DOCSLIB.ORG

Multiplexed Quantum Random Number Generation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Multiplexed Quantum Random Number Generation Multiplexed Quantum Random Number Generation Ben Haylock1, Daniel Peace1, Francesco Lenzini1, Christian Weedbrook2, and Mirko Lobino1,3 1Centre for Quantum Dynamics, Griffith University, Brisbane, 4111, Australia 2Xanadu, 372 Richmond St. W., Toronto, M5V 2L7, Canada 3Queensland Micro- and Nanotechnology Centre, Griffith University, Brisbane, 4111, Australia May 8, 2019 Fast secure random number generation is es- trust in the generator. These generators require an ex- sential for high-speed encrypted communication, perimental violation of a Bell-type inequality, an ex- and is the backbone of information security. tremely difficult task, limiting generation rates to well Generation of truly random numbers depends on below practical requirements (<kbit/s) [10, 11]. Other the intrinsic randomness of the process used and approaches based on the Kochen-Specker theorem to is usually limited by electronic bandwidth and prove value indefiniteness of the measurement, have signal processing data rates. Here we use a mul- demonstrated faster but not yet usable generation rates tiplexing scheme to create a fast quantum ran- (25kbit/s) [12, 13]. Recent advances[14] have built upon dom number generator structurally tailored to the notion of Bell inequality violations using device in- encryption for distributed computing, and high dependent quantum random number generators. Re- bit-rate data transfer. We use vacuum fluctua- markably, these allow the closure of any security loop- tions measured by seven homodyne detectors as holes related to the how the device is made, i.e., in- quantum randomness sources, multiplexed using dependent of the device implementations. Currently, a single integrated optical device. We obtain a high-speed (Mbit/s-Tbit/s) quantum random number real-time random number generation rate of 3.08 generation relies on trusted or semi-trusted generators, Gbit/s, from only 27.5 MHz of sampled detector where the independence of the randomness from classi- bandwidth. Furthermore, we take advantage of cal noise is experimentally tested [15{22]. While these the multiplexed nature of our system to demon- systems have no quantum physical guarantee of their strate an unseeded strong extractor with a gen- randomness, they are usually denoted as QRNGs due to eration rate of 26 Mbit/s. the quantum mechanical origin of the randomness. This trade-off between speed and security is mostly caused by the experimental complexity of fully secure imple- 1 Introduction mentations. Entropy sources sufficient for randomness generation Information security[1] is a foundation of modern infras- rates up to 1.2Tb/s have been demonstrated[23], How- tructure with quantum optics set to play a prevalent role ever, these systems are not capable of real time ran- in the next generation of cryptographic hardware[2]. dom number generation at full speed due to process- Randomness is a core resource for cryptography and ing bandwidth limitations, instead performing off-line considerable effort has gone into making systems suit- processing on captured data to generate randomness. able for supplying high bit rate streams of random bits. Thus these schemes are not suited for providing high- arXiv:1801.06926v3 [quant-ph] 6 May 2019 The randomness properties of the source have a pro- speed random numbers for cryptography. Regardless of found effect on the security of the encryption, with sev- generation procedure, implementations of randomness eral examples of compromised security from an attack extraction are limited by electronic logic speeds or de- on the random number generator [3{5]. In this area, tection bandwidths. Therefore, for high speed real time quantum optics has provided advantages over previ- random number generation, the most feasible solution ous methods, enabling random number generation with is to create many parallel sources with lower entropy high speeds and enhanced security [6{8]. rates. The gold standard for security in random number Multiplexed quantum random number generation has generators comes from device independent quantum previously been theoretically proposed as a solution random number generators (QRNGs) [9], where the to post-processing bottlenecks in the real-time rate of output is certified as random regardless of the level of QRNGs [7,8]. Previous demonstrations of a parallel nature remain focused on increasing single-channel data Ben Haylock: This author contributed equally to this work rates. Gr¨afeet al. extend single photon path-encoding Daniel Peace: This author contributed equally to this work based QRNGs to the multi-mode case increasing the bi- Mirko Lobino: m.lobino@griffith.edu.au trate for a fixed measured photon flux[24]. Haw et al. Accepted in Quantum 2019-05-01, click title to verify 1 sample two separate frequency slices of their homodyne detector bandwidth in a vacuum fluctuation QRNG, enabling them to generate randomness at twice their digitization