I'm fairly new to BLE and am exploring the security of advertising packets. I was hoping to find some recommendations for resources/general advice on how should learn/implement lightweight encryptions for advertising packets. The data I would work with isn't highly sensitive and after looking into it I'm leaning towards using an ECB and two TI Launchpads to develop with.
For your own private project it might be suitable to use symmetric encryption such as AES. You would need one key on all devices to en- and decrypt your messages.
Depending on your choice of language there are small libraries like tiny-AES availible. Larger collection of cryptographic tools like mbedtls or cryptopp exist but might be overkill for your purpose.
Also take a look at the tools provided by TI, there might be some libraries included in your SDK.