Source-Device-Independent Ultrafast Quantum Random Number Generation

Abstract

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....

Machine Learning Cryptanalysis of a Quantum Random Number Generator

“…For the entropy source consisting of quantum and classical noise, although the quantum effect is the dominant entropy source, due care must be taken to ensure that the effect of the hidden correlations such as memory effects and biases are minimized [9]. To further bound the effect of the random classical noise, which ultimately could be deterministic, quantification of entropy independent of the classical noise or the presence of the eavesdropper should be used [19,31].…”

Real-Time Source-Independent Quantum Random-Number Generator with Squeezed States

“…The SI-QRNG is self testing and changes its output secure bit rate depending on the check measurement data. Although theoretical proposal for using squeezed states as sources of entropy for a QRNG have been suggested [30,35], we report the first experimental use of squeezed states as an entropy source for a QRNG.…”

Implementation vulnerabilities in general quantum cryptography

“…Similarly to QKD, a QRNG system also consists of quantum state preparation and measurement, however, the states are measured locally without long-distance transmission. SI QRNG protocols [16,48,49] assume that the state preparation setup is untrusted, while the measurement setup is trusted. We survey the protocol in [16] and its experimental demonstration.…”