arXiv subjects

Cameron Foreman

Publications and source records attributed to Cameron Foreman.

8 recordsLinked to original sources

arXiv2026

High-rate and computationally-efficient seedless extractors for device-independent quantum cryptography

Device-independent (DI) quantum cryptography provides secure cryptography with minimal trust in, or characterisation of, the used quantum devices. An essential component of DI protocols is the use of randomness extractors for privacy amplification, but these typically require an initial seed of randomness that introduces a potential vulnerability. To solve this problem, the security of seedless extractors was proven in Quantum 9, 1654 (2025). The core idea was to use the Bell violation of the raw data, rather than its min-entropy, as the extractor promise. However, the large fluctuations in the Bell inequality used required many rounds to precisely estimate the Bell violation, consuming substantial randomness and making the protocol very inefficient. In this work, we present a new proof technique based on a truncation method that allows the user to estimate the protocol parameters with an asymptotically vanishing fraction of rounds and, as a consequence, achieves the optimal rate of one key bit per singlet. Notably, we prove this result using seedless extractors that can be implemented efficiently.

quant-ph↗

arXiv2025

Certified randomness amplification by dynamically probing remote random quantum states

Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have required physically co-located, loophole-free Bell tests, constraining the feasibility of remote operation. Here we realize certified randomness amplification across a network by dynamically probing large, entangled quantum states on Quantinuum's 98-qubit Helios trapped-ion quantum processor. Our protocol is secure even if the remote device acts maliciously or is compromised by an intercepting adversary, provided the samples are generated quickly enough to preclude classical simulation of the quantum circuits. We stream quantum gates in real time to the quantum processor, maintain quantum state coherence for $\approx 0.9$ seconds, and then reveal the measurement bases to the quantum processor only milliseconds before measurement. This limits the time for classical spoofing to 30 ms and constrains the location of hypothetical adversaries to a $4{,}500$ km radius. We achieve a fidelity of 0.586 on random circuits with 64 qubits and 276 two-qubit gates, enabling the amplification of realistic imperfect randomness with a low entropy rate into nearly perfect randomness.

quant-ph↗

arXiv2025

An efficient construction of Raz's two-source randomness extractor with improved parameters

Randomness extractors are algorithms that distill weak random sources into near-perfect random numbers. Two-source extractors enable this distillation process by combining two independent weak random sources. Raz's extractor (STOC '05) was the first to achieve this in a setting where one source has linear min-entropy (i.e., proportional to its length), while the other has only logarithmic min-entropy in its length. However, Raz's original construction is impractical due to a polynomial computation time of at least degree 4. Our work solves this problem by presenting an improved version of Raz's extractor with quasi-linear computation time, as well as a new analytic theorem with reduced entropy requirements. We provide comprehensive analytical and numerical comparisons of our construction with others in the literature, and we derive strong and quantum-proof versions of our efficient Raz extractor. Additionally, we offer an easy-to-use, open-source code implementation of the extractor and a numerical parameter calculation module.

cs.CR↗

arXiv2024

Local contextuality-based self-tests are sufficient for randomness expansion secure against quantum adversaries

In quantum cryptography, secure randomness expansion involves using a short private string of random bits to generate a longer one, even in the presence of an adversary who may have access to quantum resources. In this work, we demonstrate that local contextuality-based self-tests are sufficient to construct a randomness expansion protocol that is secure against computationally unbounded quantum adversaries. Our protocol is based on self-testing from non-contextuality inequalities and we prove that our scheme asymptotically produces secure random numbers which are $\mathcal{O}(m\sqrt{\epsilon})$-close to uniformly distributed and private, where $\epsilon$ is the robustness parameter of the self-test and $m$ is the length of the generated random bit string. Our protocol is semi-device-independent in the sense that it inherits any assumptions necessary for the underlying self-test.

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arXiv2024

Statistical testing of random number generators and their improvement using randomness extraction

Random number generators (RNGs) are notoriously challenging to build and test, especially for cryptographic applications. While statistical tests cannot definitively guarantee an RNG's output quality, they are a powerful verification tool and the only universally applicable testing method. In this work, we design, implement, and present various post-processing methods, using randomness extractors, to improve the RNG output quality and compare them through statistical testing. We begin by performing intensive tests on three RNGs -- the 32-bit linear feedback shift register (LFSR), Intel's 'RDSEED,' and IDQuantique's 'Quantis' -- and compare their performance. Next, we apply the different post-processing methods to each RNG and conduct further intensive testing on the processed output. To facilitate this, we introduce a comprehensive statistical testing environment, based on existing test suites, that can be parametrised for lightweight (fast) to intensive testing.

cs.CR↗

arXiv2024

Seedless extractors for device-independent quantum cryptography

Device-independent (DI) quantum cryptography aims at providing secure cryptography with minimal trust in, or characterisation of, the underlying quantum devices. A key step in DI protocols is randomness extraction (or privacy amplification), which typically requires a \textit{seed} of additional bits with sufficient entropy and statistical independence from any bits generated during the protocol. In this work, we propose a method for extraction in DI protocols that does not require a seed and is secure against computationally unbounded quantum adversaries. The core idea is to use the Bell violation of the raw data, rather than its min-entropy, as the extractor promise. We present a complete security proof in a model where the experiment uses memoryless measurement devices acting on an arbitrary joint (across all rounds) state. Our results mark a first step in this alternative, seedless, approach to extraction in DI protocols.

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arXiv2024

Cryptomite: A versatile and user-friendly library of randomness extractors

We present Cryptomite, a Python library of randomness extractor implementations. The library offers a range of two-source, seeded and deterministic randomness extractors, together with parameter calculation modules, making it easy to use and suitable for a variety of applications. We also present theoretical results, including new extractor constructions and improvements to existing extractor parameters. The extractor implementations are efficient in practice and tolerate input sizes of up to $2^{40}>10^{12}$ bits. Contrary to alternatives using the fast Fourier transform, we implement convolutions efficiently using the number-theoretic transform to avoid rounding errors, making them well suited to cryptography. The algorithms and parameter calculation are described in detail, including illustrative code examples and performance benchmarking.

cs.CR↗

arXiv2020

Practical randomness amplification and privatisation with implementations on quantum computers

We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private numbers, even if using an uncharacterised quantum device potentially built by an adversary. Our generation rates are linear in the repetition rate of the quantum device and the classical randomness post-processing has quasi-linear complexity - making it efficient on a standard personal laptop. The statistical analysis is also tailored for real-world quantum devices. Our protocol is then showcased on several different quantum computers. Although not purposely built for the task, we show that quantum computers can run faithful Bell tests by adding minimal assumptions. In this semi-device-independent manner, our protocol generates (near-)perfectly unbiased and private random numbers on today's quantum computers.

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