https://en.wikipedia.org/wiki/Pershing_II
This was a big upgrade on the original Pershing missile that kept the same launcher but was competitive with the Soviet SS-20 that weighed three times as much because it had an autonomous guidance that could directly impact a target even when the mobile launcher was at an unsurveyed location.
This is not advanced or exotic technology for a missile with the P II's range, you don't need exotic materials (that little dome on the bottom is a radar antenna, not a heat shield) and it can get 25 g acceleration with those little fins that you might not notice if you don't look carefully. Thus it is something third-world countries can field if they want to.
That kind of missile can break unpredictably two or more times on reentry and thus confound anti-missile defenses of all kinds. The Russians had a nuclear-armed ABM system in the Moscow area at that time (and still do) and they found it intimidating.
That kind of nuclear-armed ABM might be able to fire a large number of shots and get lucky, but the kinetic kill systems that we use to protect our naval groups would be helpless against it.
That's why China is developing an anti-ship weapon with similar capabilities; instead of soaking up the inaccuracy of the launch point, the missile can handle the uncertainty of where a ship is going to be when the missile arrives.
With a nuclear warhead that kind of missile could obliterate an aircraft carrier -- but even with conventional warheads it could cause a lot of trouble, this is what a smaller ship looks like when it has been hit by 4 2000 lb conventional bombs
https://en.wikipedia.org/wiki/Joint_Direct_Attack_Munition#/...
That won't sink a carrier but it could stop flight operations for a while and have them steaming back to San Diego.