rate[25]. Both demonstrations remain ul- timately rate-limited by generation[24] or detection[25] rates. The goal of multiplexing should be to increase the data rate regardless of single channel bandwidth limitations as shown by IDQuantique by multiplexing together four separate devices on a single interface[26]. A multiplexing architecture is more versatile than in- Figure 1: Scheme for multiplexed quantum random number creasing the rate of a single data stream, allowing the generator based on quadrature measurements of the vacuum use of more complex extraction techniques and random- state. A low noise, Koheras Boostik laser at 1550nm is cou- pled in and out of a lithium niobate waveguide network through ness distribution at rates faster than a single channel butt-coupled fiber arrays. Light from the outputs is sent into capacity. Randomness extractors are algorithms which, seven homodyne detectors. The detector signals are sent to the given a bit string from a weakly random physical source, ADC and FPGA for digitization, processing and randomness ex- produce a shorter sequence of truly random bits[27]. traction. This schematic shows four channels, the experimental Previous works have largely used seeded extractors, implementation used up to seven channels. which require a uniform random seed to convert the in- put to random bits. Such extraction is often described as randomness expansion, as it cannot extract true ran- The homodyne detectors (HDs) used in this demon- domness without already having some at the input[6]. stration follow the design of Kumar et al.[33] and Seeded extractors rely on the uniformity of the seed and have an electronic bandwidth of 100MHz. The quan- independence of the output from this seed for security. tum efficiencies of the photodiodes used (PD20, oe- We can relax both of these requirements with a multi- market) are >67% (70% typical). The quantum signal source extractor. to classical noise ratio (QCNR) is defined as QCNR= 2 2 2 A single random output is produced from two weakly 10 log10(σQ/σE) where σQ is the quantum noise vari- random inputs in a multi-source extractor. The main 2 ance, and σE is the classical noise variance. Using advantage of this approach is that random numbers can 2 2 2 the equation σQ = σM − σE, QCNR can be calculated be generated without any initial random seed. Many from experimental measurement of the variance of the examples of multi-source extractors exist that allow for output of the homodyne detector with the local oscil- unseeded extraction with low entropy loss, including 2 2 lator off (σE), and with the local oscillator on (σM ). constructions which are strong extractors in the pres- Figure2(a) shows the results for all seven homodyne ence of quantum side information[28]. detectors. We see that for all channels of our design We experimentally demonstrate a high-speed paral- this ratio exceeds 10dB across 30 MHz, with a mea- lel quantum random generator whose total rate is not sured common mode rejection ratio of >27dB across limited by generation or detection rates but rather by all seven detectors. To confirm that our detectors were the number of parallel channels used. While Gbps measuring vacuum fluctuations, we determine the lin- real-time generation rates have been previously been earity of the noise as a function of the laser power (see demonstrated[29{31], our scheme provides a simple Figure2(b)). As the QCNR is the ratio between this method scheme to overcome electronic and processing response and the value at zero power (blue trace), it bandwidth limitations. also scales linearly with input power. The indepen- dence of the outcomes of each of the channels was veri- fied from cross-correlation measurements shown in Fig- 2 Random Number Generation Scheme ure2(c).√ The cross-correlation for ideal uniform data is 1/ n = 3.16 × 10−4. All 21 channel pairing cross- A schematic of the multiplexed QRNG scheme is shown correlations lie between 2.83 × 10−4 and 3.51 × 10−4. in Figure1. The noise source of each channel of our mul- Integrated optics provides a compact and stable way tiplexed design comes from homodyne measurements to implement the set of beamsplitters needed to feed of vacuum state [15, 32] (see inset in Figure2(a)). A many homodyne detectors. We fabricate a 1:32 mul- laser is sent onto a 50-50 beamsplitter while vacuum en- tiplexer using annealed proton exchanged waveguides ters the other port, subsequently the two outputs of the in lithium niobate with a device footprint of 60mm x beamsplitter are detected on two photodiodes and the 5mm[34]. The device has insertion losses of ≈7 dB difference between the two photocurrents is amplified. (≈22dB total loss per channel) and we choose balanced The homodyne current is proportional to a measure- outputs to send to the seven homodyne detectors. To- ment of the quadrature operator of the vacuum state, tal input power to the array is approximately 160mW and its value is independent and unpredictable within (≈1mW per channel at output), which will ultimately a Gaussian distribution with zero mean.
