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If I understand well, it is now well documented that all Intel chips should be considered as back doored because of the Intel Management Engine. I guess one should now consider that all chips over a given complexity are possibly back-doored in this way or in hardware. It is also reported that the Russians are switching back to typewriters.

http://www.telegraph.co.uk/news/worldnews/europe/russia/10173645/Kremlin-returns-to-typewriters-to-avoid-computer-leaks.html

http://www.bbc.com/news/world-europe-23282308

However mechanical typewriters can also be bugged, and it is not that convenient for file sharing, steganography of the data on images, etc.

https://www.nsa.gov/about/cryptologic-heritage/historical-figures-publications/publications/assets/files/gunman-project/Learning_From_the_Enemy_The_GUNMAN_Project.pdf

So my question is: would the 'good' technical solution, for writing a text and encrypt it keeping the highest level of certainty that one is not spied on, be to:

  • put together an Arduino microcontroller (simple enough to not be back-doored), 2 SD card readers (one for SD card with text content, the other one for SD card with exclusively encrypted text content), a primitive keyboard, a simple 16 lines LSC screen, and

  • use the Arduino as a primitive word processor + AES encrypter

  • plugging only the encrypted SD card on other machines?

Do you think this would be safe? Do you think one can get a safe system in a simpler way?

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You state that "I guess one should now consider that all chips over a given complexity are possibly back-doored in this way or in hardware" and then ask "what kind of chips can be safe?" The Arduino or Raspberry Pi, although less complex than PC chips, are still much more complex than the room-sized supercomputers of old.

Additionally, you make the assumption that hardware may be backdoored but the OS may not. I think that contradicts the premise of your question: how we keep digital communications from being snooped upon?

I'm going to steal from @Hector above. Based upon the question, I can really only see one possible technical solution: air-gap the devices and only allow specific USB disks between the two communicating devices. No other USB disks would be allowed, and the message disk would only be allowed in the communicating devices. Then, to encrypt that communication, use only a one-time cipher based on something random and then padded with a list of names from the Prague phone book. (czech names would make a frequency distribution crack more difficult due to the way that names are spelled). Also the drive in transit would need to be kept secure in a container that cannot be opened without destroying the USB disk, where only the sender and recipient have keys which vary from day to day.

That trades the security desired with usability, however. The users of that system would find it a huge pain in the Mikta.

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