How to ruin radio communication
Many answers have said that you can't actually develop a technology to stop modern radio communications from being secure. I was one of them at first too, but having thought it over more, I realized that it is very much doable. So lets start off by explaining how technology that will overcome modern radio secrecy works.
How Message/Locational Secrecy is Maintained Today
The question of how to hide radio communications in a warzone was solved decades ago. Ever wonder how an F-22 can be undetectable and still have the full benefits of radar and radio communications? The answer is satellites and directional transmitters (both directional radio and laser are options).
Troops trying to stay hidden send directional communications to a satellite which cant be intercepted because it does not broadcast in all directions, then the satellite does all the actual broadcasting and recon. Yes, everyone knows where every satellite is, but actually destroying something that high up is very challenging. Also, once the satellite receives a message, it knows where it came from, so it can also send directional communications back. So, yes you know the recon satellite is a recon satellite, but there is no tactical information to intercept without getting directly between the satellite and the ground target... which you cant do if you don't know where the ground target is.
Even if you could, it is encrypted. The kind of math behind encryption technology makes decryption technology advance exponentially slower than encryption. So, handwaving that some future tech makes breaking encryption more possible is actually very silly since all foreseeable advances in technology will only harden the relative effectiveness of encryption.
Another common means of communications is point-to-point. This could be wires or direct communication between ground based directional transmitters. By networking together a number of point-to-point connections, you can establish undetectable communications across a theater of operation.
How to Break the Modern Chain of Secrecy
The weak link in satellite communications is the satellite itself. In a properly working military communications satellite, a message is encrypted on the ground, routed through the satellite, and then decrypted at its destination... but the satellite itself could be an agent for a Man-in-the-middle attack. Many military R&D projects these days involve multiple countries working together; so, if two countries are working on a shared satellite network, then it would behoove them to both try to sneak backdoors into the system to make sure that the other countries can't just lock them out.
The way a MitM attack works is you take a communication node between two points and instead of forwarding an encrypted message between the two, you establish separate encrypted connections with each party and decrypt the information from one, read it, then encrypt it again to send it on so that it just looks like end-to-end encryption, but really is not.
So, with both countries having backdoors and compromised encryption chains, when the fighting breaks out, both sides exploit their backdoors to read the other nations' communications. These back doors are built into the satellite's hardware; so, simply locking each other out proves much more impossible than either side expected... so, they are both stuck with insecure satellite networks... at least until they can develop and launch their own satellites, and update all their hardware to use the new networks.
Barring this, there is also the possibility of simply shooting down enemy satellites depriving them of communications all together.
What about point-to-point? This is in some ways even less secure than satellites. The number of options a hacker has when he gains physical access to a network goes up exponentially. Your point-to-point transmitters and wires are on the ground which means they are much easier to tamper with; so, while they may be secure "out-of-the-box", there are only so many good places to put them, especially in mountainous areas. The enemy only needs physical access to one transmitter to modify it with malicious intent. Once they take over 1 relay or tap into 1 line, they are inside your communications network and able to perform not just packet sniffing, but full cyber attacks against the whole network, and physically identify the location of other relays in your network.
How to securely communicate with satellites and point-to-point compromised.
Mission-type Tactics
First of all, every modern military needs a communications blackout plan. So before you even consider the technological part of the question, you should consider the military doctrine aspect. Mission-type tactics is a military doctrine widely used by westernized militaries that puts the job of assigning objectives in the hands of upper leadership, but leaves it to lesser field commanders to actually decide how to achieve those objectives. This means that even when communication becomes limited, that local units can continue to make important tactical choices in real time.
In contrast, militaries with a more authoritarian, centralized leadership model rely much more on constant communication for mission approval and orders.
So, by focusing on a Mission-Type Tactics military doctrine. A unit could receive orders by letter and have no problem figuring out everything they need to do for the next week before the next letter arrives because they are already trained to operate with minimal oversight.
Alternative High Tech Methods
Even though modern militaries makes heavy use of satellite and point-to-point communications, there are also redundant systems in place just in case. Perhaps the most secure redundant system is underground fiber optics. Fiber optic cables are made from materials that can not be detected with metal detectors; so, when you bury them, they are virtually impossible to find; so, the only point of vulnerability are the actual military outposts themselves.
A normal communications network is made of many relay points that automatically switch traffic from one node to the next, but in a setting where networks are being compromised on a large scale, you can limit risk by air gapping communications. This means that each base is connected only to adjacent bases, and it is up to a human operator to receive and forward a message. While this slows down communication, it makes hacking an entire network from one seized base impossible.
Air-gapped fiber optic networks wont be the most efficient form of communications, but it will be way more efficient than sending people by vehicle to deliver messages and is incredibly resilient compared to other methods. So, instead of spending hours or days sending a letter 1000s of miles to communicate a change in orders, you could spend minutes bouncing a communication from station to station delivering it to (or at least near-to) the front-line.
You also need to consider civilian communications networks. Even if you compromise an enemy's military channels does not mean there are not also extensive civilian communications options. Cell phones don't have a very long range. So, the only place to detect cellphone traffic is if you are very close, and even if you are close, you could be in a country with a hundred million civilians communicating over dozens of independently secured apps and just a few thousand total combatants. Isolating civilian traffic would become an intractable problem... in fact what civilians have to say itself could even have military value. Russia learned this the hard way when invading Ukraine. A lot of the reason Ukrainian forces were able to out maneuver Russia in the early parts of the conflict was that civilians with cellphones where reporting Russian troop movements directly to the military. No fancy radar stations or recon teams, just lots of guys with eyes and internet access.