Load more

Recommended publications
  • True Random Number Generators Secure in a Changing Environment
    True Random Number Generators Secure in a Changing Environment Boaz Barak, Ronen Shaltiel, and Eran Tromer Department of Computer Science and Applied Mathematics Weizmann Institute of Science , Rehovot, ISRAEL Email: {boaz,ronens,tromer}@wisdom.weizmann.ac.il Abstract. A true random number generator (TRNG) usually consists of two components: an “unpredictable” source with high entropy, and a randomness extractor — a function which, when applied to the source, produces a result that is statistically close to the uniform distribution. When the output of a TRNG is used for cryptographic needs, it is pru- dent to assume that an adversary may have some (limited) influence on the distribution of the high-entropy source. In this work: 1. We define a mathematical model for the adversary’s influence on the source. 2. We show a simple and efficient randomness extractor and prove that it works for all sources of sufficiently high-entropy, even if individual bits in the source are correlated. 3. Security is guaranteed even if an adversary has (bounded) influence on the source. Our approach is based on a related notion of “randomness extraction” which emerged in complexity theory. We stress that the statistical ran- domness of our extractor’s output is proven, and is not based on any unproven assumptions, such as the security of cryptographic hash func- tions. A sample implementation of our extractor and additional details can be found at a dedicated web page [Web]. 1 Introduction 1.1 General setting It is well known that randomness is essential for cryptography. Cryptographic schemes are usually designed under the assumption of availability of an endless stream of unbiased and uncorrelated random bits.
    [Show full text]
  • Extracting Randomness from Extractor-Dependent Sources
    Extracting Randomness from Extractor-Dependent Sources Yevgeniy Dodi Vinod Vaikuntanathan NYU MIT Daniel Wichs Northeastern University and NTT Research Inc. February 19, 2020 Abstract We revisit the well-studied problem of extracting nearly uniform randomness from an arbi- trary source of sufficient min-entropy. Strong seeded extractors solve this problem by relying on a public random seed, which is unknown to the source. Here, we consider a setting where the seed is reused over time and the source may depend on prior calls to the extractor with the same seed. Can we still extract nearly uniform randomness? In more detail, we assume the seed is chosen randomly, but the source can make arbitrary oracle queries to the extractor with the given seed before outputting a sample. We require that the sample has entropy and differs from any of the previously queried values. The extracted output should look uniform even to a distinguisher that gets the seed. We consider two variants of the problem, depending on whether the source only outputs the sample, or whether it can also output some correlated public auxiliary information that preserves the sample’s entropy. Our results are: Without Auxiliary Information: We show that every pseudo-random function (PRF) with a sufficiently high security level is a good extractor in this setting, even if the distin- guisher is computationally unbounded. We further show that the source necessarily needs to be computationally bounded and that such extractors imply one-way functions. With Auxiliary Information: We construct secure extractors in this setting, as long as both the source and the distinguisher are computationally bounded.
