Pseudorandomness ≈ PseudorandomnessPseudorandomness
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Scrambled Linear Pseudorandom Number Generators Open
F 2 -linear pseudorandom number generators are very popular due to their high speed, to the ease with which generators with a sizable state space can be created, and to their provable theoretical properties. However, they suffer from linea…
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Efficient Quantum Pseudorandomness Open
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g., in computation, communication, and control. Fully random transformations require exponential time for either classical or quantum syst…
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Quantum Cryptography in Algorithmica Open
We construct a classical oracle relative to which P = NP yet single-copy secure pseudorandom quantum states exist. In the language of Impagliazzo's five worlds, this is a construction of pseudorandom states in "Algorithmica," and hence sho…
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A Novel Encryption Algorithm Based on DWT and Multichaos Mapping Open
Encryption of a digital image is very important especially in applications of body area networks (BANs) since the image may include a number of privacy. Past encryption methods have disadvantages of the small key space and low ability of r…
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Locally Covert Learning Open
The goal of a covert learning algorithm is to learn a function f by querying it, while ensuring that an adversary, who sees all queries and their responses, is unable to (efficiently) learn any more about f than they could learn from rando…
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Quantum Pseudorandomness and Classical Complexity Open
We construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom st…
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Scrambled Linear Pseudorandom Number Generators Open
F 2 -linear pseudorandom number generators are very popular due to their high speed, to the ease with which generators with a sizable state space can be created, and to their provable theoretical properties. However, they suffer from linea…
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Pseudorandom Number Generation: Impossibility and Compromise Open
Pseudorandom number generators are widely used in the area of simula- tion. Defective generators are still widely used in standard library programs, although better pseudorandom number generators such as the Mersenne Twister are freely ava…
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A Lightweight Pseudorandom Number Generator for Securing the Internet of Things Open
Lightweight cryptography aims to address the security demands in resource-constrained hardware and software environments, such as the Internet of Things (IoT). These constraints severely limit solutions offered by conventional cryptographi…
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13. MRD codes: constructions and connections Open
This preprint is of a chapter to appear in {\it Combinatorics and finite fields: Difference sets, polynomials, pseudorandomness and applications. Radon Series on Computational and Applied Mathematics}, K.-U. Schmidt and A. Winterhof (eds.)…
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A note on pseudorandom Ramsey graphs Open
For fixed s \ge 3 , we prove that if optimal K_s -free pseudorandom graphs exist, then the Ramsey number r(s,t) is t^{s-1+o(1)} as t \rightarrow \infty . Our method also improves the best lower bounds for r(C_{\ell},t) obtained by Bohman a…
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Pseudorandom hypergraph matchings Open
A celebrated theorem of Pippenger states that any almost regular hypergraph with small codegrees has an almost perfect matching. We show that one can find such an almost perfect matching which is ‘pseudorandom’, meaning that, for instance,…
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Quantum-key-distribution protocol with pseudorandom bases Open
Quantum key distribution (QKD) offers a way for establishing\ninformation-theoretically secure communications. An important part of QKD\ntechnology is a high-quality random number generator (RNG) for quantum states\npreparation and for pos…
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Conspiracies between Learning Algorithms, Circuit Lower Bounds and Pseudorandomness Open
We prove several results giving new and stronger connections between learning, circuit lower bounds and pseudorandomness. Among other results, we show a generic learning speedup lemma, equivalences between various learning models in the ex…
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Design and Test of an Integrated Random Number Generator with All-Digital Entropy Source Open
In the cybersecurity field, the generation of random numbers is extremely important because they are employed in different applications such as the generation/derivation of cryptographic keys, nonces, and initialization vectors. The more u…
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On the arithmetic autocorrelation of the Legendre sequence Open
The Legendre sequence possesses several desirable features of pseudorandomness in view of different applications such as a high linear complexity (profile) for cryptography and a small (aperiodic) autocorrelation for radar, gps, or sonar. …
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Development of Additive Fibonacci Generators with Improved Characteristics for Cybersecurity Needs Open
Pseudorandom sequence generation is used in many industries, including cryptographic information security devices, measurement technology, and communication systems. The purpose of the present work is to research additive Fibonacci generat…
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http://discreteanalysisjournal.com/article/2105-notes-on-nilspaces-algebraic-aspects Open
Notes on nilspaces: algebraic aspects, Discrete Analysis 2017:15, 59 pp. One of the fundamental insights in modern additive combinatorics is that there is a hierarchy of notions of "pseudorandomness" or "higher order Fourier uniformity" th…
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Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality Open
A fundamental issue in the AdS/CFT correspondence is the wormhole growth paradox. Susskind's conjectured resolution of the paradox was to equate the volume of the wormhole with the circuit complexity of its dual quantum state in the CFT. W…
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Derandomizing Quantum Circuits with Measurement-Based Unitary Designs Open
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph stat…
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Entropy Samplers and Strong Generic Lower Bounds For Space Bounded Learning Open
With any hypothesis class one can associate a bipartite graph whose vertices are the hypotheses H on one side and all possible labeled examples X on the other side, and an hypothesis is connected to all the labeled examples that are consis…
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Quantum attacks on Sum of Even-Mansour pseudorandom functions Open
At CRYPTO 2019, constructions of a pseudorandom function from public random permutations were presented. We consider one of the constructions called Sum of Even-Mansour (SoEM), and present quantum attacks against the construction. Our atta…
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Cryptanalysis of the Legendre PRF and Generalizations Open
The Legendre PRF relies on the conjectured pseudorandomness properties of the Legendre symbol with a hidden shift. Originally proposed as a PRG by Damgård at CRYPTO 1988, it was recently suggested as an efficient PRF for multiparty computa…
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Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-Spin System Open
Quantum pseudorandomness, also known as unitary designs, comprises a powerful resource for emergent quantum technologies. Although in theory pseudorandom unitary operators can be constructed efficiently, realizing these objects in realisti…
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Explicit Resilient Functions Matching Ajtai-Linial Open
A Boolean function on n variables is q-resilient if for any subset of at most q variables, the function is very likely to be determined by a uniformly random assignment to the remaining n-q variables; in other words, no coalition of at mos…
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Robustness of average-case meta-complexity via pseudorandomness Open
We show broad equivalences in the average-case complexity of many different meta-complexity problems, including Kolmogorov complexity, time-bounded Kolmogorov complexity, and the Minimum Circuit Size Problem. These results hold for a wide …
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Quantum Pseudoentanglement Open
Entanglement is a quantum resource, in some ways analogous to randomness in classical computation. Inspired by recent work of Gheorghiu and Hoban, we define the notion of "pseudoentanglement", a property exhibited by ensembles of efficient…
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Attacking the linear congruential generator on elliptic curves via lattice techniques Open
In this paper we study the linear congruential generator on elliptic curves from the cryptographic point of view. We show that if sufficiently many of the most significant bits of the composer and of three consecutive values of the sequenc…
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A new pseudorandom bits generator based on a 2D-chaotic system and diffusion property Open
A remarkable correlation between chaotic systems and cryptography has been established with sensitivity to initial states, unpredictability, and complex behaviors. In one development, stages of a chaotic stream cipher are applied to a disc…
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A New Approach to the Development of Additive Fibonacci Generators Based on Prime Numbers Open
Pseudorandom number and bit sequence generators are widely used in cybersecurity, measurement, and other technology fields. A special place among such generators is occupied by additive Fibonacci generators (AFG). By itself, such a generat…