They generally do open source their crypto systems (at least the algorithms themselves), given that that is practically a requirement for any crypto system to be adopted in a widespread way (no one who is serious about security is going to use home-baked closed-source cryptosystems).

Examples: https://en.wikipedia.org/wiki/Speck_(cipher) and https://en.wikipedia.org/wiki/Simon_%28cipher%29 and https://en.wikipedia.org/wiki/GOST_(block_cipher)

Not too sure about the NSA - I know they subcontract a lot, so may be harder to weed out. GCHQ have some fascinating stuff out there though https://github.com/gchq/CyberChef/blob/master/src/core/opera...