    [Show full text]
  • Key Derivation and Randomness Extraction
    Key Derivation and Randomness Extraction Olivier Chevassut1, Pierre-Alain Fouque2, Pierrick Gaudry3, and David Pointcheval2 1 Lawrence Berkeley National Lab. – Berkeley, CA, USA – [email protected] 2 CNRS-Ecole´ normale sup´erieure – Paris, France – {Pierre-Alain.Fouque,David.Pointcheval}@ens.fr 3 CNRS-Ecole´ polytechnique – Palaiseau, France – [email protected] Abstract. Key derivation refers to the process by which an agreed upon large random number, often named master secret, is used to derive keys to encrypt and authenticate data. Practitioners and standard- ization bodies have usually used the random oracle model to get key material from a Diffie-Hellman key exchange. However, proofs in the standard model require randomness extractors to formally extract the entropy of the random master secret into a seed prior to derive other keys. This paper first deals with the protocol Σ0, in which the key derivation phase is (deliberately) omitted, and security inaccuracies in the analysis and design of the Internet Key Exchange (IKE version 1) protocol, corrected in IKEv2. They do not endanger the practical use of IKEv1, since the security could be proved, at least, in the random oracle model. However, in the standard model, there is not yet any formal global security proof, but just separated analyses which do not fit together well. The first simplification is common in the theoretical security analysis of several key exchange protocols, whereas the key derivation phase is a crucial step for theoretical reasons, but also practical purpose, and requires careful analysis. The second problem is a gap between the recent theoretical analysis of HMAC as a good randomness extractor (functions keyed with public but random elements) and its practical use in IKEv1 (the key may not be totally random, because of the lack of clear authentication of the nonces).
    [Show full text]
  • Human Assisted Randomness Generation Using Video Games
    Human Assisted Randomness Generation Using Video Games Mohsen Alimomeni, Reihaneh Safavi-Naini University of Calgary, Department of Computer Science malimome,[email protected] January 19, 2014 Abstract Random number generators have direct applications in information security, online gaming, gambling, and computer science in general. True random number generators need an entropy source which is a physical source with inherent uncertainty, to ensure unpredictability of the output. In this paper we propose a new indirect approach to collecting entropy using human errors in the game play of a user against a computer. We argue that these errors are due to a large set of factors and provide a good source of randomness. To show the viability of this proposal, we design and implement a game, conduct a user study in which we collect user input in the game, and extract randomness from it. We measure the rate and the quality of the resulting randomness that clearly show effectiveness of the approach. Our work opens a new direction for construction of entropy sources that can be incorporated into a large class of video games. 1 Introduction Randomness has a central role in computer science and in particular information security. Security of cryptographic algorithms and protocols relies on keys that must be random. Random coins used in randomized encryption and authentication algorithms and values such as nonces in protocols, must be unpredictable. In all these cases, unpredictability of random values is crucial for security proofs. There are also applications such as online games, gambling applications and lotteries in which unpredictability is a critical requirement.
    [Show full text]
  • Good Quantum Codes with Low-Weight Stabilizers Sergey Bravyi, IBM Watson Research Center Tuesday, January 21, 2014, ** 2:00 Pm, This Week Only ** 107 Annenberg
    Good quantum codes with low-weight stabilizers Sergey Bravyi, IBM Watson Research Center Tuesday, January 21, 2014, ** 2:00 pm, this week only ** 107 Annenberg Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their potential applications in fault-tolerant quantum computing. However, all families of quantum LDPC codes known to this date suffer from a poor distance scaling limited by the square-root of the code length. This is in a sharp contrast with the classical case where good families of LDPC codes are known that combine constant encoding rate and linear distance. In this talk I will describe the first family of good quantum codes with low-weight stabilizers. The new codes have a constant encoding rate, linear distance, and stabilizers acting on at most square root of n qubits, where n is the code length. For comparison, all previously known families of good quantum codes have stabilizers of linear weight. The proof combines two techniques: randomized constructions of good quantum codes and the homological product operation from algebraic topology. We conjecture that similar methods can produce good stabilizer codes with stabilizer weight n^a for any a>0. Finally, we apply the homological product to construct new small codes with low-weight stabilizers. This is a joint work with Matthew Hastings Preprint: arXiv:1311.0885 Quantum Information, Entanglement, and Many-body Physics Fernando Brandao, University College London Tuesday, January 28, 2014, 4:00 p.m. 114 East Bridge Quantum information science has been developed in the past twenty years with an eye on future technologies, such as quantum computers and quantum cryptography.
