Full randomness from arbitrarily deterministic events

Gallego, Rodrigo; Masanes, Lluís; Torre, Gonzalo de la; Dhara, Chirag; Aolita, Leandro; Acín, Antonio

doi:10.1038/ncomms3654

Cited by 158 publications

(219 citation statements)

References 26 publications

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“…Consequently, in the limit of large n, the probability of Eve guessing the value of A correctly becomes 1/2; that is, A is uniformly random and independent of any information held by Eve. This observation is not only relevant for key distribution 21 , but has been crucial for randomness amplification 26 . …”

Section: Competing Financial Interestsmentioning

confidence: 89%

“…If someone we trust tells us that such and such a fraction of the choices made by our random number generators cannot be determined by the adversary, then privacy is still possible because local randomness can be amplified 26 . Randomness amplification can itself be done with device-independent protocols, and it works even if the fraction of initial randomness is arbitrarily small or the devices are noisy 27,28 .…”

Section: Should We Trust Ourselves?mentioning

confidence: 99%

“…As long as this control is not complete, Alice and Bob can do something about it. It turns out that 'free will' or, more specifically, the ability to make unpredictable, and, therefore, random, choices can be amplified 26 . Randomness amplification has recently triggered a flurry of research activity, culminating in a striking result: anything that is not completely deterministic can be made completely random 27,28 .…”

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confidence: 99%

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The ultimate physical limits of privacy

Ekert

Renner

2014

Nature

123

104

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Among those who make a living from the science of secrecy, worry and paranoia are just signs of professionalism. Can we protect our secrets against those who wield superior technological powers? Can we trust those who provide us with tools for protection? Can we even trust ourselves, our own freedom of choice? Recent developments in quantum cryptography show that some of these questions can be addressed and discussed in precise and operational terms, suggesting that privacy is indeed possible under surprisingly weak assumptions.Edgar Allan Poe, an American writer and an amateur cryptographer, once wrote "… it may be roundly asserted that human ingenuity cannot concoct a cipher which human ingenuity cannot resolve …" 1 . Is it true? Are we doomed to be deprived of our privacy, no matter how hard we try to retain it? If the history of secret communication is of any guidance here, the answer is a resounding 'yes'. There is hardly a shortage of examples illustrating how the most brilliant efforts of code-makers were matched by the ingenuity of code-breakers 2 . Even today, the best that modern cryptography can offer are security reductions, telling us, for example, that breaking RSA, one of the most widely used public key cryptographic systems, is at least as hard as factoring large integers 3 . But is factoring really hard? Not with quantum technology. Indeed, RSA, and many other public key cryptosystems, will become insecure once a quantum computer is built 4 . Admittedly, that day is probably decades away, but can anyone prove, or give any reliable assurance, that it is? Confidence in the slowness of technological progress is all that the security of our best ciphers now rests on.This said, the requirements for perfectly secure communication are well understood. When technical buzzwords are stripped away, all we need to construct a perfect cipher is shared private randomness, more precisely, a sequence of random bits known as a 'cryptographic key'. Any two parties who share the key, we call them Alice and Bob (not their real names, of course), can then use it to communicate secretly, using a simple encryption method known as the one-time pad 5 . The key is turned into a meaningful message by one party telling the other, in public, which bits of the key should be flipped. An eavesdropper, Eve, who has monitored the public communication and knows the general method of encryption but not the key will not be able to infer anything useful about the message. It is vital though that the key bits be truly random, never reused, and securely delivered to Alice and Bob, who may be miles apart. This is not easy, but it can be done, and one can only be amazed how well quantum physics lends itself to the task of key distribution.Quantum key distribution, proposed independently by Bennett and Brassard 6 and by Ekert 7 , derives its security either from the Heisenberg uncertainty principle (certain pairs of physical properties are complementary in the sense that knowing one property necessarily precludes knowledge about the othe...

