In this talk, I will briefly introduce Quantinuum and the quantum computers we develop. I will then present our recent advances in device-independent (DI) quantum cryptography, in which devices are treated as untrusted black boxes. Specifically, I will discuss two new protocols: the first generates DI randomness from a quantum computational advantage — and was demonstrated for the first time on our 56-qubits quantum computer H2; the second amplifies weak randomness using Bell inequality violations. Along the way, I will also address some of the key challenges faced when implementing quantum cryptography protocols in the real-world. The talk is a mix of foundations and pragmatism.