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I have a private client/server application that trying to secure the data transmitted through public network. The encryption/decryption method is private too. Client and server uses DH key exchange to agree a small size (8 bytes) session data key. This 8-byte session key is used to encrypt/decrypt the data.
Since Encrypt/Decrypt method is private (derived from TDES), how secure is the data in public network?

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If by "private client/server" you mean "nobody but me has access to them", what you're doing seem to be overkill. And since your Encryp/Decryp method is private and derived, it may weaken the encryption if not implemented correctly.

This seem to be a classic case for a symmetric key encryption; just generate a 128/256 bit master AES key, and embed it in both binaries. Generate an encryption key+IV on client, and send it to the server with a checksum, encrypted by your master AES key. Then use it for communication. No need for DH.

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