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Section: Competing Financial Interestsmentioning

confidence: 89%

Section: Should We Trust Ourselves?mentioning

confidence: 99%

mentioning

confidence: 99%

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The ultimate physical limits of privacy

Ekert

Renner

2014

Nature

123

104

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“…It is remarkable that even this assumption can be partially relaxed, giving rise to the possibility of randomness amplification [12][13][14][15][16][17][18][19], but we don't consider this task in this paper.…”

Section: Scenarios For Quantum Randomnessmentioning

confidence: 99%

Quantum randomness extraction for various levels of characterization of the devices

Law

Thinh

Bancal

et al. 2014

J. Phys. A: Math. Theor.

137

132

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The amount of intrinsic randomness that can be extracted from measurement on quantum systems depends on several factors: notably, the power given to the adversary and the level of characterization of the devices of the authorized partners. After presenting a systematic introduction to these notions, in this paper we work in the class of least adversarial power, which is relevant for assessing setups operated by trusted experimentalists, and compare three levels of characterization of the devices. Many recent studies have focused on the so-called "device-independent" level, in which a lower bound on the amount of intrinsic randomness can be certified without any characterization. The other extreme is the case when all the devices are fully characterized: this "tomographic" level has been known for a long time. We present for this case a systematic and efficient approach to quantifying the amount of intrinsic randomness, and show that setups involving ancillas (POVMs, pointer measurements) may not be interesting here, insofar as one may extract randomness from the ancilla rather than from the system under study. Finally, we study how much randomness can be obtained in presence of an intermediate level of characterization related to the task of "steering", in which Bob's device is fully characterized while Alice's is a black box. We obtain our results here by adapting the NPA hierarchy of semidefinite programs to the steering scenario.

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“…For instance, in the Device Independent (DI) framework, H min (Z|E) can be related to violation of a Bell's inequality. However, these protocols are very demanding from the experimental point of view since they require a loohole-free Bell tests [14][15][16].In this work we propose and experimentally realize an efficient protocol for the secure and ultra-fast generation of random numbers able to evaluate a lower bound for the conditional quantum min-entropy. The method assumes a trusted measurement device and a complete untrusted source, i.e.…”

mentioning

confidence: 99%

Source-Device-Independent Ultrafast Quantum Random Number Generation

Marangon¹,

Vallone²,

Villoresi³

2017

Phys. Rev. Lett.

137

126

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Secure random numbers are a fundamental element of many applications in science, statistics, cryptography and more in general in security protocols. We present a method that enables the generation of high-speed unpredictable random numbers from the quadratures of an electromagnetic field without any assumption on the input state. The method allows to eliminate the numbers that can be predict due the presence of classical and quantum side information. In particular, we introduce a procedure to estimate a bound on the conditional min-entropy based on the Entropic Uncertainty Principle for position and momentum observables of infinite dimensional quantum systems. By the above method, we experimentally demonstrated the generation of secure true random bits at a rate greater than 1 Gbit/s.Introduction -Quantum Random Number Generators (QRNG) exploits intrinsic probabilistic quantum processes to generate true random numbers. Indeed, the expression "QRNG" was first introduced for a device based on the decay of radioactive nuclei [1]. Afterwards, QRNGs exploiting the versatility of light were realized: such devices are based on optical processes such as photon welcher weg [2][3][4], photon time of arrival [5][6][7] or vacuum quadratures [8][9][10][11].Usually, the assessment of the randomness of the generated numbers is obtained by applying statistical tests on the output bits. In most of the QRNGs, passing the tests is the only method used to certify the randomness. In case of failure (attributed to hardware problem since the process is assumed to be "random"), numbers are algorithmically post-processed until the tests are passed.However, this procedure con only certifies that the numbers are identically and independently distributed (i.i.d.) with respect to those [12] applied tests. Indeed, a posteriori statistical tests cannot certify that the numbers are not known to someone possessing side information about the generator. For instance, it is not possible to eliminate hardware noise, which is a source of classical side information for an eavesdropper, Eve, who may be able to control it. Hence, a statistical test a posteriori cannot establish whether the numbers are originated by the quantum process or by the noisy hardware. Moreover, even assuming a QRNG with an ideal noiseless hardware, a statistical test cannot reveal whether the outputs arise from a a quantum measurements and then are intrinsically random. For instance, a polarization welcher weg QRNG with an optical source emitting photons in a completely mixed polarization state can be seen as the photonic version of a fair coin. The random sequence can be predicted by Eve if she knows "the coin's equations of motion" (namely she has classical side information) or if she holds a quantum system correlated with the QRNG (namely she has quantum side information).The quantity that evaluates the amount of side information on a random sequence Z is the so called conditional quantum min-entropy H min (Z|E) [13]. However, such min-entropy is generally hard to estimate....

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Full randomness from arbitrarily deterministic events

Cited by 158 publications

References 26 publications

The ultimate physical limits of privacy

The ultimate physical limits of privacy

Quantum randomness extraction for various levels of characterization of the devices

Source-Device-Independent Ultrafast Quantum Random Number Generation

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