You should know that you don't understand enough about Bitcoin to reason about it [+], and before trusting my representations about it, you should know that I am approximately the most skeptical person about it in the entire tech community.
+ This phrasing is rather more robust than I'd prefer, but you're dangerously mistaken about something which many people will attempt to get you to equate with money.
The Bitcoin protocol does not trust owners of large amounts of bitcoins. An emergent behavior of the protocol is that it trusts people with large amounts of hash power over given periods of time. Why not trust every client equally? Because Satoshi believed that IP addresses were really easy to conjure up, and compute farms were really hard to conjure up, so a malicious actor could easily get a majority of the network if you were counting via IP addresses but it would be hard if you required computational proof of work.
This is one of the core engineering decisions in Bitcoin. One of the other ones is, to incentivize people to spend computational power on computations which have no utility the overwhelming majority of the time, periodically they're allowed by the protocol to claim bitcoins which are created from nothing. Every bitcoin in circulation first came into possession by someone who won a lottery with tickets basically bought by the expenditure of hash power.
Response to edit: In a war during which 75% of the world's datacenters are destroyed, the Internet collapses, Bitcoin dies along with many hundreds of millions of people, and cryptocurrency enthusiasts join Beanie Baby collectors in the long line of people who will not find their favorite hobbies treated well in a nuclear winter.
If you're answering purely as a math abstraction, though, the protocol will eventually self-correct by picking a new, lower block difficulty, with the goal being creating a new block approximately every ten minutes. The approximate upper bound on how long it would take to recalibrate if you lost 3/4th of the hashing power is plus or minus eight weeks. (I originally said "an hour", which is clearly in error.) During the interim, Bitcoin would be possible to transact in and mine but it would be slower than previously -- instead of it requiring about an hour to know that a given transaction was safe to rely on, it would require about four hours.
But again: Bitcoin is very much not robust against "the end of the world."