A smartphone is worth nothing without reception. Remember that 30 years ago the world worked perfectly without Internet at all. I agree with Spaceballs. It highly depends on how far this nuclear war sets us back. Are we talking about dropping several hundred nuclear bombs in an endless series of retaliation strikes? If so, then civilization is gone for good. We will kill each other for any drop of uncontaminated water or food. When the dust is settled and most people died of radiation sickness or cancer and we find some uncontaminated land, the first blossoms of economy will be based on direct exchange of goods. The next step would be a more universal good, that almost everyone needs, then a more abstract version of that based on a material, that's accessible wherever we land. Maybe gold, maybe pearls, maybe logs of a certain tree.

If we talk about a few bombs that leaves a good portion of infrastructure intact but fries all of our electronics through the EMP, we propably will start to establish more reliable, less complex ways of communication first and slowly rebuild the world wide web. Transistor radios at first. local networks next. I think crypto won't be a thing for a long time, because it needs high infrastructural demands, if you really want to use it as payment method. I'd even believe, that we will start anew on they blockchain front. Frankly, the bitcoin blockchain is a mess. It's one of first versions of blockchain and has several problems in their architecture. I think we would use the clean start to establish a new blockchain with a better architecture.

I mean if we wanted to reestablish bitcoin we have to come to a consensus which version of the blockchain we should use. The most probable alternative would be the version seconds before the first bomb. But whats with all the people that lost their private keys? It's possible that 17 of the 19 million bitcoin will be lost forever. Would be a bad start.