.