how did military commanders in olden times send instructions across hundreds of miles without concern of forgery or interception?

Why do you assume, they had no such concern? There were seals to ensure authenticity and avoid man in the middle attacks. There were encoded messages, smoke, flags, light and sound signals. Trusted couriers, pigeons, etc ...

I am not an expert on this and it's just my understanding from general history things.

I think wax seals were a big part of it. If you have a ring you can make a bunch of wax seals but it's really hard to make a copy of the ring from a wax seal. Give each general a document with the royal seal on it and the next time they get an order with the royal seal you can compare it with the seal you already have. If you use the wax seal to close the letter so that you need to break the wax to open the letter you can be fairly certain that the one with the ring that wrote it and that nobody else has opened it.

I also think chains of commands is important. King gives letter to messenger Steve. Steve then gives it to Dave and Dave knows who Steve is so he trust the message. Dave then gives it to Rodney and Rodney gives it to a Lord. Each person knows who the person they are getting a message from is so the chain is trusted. Should Ivan kill Dave and try to give a fake message to Rodney they Rodney would just go "where the fuck is dave" and not deliver the message.

They used end-to-end encryption where the sender stuffed the message into one end of a pigeon and the receiver would pull it out of the other end. The opposing forces didn’t have the time to check every single pigeon for intel so it did the trick until some genius decided to standardize putting an “Intel Inside” sticker on the fastest carrier pigeons.

In battle terms, messengers and flags were key. The messenger core often included the children of officers etc. This meant it wasn't a random person delivering the orders, but a trusted person.

Flags etc could also be used for simple transmission. It was often limited to predefined messages, but that was generally enough to send units around.

These 2 methods were why knowing where the commander was in a battle was so important. A big, showy banner could make them an arrow magnet. It also let everyone know where orders were coming from, and where to send reports.

The fog of war was ever present however. Messages could get lost, or misunderstood. The best commanders had highly competent underlings. A sub-commander sending in the reserves, without orders, could win or lose a battle.

As for longer ranges. There were several ways. Chains of trust were the most common. Knights etc would travel regularly. They got to know each other and so could vouch for each other's identity. This is part of where knightly honor comes from. You faked messages and both you and your family would suffer for it. The unique armour designs also helped with identification. It's hard to fake a suit of armour quickly, and taking one by force was difficult.

This also formalised into messenger cores. Various chains of trust were formed to identify imposters. Pomp and ceremony, along with expensive indicators made faking difficult, dangerous and expensive.

Another option was message relay towers. The Romans used timed lights to send messages along walls. Simple messages could be sent long distances without much risk of corruption. Semaphore towers served a similar purpose, with the ability to send complex messages. They were expensive to build and operate however, so tended to be for critical lines of communication only.

Combined with all this was a continuous arms race of message validation Vs forgeries, encryption Vs code breaking. Many cyphers were developed and broken. Things like signet rings were a classic. It's easy to seal a message with one (pressed into hot wax), and relatively hard to fake. Your seal also lived on your finger, so very difficult to steal.

Nobody else has mentioned deliberate obfuscation techniques.

For example, if you're sending field commanders instructions in writing, you brief them in advance that if you use certain codewords, modify certain data. I.e if you use the word "glorious" to describe reinforcement troops, double the number. If you describe them as "experienced" halve the number.

So if the letter does fall into enemy hands, the data will be wrong.

They used messengers, forgery was prevented by use of wax seals or similar, interception is down to the luck and skill of your messengers. Dressing like a civilian helps avoid detection, but they could be executed as spies.

The cipher used by Mary Queen of Scots in the 1500s was just broken this year. It’s a good example of how communications were secured back in the day.

https://www.smithsonianmag.com/history/codebreakers-discoverand-decipherlong-lost-letters-by-mary-queen-of-scots-180981613/

They worried all the time about it; systems weren't perfect.

Interception was usually the bigger issue. Messengers would have orders to destroy their messages if caught, but that didn't always happen. You might even have just a failure to transmit a message; a lot of the theory for modern Internet packet switching came from military communication.

Forgery could happen. This was usually counteracted by knowing the sender's handwriting or applying a seal or stamp to the communication. It wasn't perfect, but it did ok.

Forgery and interception happened all the time. So did just pure confusion and chaos. Here is a lovely example from the legendary Battle of Karánsebes:

To add to other comments:

There are ways of folding envelopes or letter packages that are destructive in opening, so that tampering could be noticed.

The practice is called letter locking, here's some links:

https://en.m.wikipedia.org/wiki/Letterlocking

https://arstechnica.com/science/2021/03/locked-for-300-years-virtual-unfolding-has-now-revealed-this-letters-secrets/

Encryption has been around since Roman times, and probably long before that. Even if not, bear in mind most military leaders then had people from their own lands in their ranks so it would be easy to find a trusted person to deliver the message.

The Two Generals Problem

In addition to other comments, Julius Caesar even has a simple encryption technique, the Caesar cypher, named for him because he regularly used it.

They often didn't. Sure the other responses.said how they did when they did, but realistically communication was too slow to be useful for a lot of messages we would send today. Your general made plans before the battle and then watched helplessly as it happened ,unable to adjust anything in time.

Asymmetric cryptography was a game changer, before that communicating parties had to exchange the secret keys used for encryption which was very risky.

First of all they used curriers. A sometimes risky job, but a fine way to get your message from A to B without having to trust to many links.

Secondly, even though we sometimes think of old times as simple and primitive, they did have ways to either encrypt a message with code language, or have certain secret signs on letters and packages to let the recipient know, that this is not forgery.

Sealed letters were another way to make sure the message wasn’t tampered with or read.

Look at the tom Scott two generals problem video

Was It aliens, coming down from the heavens, filling up at the Pramid of Cheops (it was a powerplant after all) and afterwards help doing chores? Ancient Astronauts Believers say an astounding 'yes'

Carrier pigeons? Idk.