    [Show full text]
  • Cryptographic Extraction and Key Derivation: the HKDF Scheme
    Cryptographic Extraction and Key Derivation: The HKDF Scheme Hugo Krawczyk∗ Abstract In spite of the central role of key derivation functions (KDF) in applied cryptography, there has been little formal work addressing the design and analysis of general multi-purpose KDFs. In practice, most KDFs (including those widely standardized) follow ad-hoc approaches that treat cryptographic hash functions as perfectly random functions. In this paper we close some gaps between theory and practice by contributing to the study and engineering of KDFs in several ways. We provide detailed rationale for the design of KDFs based on the extract-then-expand approach; we present the first general and rigorous definition of KDFs and their security which we base on the notion of computational extractors; we specify a concrete fully practical KDF based on the HMAC construction; and we provide an analysis of this construction based on the extraction and pseudorandom properties of HMAC. The resultant KDF design can support a large variety of KDF applications under suitable assumptions on the underlying hash function; particular attention and effort is devoted to minimizing these assumptions as much as possible for each usage scenario. Beyond the theoretical interest in modeling KDFs, this work is intended to address two important and timely needs of cryptographic applications: (i) providing a single hash-based KDF design that can be standardized for use in multiple and diverse applications, and (ii) providing a conservative, yet efficient, design that exercises much care in the way it utilizes a cryptographic hash function. (The HMAC-based scheme presented here, named HKDF, is being standardized by the IETF.) ∗IBM T.J.
    [Show full text]
  • Quantum-Proof Extractors: Optimal up to Constant Factors
    Quantum-Proof Extractors: Optimal up to Constant Factors Kai-Min Chung∗ Gil Cohen† Thomas Vidick‡ Xiaodi Wu§ Abstract We give the first construction of a family of quantum-proof extractors that has optimal seed length dependence O(log(n/ǫ)) on the input length n and error ǫ. Our extractors support any α min-entropy k = Ω(log n + log1+ (1/ǫ)) and extract m = (1 α)k bits that are ǫ-close to uniform, for any desired constant α > 0. Previous constructions had− a quadratically worse seed length or were restricted to very large input min-entropy or very few output bits. Our result is based on a generic reduction showing that any strong classical condenser is au- tomatically quantum-proof, with comparable parameters. The existence of such a reduction for extractors is a long-standing open question; here we give an affirmative answer for condensers. Once this reduction is established, to obtain our quantum-proof extractors one only needs to con- sider high entropy sources. We construct quantum-proof extractors with the desired parameters for such sources by extending a classical approach to extractor construction, based on the use of block-sources and sampling, to the quantum setting. Our extractors can be used to obtain improved protocols for device-independent randomness expansion and for privacy amplification. 1 Introduction A randomness extractor is a deterministic procedure that extracts almost uniform random bits from a weak source of randomness using a seed, a short uniform random string, as a catalyst. Originally introduced as tools for derandomization [36], extractors have found uses and surprising connections in many areas such as pseudorandomness [35, 50], complexity theory [17, 45, 31], cryptography [5, 14], and combinatorics [1, 8, 7] to name a few.
