  Device-independent (DI) quantum cryptography aims at providing secure
cryptography with minimal trust in, or characterisation of, the underlying
quantum devices. An essential step in DI protocols is randomness extraction (or
privacy amplification) which requires the honest parties to have a seed of
additional bits with sufficient entropy and statistical independence of any
bits generated during the protocol. In this work we introduce a method for
extraction in DI protocols which does not require a seed and is secure against
computationally unbounded quantum adversary. The key idea is to use the Bell
violation of the raw data, instead of its min-entropy, as the extractor
promise.
