Set in the distant future, a notorious terrorist group infamously known as "51 Crew" is planning an ambush near the orbit of Thebe, Jovian moon. In the next few hours an armoured shuttle holding a prisoner which is being escorted by 4 fighters will flyby between Europa and Thebe according to their reliable intel, so they hope to retrieve the prisoner before the shuttle had the chance to slingshot away to Mars where the security is tight. Assuming the shuttle and 4 fighters are using block chain technology for their force shield, so each spaceship had their own unique frequency that is not shared among themselves. There is no way for the terrorist to break through the force shield using firepower alone, brute force method is too time consuming and guess work isn't their style either. The working principle of block chain force shield is this: each vessel had a force field generator which requires 1 unique keycode to operate. To allow their own energy based attacks to go through their own force shield but not any other requires a clever network so that's where block chain technology comes in. Time is running out, is there any way for the terrorist group to compromise the block chain force shield and retrieve the prisoner? No FTL and ET.
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Sounds as if the force shields are not blockchain technology by themselves. They simply require some sort of setting that can be represented by a number. Knowing this setting renders the force shield vulnerable.
You write that the setting must be known by systems on each ship, so that outgoing fire can pass the own force shield. That alone is no reason to encrypt the setting, simply transmit it on a secure, air gapped network.
One could imagine that the setting must also be known for sensors and communications, since laser cannon, lidar, and laser communications are just a difference in signal strength. That would mean the other ships in the squadron need the settings as well. Still no need for blockchain technology, simply use an one-time pad that was exchanged at base.
It sounds as if you fell prey to hype driven development. There is no reason why your force shields need blockchain technology.
One possible solution: The owners of the ship don't quite trust their crews, so they installed overrides on their shield. These overrides are signed using public/private key pairs and the integrity of the public keys is assured via blockchain.
The attack would be an attempt to insert fraudulent override public keys into the system so that the matching private key can be used to deactivate the force shield. This is no different from an attack on any other blockchain infrastructure, e.g. in finance.
If firepower and brute force can't work, only underhanded tactics can get you through.
You either have a physical spy on one of the ships transmitting the codes or a viral spy transmitting the codes from inside the ship's computer.
You actually want a weak spot in the distributed shielding technology.
You already have one: the ships need to be able to communicate. One-time-pad encryption guarantees that you can neither eavesdrop nor forge communications, no matter your technology.
But if you can prevent the ships from exchanging their shield configurations by jamming, or just by shooting sticky space-tar balls at lidar ports, then each shield gets locked in its current configuration and the network falls out of sync. At that point, you might happen to know that the settings are actually cyclic (assume there aren't all that many stable shield frequency configurations after all), so if you can also keep the others off your hide for long enough, you can overpower the one ship by brute force.
Duplicate the frequency-hopping of the first shot they fire at you and continue bombarding the ship with that and random attempts. After a while, unable to coordinate a "unused" schema with its siblings, the target ship will settle once again on the schema it was using when it first fired - and at that point, the "cloned" shots will get through.