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How to Extract Useful Randomness from Unreliable Sources.

Divesh Aggarwal, Maciej Obremski, João Ribeiro, Luisa Siniscalchi, Ivan Visconti

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

For more than 30 years, cryptographers have been looking for public sources of uniform randomness in order to use them as a set-up to run appealing cryptographic protocols without relying on trusted third parties. Unfortunately, nowadays it is fair to assess that assuming the existence of physical phenomena producing public uniform randomness is far from reality.

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For more than 30 years, cryptographers have been looking for public sources of uniform randomness in order to use them as a set-up to run appealing cryptographic protocols without relying on trusted third parties. Unfortunately, nowadays it is fair to assess that assuming the existence of physical phenomena producing public uniform randomness is far from reality.
Quantum random number generators provide physical randomness by converting intrinsically probabilistic measurement outcomes into usable digital values. This white paper presents a simple five-bit protocol for generating uniformly distributed decimal digits from an ideal 50/50 quantum source. Five independent binary outcomes produce 2⁵ = 32 possible sequences. By rejecting the two extreme runs, 00000 and 11111, exactly 30 admissible sequences remain, allowing a direct uniform mapping onto the ten decimal digits.The main contribution of this note is not entropy-optimal extraction, but transparency: the protocol is easy to inspect, easy to implement, and easy to explain to nontechnical users. This makes it especially relevant for trust-critical public-facing applications where visible fairness may matter more than maximum entropy efficiency. A small efficiency improvement is also introduced. Instead of discarding a rejected extreme run entirely, the rejected all-A or all-B sequence is recycled as a single fair starting bit for the next five-bit candidate block. Under the assumption of independent fair input bits, this carry-forward rule preserves exact decimal uniformity while improving the expected raw-bit cost from 16/3 ≈ 5.333 bits per digit to 79/15 ≈ 5.267 bits per digit.The paper also discusses practical implementation using a beam-splitter-style quantum randomness source, limitations under detector imbalance, and the proper cryptographic positioning of the method. The protocol can serve as a transparent entropy source or educational QRNG digitization scheme, but cryptographic deployment would still require standard health testing, calibration, and extraction.
As our foundational understanding of quantum information theory broadens, it remains to be seen whether novel foundational developments will lead to corresponding applications. Promising branches are quantum networks and quantum cryptography, which are more intertwined by the day. In particular, a fascinating phenomena is that in networks with independent sources, Bell nonlocality can take place without the need for measurement settings for the parties, i.e. in each round, each source is asked to produce the same state and each party measures the same measurement. This is in stark contrast to standard Bell nonlocality, where seed randomness is necessary to certify nonlocality and through it, randomness of the outcomes. Building on nonlocality without seed randomness in networks, we propose a device-independent quantum key distribution protocol (which can be extended to quantum conference key agreement if it involves more than 2 parties) which allows for the generation of shared secret keys without the need for input randomness. We rely on recent results on nonlocality in networks and its robustness, showing how in a ring network with NNN bipartite sources, one must only make standard assumptions in order to run the protocol, while no trust is required from the devices themselves. We thus give a device-independent proof of security under this network assumption in the IID setting. In summary, we propose a first-of-a-kind protocol for Device-Independent Quantum Key Distribution which is native to the network setting, and which does not demand input randomness from the parties in order to produce output randomness.
A non-repudiation cryptographic protocol based on hybrid cryptosystem is proposed and it is a more perfect protocol.It can realize the true fairness and non-repudiation of both parties even the channels are unreliable and insecure.Usually the protocol only needs three interactions of participants and the transferring data keep confidential for others except for the sender and the receiver,whose transactions are protected.The Trusted Third Party(TTP) performs evidences verification,generation and publication and its bottleneck problem is solved completely.Finally,we give its formal analysis and prove the protocol's fairness,correctness and security.