    [Show full text]
  • Generating Random Numbers with Minimal Assumptions
    Physical Randomness Extractors: Generating Random Numbers with Minimal Assumptions Kai-Min Chung∗ Yaoyun Shi† Xiaodi Wu‡ March 9, 2015 Abstract How to generate provably true randomness with minimal assumptions? This question is im- portant not only for the efficiency and the security of information processing, but also for understanding how extremely unpredictable events are possible in Nature. All current solutions require special structures in the initial source of randomness, or a certain independence relation among two or more sources. Both types of assumptions are impossible to test and difficult to guarantee in practice. Here we show how this fundamental limit can be circumvented by extrac- tors that base security on the validity of physical laws and extract randomness from untrusted quantum devices. In conjunction with the recent work of Miller and Shi (arXiv:1402:0489), our physical randomness extractor uses just a single and general weak source, produces an arbi- trarily long and near-uniform output, with a close-to-optimal error, secure against all-powerful quantum adversaries, and tolerating a constant level of implementation imprecision. The source necessarily needs to be unpredictable to the devices, but otherwise can even be known to the adversary. Our central technical contribution, the Equivalence Lemma, provides a general principle for proving composition security of untrusted-device protocols. It implies that unbounded ran- domness expansion can be achieved simply by cross-feeding any two expansion protocols. In particular, such an unbounded expansion can be made robust, which is known for the first time. Another significant implication is, it enables the secure randomness generation and key distribution using public randomness, such as that broadcast by NIST’s Randomness Beacon.
    [Show full text]
  • Quantum Noise Extraction from the Interference of Laser Pulses in Optical Quantum Random Number Generator
    Quantum noise extraction from the interference of laser pulses in optical quantum random number generator ROMAN SHAKHOVOY1,2*, DENIS SYCH1,2,3, VIOLETTA SHAROGLAZOVA1,2,4, ALEXANDER UDALTSOV1,2, ALEKSEY FEDOROV1,2,5, AND YURY KUROCHKIN1,2,6 1Russian Quantum Center, 45 Skolkovskoye shosse, Moscow, Russian Federation 2QRate, 100 Novaya str., Skolkovo, Russian Federation 3P.N. Lebedev Physical Institute, Russian Academy of Sciences, 53 Leninsky prosp., Moscow, Russian Federation 4Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow, Russian Federation 5Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Russian Federation 6NTI Center for Quantum Communications, National University of Science and Technology MISiS, 4 Leninsky prospekt, Moscow, Russian Federation *[email protected] Abstract: We propose a method for quantum noise extraction from the interference of laser pulses with random phase. Our technique is based on the calculation of a parameter, which we called the quantum reduction factor, and which allows determining the contributions of quantum and classical noises in the assumption that classical fluctuations exhibit Gaussian distribution. To the best of our knowledge, the concept of the quantum reduction factor is introduced for the first time. We use such an approach to implement the post-processing-free optical quantum random number generator with the random bit generation rate of 2 Gbps. 1. Introduction Numerous quantum random number generators (QRNGs) based on various quantum effects have been demonstrated over the last two decades [1]. Among them, QRNGs employing different phenomena of quantum optics seem to be very convenient, relatively cheap, and, what is more important nowadays, could provide high random bit generation rates.
    [Show full text]
  • Leftover Hash Lemma and Its Applications
    Leftover Hash Lemma and its Applications rkm0959 (Gyumin Roh) October 18th Outline Introduction and Motivation Bunch of Terminology The Leftover Hash Lemma Application 1: Random Number Generation Application 2: Quantum Key Distribution Application 3: Learning With Errors Further Works References Table of Contents Introduction and Motivation Bunch of Terminology The Leftover Hash Lemma Application 1: Random Number Generation Application 2: Quantum Key Distribution Application 3: Learning With Errors Further Works References I Suppose I have a secret bit string of length 8, b1b2b3 ··· b8. I It doesn’t serve real meaning, just for password purposes. I You do somehow know that b1 6= b2, b2 = b3, b4 = 1. I You want to find my bit string by brute-force. I How many possibilities do you need to check? Introduction I Let’s begin with a simple puzzle :) I How many possibilities do you need to check? Introduction I Let’s begin with a simple puzzle :) I Suppose I have a secret bit string of length 8, b1b2b3 ··· b8. I It doesn’t serve real meaning, just for password purposes. I You do somehow know that b1 6= b2, b2 = b3, b4 = 1. I You want to find my bit string by brute-force. Introduction I Let’s begin with a simple puzzle :) I Suppose I have a secret bit string of length 8, b1b2b3 ··· b8. I It doesn’t serve real meaning, just for password purposes. I You do somehow know that b1 6= b2, b2 = b3, b4 = 1. I You want to find my bit string by brute-force.
