Hello
I also had this problem when attempting the security update via the App Store on my mid 2010 Macbook Pro. It sent my machine into a kernel panic loop and the only way out of it was to reinstall the OS (El Capitan). I've done that 3 times now - lots of time to get the vacuum cleaner out and do some housework so no time wasted at all. Hah! However, each time I tried to bring the machine back up-to-date, the updates sent everything back to the kernel panic loop. I joined this forum to try to find the answer; this post and another one that I can't now find, helped me out enormously.
I'd like to send a big, big thank you to BobHarris and EauRouge for your answers to alexd0001's question and for getting me thinking about what might have been causing the problem. Your comments on this and the other post got me to the answer I needed.
It turns out that the security software my bank urges its users to use, was fighting against the security update that Apple was trying to upload - you couldn't make this up, eh? I removed the bank's software (which I've been told I shouldn't really need seeing as it's on a Mac but please feel free to correct me if that's wrong!) and Hey Presto! It's all working properly, I've not had to upgrade to High Sierra (which is great as El Cap suits my machine and my requirements perfectly) and I've been able to install the Apple security update without causing another kernel panic loop.
I'm really grateful for the help I've received here. Thank you.