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Simpósio Brasileiro de Cibersegurança (SBSeg)

A publicly verifiable protocol for random number generation

João Penna, Jeroen van de Graaf

Published Nov 6, 2017• 0 citations
Publisher

Abstract

Chance plays an essential role in many decision procedures such as lotteries, draws etc. As such procedures are moving on-line, several web services offering randomness have appeared over the last few years. NIST’s randomness beacon, which publishes a sequence of 512 random bytes every minute, unfortunately lacks transparency: the beacon does not eliminate the possibility of an insider attack who knows the outcomes beforehand. We propose an improvement of NIST’s beacon which is publicly verifiable and fully transparent: any outsider who did not witness the bit generation in person but has internet access can convince himself that the beacon acted honestly, provided he can be sure that fresh, independent random bits were contributed to the seed value. Our proposal is based on a novel cryptographic assumption: the existence of functions that are slow to compute even on the fastest supercomputers.

DOI
10.5753/sbseg.2017.19527

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Chance plays an essential role in many decision procedures such as lotteries, draws etc. As such procedures are moving on-line, several web services offering randomness have appeared over the last few years. NIST’s randomness beacon, which publishes a sequence of 512 random bytes every minute, unfortunately lacks transparency: the beacon does not eliminate the possibility of an insider attack who knows the outcomes beforehand. We propose an improvement of NIST’s beacon which is publicly verifiable and fully transparent: any outsider who did not witness the bit generation in person but has internet access can convince himself that the beacon acted honestly, provided he can be sure that fresh, independent random bits were contributed to the seed value. Our proposal is based on a novel cryptographic assumption: the existence of functions that are slow to compute even on the fastest supercomputers.
Abstract. We formalize the use of Bitcoin as a source of publicly-verifiable randomness. As a side-effect of Bitcoin’s proof-of-work-based consensus system, random values are broadcast every time new blocks are mined. We can derive strong lower bounds on the computational min-entropy in each block: currently, at least 68 bits of min-entropy are produced every 10 minutes, from which one can derive over 32 near-uniform bits using standard extractor techniques. We show that any attack on this beacon would form an attack on Bitcoin itself and hence have a monetary cost that we can bound, unlike any other construc-tion for a public randomness beacon in the literature. In our simplest construction, we show that a lottery producing a single unbiased bit is manipulation-resistant against an attacker with a stake of less than 50 bitcoins in the output, or about US$12,000 today. Finally, we propose making the beacon output available to smart contracts and demonstrate that this simple tool enables a number of interesting applications. 1
Quantum random number (QRNG) beacons distinguish themselves from classical counterparts by providing intrinsic unpredictability originating from the fundamental laws of quantum mechanics. Most demonstrations have focused on certifiable randomness generators to guarantee the public that their genuineness is independent from imperfect implementations. These efforts however do not benefit applications where multiple distrusted users need a common set of random numbers, as they must rely on the honesty of beacon owners. In this paper, we formally introduce a design and proof-of-principle experiment of the first consensus protocol producing QRNs in a decentralized environment (dQRNG). Such protocol allows N number of participants contribute in the generation process and publicly verify numbers they collect. Security of the protocol is guaranteed given(N-1) dishonest participants. Our method is thus suited for distribute systems that requires a bias-resistant, highly secure, and public-verifiable random beacon.
The extraction of randomness from weakly random seeds is a topic of central importance in cryptography. Weak sources of randomness can be considered to be either private or public, where public sources such as the NIST randomness beacon broadcast the random bits once they are generated. The problem of device-independent randomness extraction from weak public sources against no-signalling adversaries has remained open. In this paper, we show protocols for device-independent and one-sided device-independent amplification of randomness from weak public Santha Vazirani (SV) sources that use a finite number of devices and are secure against no-signaling adversaries. Specifically, under the assumption that the device behavior is as prescribed by quantum mechanics the protocols allow for amplification of public εεε-SV sources for arbitrary initial ε∈[0,0.5)ε\in [0,0.5)ε∈[0,0.5). On the other hand, when only the assumption of no-signaling between the components of the device is made, the protocols allow for amplification of a limited set of weak public SV sources.
Random beacons—services that periodically emit public, unpredictable, and unbiasable random values—underpin blockchains, lotteries, sharding, and cryptographic parameter generation. To remove single points of trust, modern beacons are distributed, but they rest on classical hardness assumptions that quantum computers threaten. Quantum random beacons instead draw unpredictability directly from quantum mechanics and are quantum-safe by construction. Existing systems sit at two extremes: single-device protocols based on random circuit sampling trust one quantum server, while device-independent beacons require entangled measurement stations and do not fit the commercial quantum cloud. We present QuoRand, a quantum random beacon that combines m mutually distrusting quantum servers into one publicly verifiable source of certified randomness through a fully distributed classical protocol with no trusted party. QuoRand introduces (1) a Certified-Randomness Oracle (CRO) abstraction that captures RCS-, LWE-, and low-depth-unitary instantiations uniformly, so all guarantees hold independently of the quantum-advantage assumption; (2) a hash-chained challenge derivation that self-bootstraps each round from the previous output, removing the trusted coordinator of prior designs; and (3) a verifiable-delay-function audit lottery, drawn only after all servers commit, that renders any spoofing server accountable while amortizing verification across rounds. We prove QuoRand is unpredictable and bias-resistant under an anytrust assumption—a single honest server suffices—accountable under an honest majority, and live under partial synchrony, and confirm the soundness-cost trade-off with lightweight simulations.