    [Show full text]
  • Randomness Extraction and Key Derivation Using the CBC, Cascade and HMAC Modes⋆
    Randomness Extraction and Key Derivation Using the CBC, Cascade and HMAC Modes⋆ Yevgeniy Dodis1, Rosario Gennaro2, Johan H˚astad3, Hugo Krawczyk4, and Tal Rabin2 1 New York University. E:mail: [email protected] 2 IBM Research. E-mail: {rosario,talr}@watson.ibm.com 3 Royal Institute, Sweden. E-mail: [email protected] 4 Technion, Israel, and IBM Research. E-mail: [email protected] Abstract. We study the suitability of common pseudorandomness modes associated with cryptographic hash functions and block ciphers (CBC- MAC, Cascade and HMAC) for the task of “randomness extraction”, namely, the derivation of keying material from semi-secret and/or semi- random sources. Important applications for such extractors include the derivation of strong cryptographic keys from non-uniform sources of ran- domness (for example, to extract a seed for a pseudorandom generator from a weak source of physical or digital noise), and the derivation of pseudorandom keys from a Diffie-Hellman value. Extractors are closely related in their applications to pseudorandom functions and thus it is attractive to (re)use the common pseudoran- dom modes as randomness extractors. Yet, the crucial difference between pseudorandom generation and randomness extraction is that the former uses random secret keys while the latter uses random but known keys. We show that under a variety of assumptions on the underlying primitives (block ciphers and compression functions), ranging from ideal random- ness assumptions to realistic universal-hashing properties, these modes induce good extractors. Hence, these schemes represent a more practical alternative to combinatorial extractors (that are seldom used in prac- tice), and a better-analyzed alternative to the common practice of using SHA-1 or MD5 (as a single un-keyed function) for randomness extraction.
    [Show full text]
  • Seedless Fruit Is the Sweetest: Random Number Generation, Revisited
    Seedless Fruit is the Sweetest: Random Number Generation, Revisited Sandro Coretti∗ Yevgeniy Dodis† Harish Karthikeyan‡ New York University New York University New York University [email protected] [email protected] [email protected] Stefano Tessaro§ University of Washington [email protected] March 25, 2019 Abstract The need for high-quality randomness in cryptography makes random-number generation one of its most fundamental tasks. A recent important line of work (initiated by Dodis et al., CCS '13) focuses on the notion of robustness for pseudorandom number generators (PRNGs) with inputs. These are primitives that use various sources to accumulate sufficient entropy into a state, from which pseudorandom bits are extracted. Robustness ensures that PRNGs remain secure even under state compromise and adversarial control of entropy sources. However, the achievability of robustness inherently depends on a seed, or, alternatively, on an ideal primitive (e.g., a random oracle), independent of the source of entropy. Both assumptions are problematic: seed generation requires randomness to start with, and it is arguable whether the seed or the ideal primitive can be kept independent of the source. This paper resolves this dilemma by putting forward new notions of robustness which enable both (1) seedless PRNGs and (2) primitive-dependent adversarial sources of entropy. To bypass obvious impossibility results, we make a realistic compromise by requiring that the source pro- duce sufficient entropy even given its evaluations of the underlying primitive. We also provide natural, practical, and provably secure constructions based on hash-function designs from com- pression functions, block ciphers, and permutations. Our constructions can be instantiated with minimal changes to industry-standard hash functions SHA-2 and SHA-3, or HMAC (as used for the key derivation function HKDF), and can be downgraded to (online) seedless randomness extractors, which are of independent interest.
    [Show full text]