Find encryption/auth algorithm name

I'm looking for an expert in cryptography to find the right encryption algorithm from an existing device. We're designing an electronic board to talk with another device. We have almost 90% of the communication done, but there is an initial authorization talk with the device where we cannot be sure the type of encryption or key-exchange algorithm. We're looking for a cryptography expert to tell us the algorithm used on that encryption/key-exchange, the keys found and a detailed procedure on how we can get those keys. The communication procedure is: - We have device A (the machine with the algorithm) and device B (our board in the end) - Device A reads data from device B such description, Id, etc - Device A sends 64 bytes (different each time it is initialized) - Device B sends back 256 bytes (different each time as they seems to be correlated to previous point) - Device A sends back 256 bytes again That's what we are looking forward to discover. We will be able to successfully test if you are succeed because Device A then use the exchanged key to send another command (later on) and Device B should answer back with the correct encrypted value. That's the end of the project. The programmer/engineer for this project should let us know how to get the keys telling us exactly what we should program / get / fool device A in order to get the keys and then use that for program our device B correctly as we know the full other communication messages. We have about of 100+ valid full authentications from the real device A/device B connection. We will provide them. We suspect it is a key-exchange algorithm such Diffie-Hellman or RSA. We know it can be fooled, so we are looking the expert to tell us how. We will pay in full once the awarded engineer provides us a working example based on our captures of the messages. Please write 'caramel' word in your description so we know you read it all correctly and understand. No copy/paste bids will be considered. We will pay up to 1000 USD. Thank you!