Dear Editor,

we note that in essence, referee #2 takes a strong view that we need to present a complete proof of the randomness extraction scheme, and was not convinced by the result that the random numbers extracted from our scheme pass a number of test suites.

As we still believe that the randomness extraction scheme is a significant simplification over existing extraction schemes with more complex matrices, and therefore a newsworthy contribution to the readership of Applied Physics Letters, we try to address this concern now explicitly by providing the requested proof in our revised version, and reduced the explanation of the parallelized implementation of the algorithm to make space for it.

In essence, we show that the extraction mechanism can be written as a Toeplitz matrix multiplication, give the explicit matrix (new equation 9) and make the connection to the Krawzyck proof for its use for hashing (new reference index 42) explicit. We also made the analogy of randomness extraction and privacy amplification more explicit. We really believe that this should settle the request for an explicit proof that the extraction mechanism we use is an adequate randomness extractor.

The fundamental criticism of referee 2 seems partly based on the statement of the Vazirani/Santha paper about the impossibility of deterministic extractors. However, this is not a very practical statement, as any of lack of knowledge about all deterministic (in the sense of non-quantum origin) variables in the system would make it impossible to predict the output sequence (assuming one perhaps drops the first few bits of the random bit stream). This is not different from any of the many other, much more complicated hashing schemes that have been used for randomness extraction.

As we had to rewrite the equations from where it is obvious that we work with a linear feedback shift register-type arrangement into a more complex form, we added the new figure 5 to make the idea still accessible for less mathematically inclined readers. Consequently, the old figure 5 became now the new figure 6.

Contrary to referee 2, we do believe that the title of the work is not misleading, as it points to the physical origin of the random numbers (of which we don't claim any priority in this work), but make them really practical by the use of a simple randomness extractor.

We also don't agree with the comment of the referee that abundance of computational power in modern electronic systems in form of FPGAs makes our work not a newsworthy contribution. While of course it does not matter if the extraction is implemented directly in hardware, in a CPLD or an FPGA does not matter at all, but it does matter a lot how much resources (in terms of silicon floor space or power consumption) this process absorbs. At the time we implemented this work, we used a CPLD for it because it underlines the low complexity. Obviously one would implement it on whatever logic is available in a system, but low resource usage is always an advantage.

We also tried to compact the introduction and the entropy estimation part by removing some redundancies. We also tried to fix a number of grammatical errors, as this point was made in the earlier report.

This has been an unexpectedly lengthy journey for us - we do hope that the current version does meet the editor's standards for a publication in APL; as we feel it difficult to perceive the criticism from referee 2 as constructive, we would appreciate if an independent opinion would be sought.

With Best Regards on behalf of all authors,

Christian Kurtsiefer