Thank you all for kind comments.
It's really interesting we have similar nature. Yes, some say that there is nothing to see/love/impress from in desert. I absolutely love desert. First, desert is not crowded. Second I love desert landscapes, it's nature, animals. It's something unique and is really wild. Third, desert is relatively close to where I live. I would love to hike through Rockies or whatever really mount landscape, but we haven't it. So I explore our desert which is big enough for several years of constant hiking.
>> For these places, do you need a gov wilderness permit or just drive and go ?
Well, most of Negev desert is closed military zone. That said, on weekends (Fri-Sat) you can go there without any permission, but in all other weekdays (Sunday thru Thursday) you MUST arrange your route with IDF if you don't want to be a moving target for our tanks :D
In addition it is prohibited to move there except along marked routes. Unfortunately there are lots of travellers who harm desert nature, leaving trash, drawing on rocks, making fires ... I truly hate these people. Carried out from routes several bags of others waste. I teach my kids to do so as well.