{'fraction_non_alphanumeric': 0.022058823529411766, 'fraction_numerical': 0.002828054298642534, 'mean_word_length': 5.1, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Trading Isolation for Certifiable Randomness Expansion

A source of random bits is an important resource in
modern cryptography, algorithms and statistics. Can one ever be
sure that a "random" source is truly random, or in the case of
cryptography, secure against potential adversaries or
eavesdroppers? Recently the study of non-local properties of
entanglement has produced an interesting new perspective on this
question, which we will refer to broadly as Certifiable Randomness
Expansion (CRE). CRE refers generally to a process by which a
source of information-theoretically certified randomness can be
constructed based only on two simple assumptions: the prior
existence of a short random seed and the ability to ensure that two
or more black-box devices do not communicate (i.e. are
non-signaling). In this work we make progress on a conjecture of
[Col09] which proposes a method for indefinite certifiable
randomness expansion using a growing number of devices (we actually
prove a slight modification of the original conjecture in which we
use the CHSH game as a subroutine rather than the GHZ game as
originally proposed). The proof requires a technique not used
before in the study of randomness expansion, and inspired by the
tools developed in [RUV12]. The result also establishes the
existence of a protocol for constant factor CRE using a finite
number of devices (here the constant factor can be much greater
than 1). While much better expansion rates (polynomial, and even
exponential) have been achieved with only two devices, our analysis
requires techniques not used before in the study of randomness
expansion, and represents progress towards a protocol which is
provably secure against a quantum eavesdropper who knows the input
to the protocol.