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Pseudorandomness from Shrinkage

2012
*
2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
*

One powerful theme in complexity theory and

doi:10.1109/focs.2012.78
dblp:conf/focs/ImpagliazzoMZ12
fatcat:qnmowrrq2vbq7h3g2gnemdfrxa
*pseudorandomness*in the past few decades has been the use lower bounds to give*pseudorandom*generators (PRGs). ... More specifically, say that a circuit family has*shrinkage*exponent Γ if a random restriction leaving a p fraction of variables unset shrinks the size of any circuit in the family by a factor of p Γ+o( ... In this section, we show that even*pseudorandom*restrictions using n o(1) random bits achieve essentially the same*shrinkage*with high probability. This will be shown in Lemmas 4.2, 4.8. ...##
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Negation-limited formulas

2017
*
Theoretical Computer Science
*

As a result, the

doi:10.1016/j.tcs.2016.11.027
fatcat:lvawujcwtbegxkixyxuhy3tzzy
*shrinkage*exponent of formulas that contain a constant number of negation gates is equal to the*shrinkage*exponent of monotone formulas. ... Following Guo et al., we study how many negations are required to implement cryptographic primitives using formulas, and provide lower bounds for*pseudorandom*functions, one-way permutations, hardcore ...*Pseudorandom*Functions In this section we study the negation-limited complexity of*pseudorandom*functions. ...##
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Locally Computable UOWHF with Linear Shrinkage

2016
*
Journal of Cryptology
*

However, this construction suffers

doi:10.1007/s00145-016-9232-x
fatcat:o6n6pjucuremla3d2csjrnihty
*from*two limitations: (1) It can only achieve a sub-linear*shrinkage*of n − m = n 1− ; and (2) It has a super-constant input locality, i.e., some inputs influence a large ... This leaves open the question of realizing UOWHFs with constant output locality and linear*shrinkage*of n − m = n, or UOWHFs with constant input locality and minimal*shrinkage*of n − m = 1. ... Interestingly, Theorem 1 can be proved under the (possibly weaker) assumption that F P,n,m=O(n) is a weak*pseudorandom*generator (i.e., its output cannot be distinguished*from*truly random string with ...##
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Locally Computable UOWHF with Linear Shrinkage
[chapter]

2013
*
Lecture Notes in Computer Science
*

However, this construction suffers

doi:10.1007/978-3-642-38348-9_29
fatcat:zhgfefzzyjdela747zuhtzr46e
*from*two limitations: (1) It can only achieve a sub-linear*shrinkage*of n − m = n 1− ; and (2) It has a super-constant input locality, i.e., some inputs influence a large ... As an additional contribution, we obtain new locally-computable hardness amplification procedures for UOWHFs that preserve linear*shrinkage*. 1 We note that standard transformations*from*one-way functions ... Interestingly, Theorem 1 can be proved under the (possibly weaker) assumption that F P,n,m=O(n) is a weak*pseudorandom*generator (i.e., its output cannot be distinguished*from*truly random string with ...##
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A Remark on One-Wayness versus Pseudorandomness
[chapter]

2012
*
Lecture Notes in Computer Science
*

to be tight for 1-1

doi:10.1007/978-3-642-32241-9_41
fatcat:7vaynrvfbrfvbfandixyymo2k4
*pseudorandom*generators. ... Every*pseudorandom*generator is in particular a one-way function. If we only consider part of the output of the*pseudorandom*generator is this still one-way? ...*From*this point on, x (z, h 0 ) is uniquely defined and constant*from*z and h 0 . ...##
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Circuit Lower Bounds for MCSP from Local Pseudorandom Generators

2020
*
ACM Transactions on Computation Theory
*

ACM Subject Classification Theory of computation → Circuit complexity; Theory of computation →

doi:10.1145/3404860
fatcat:eeqmy7heabbsxcosw7yb7kjq6u
*Pseudorandomness*and derandomization ... We improve several circuit lower bounds for MCSP, using*pseudorandom*generators (PRGs) that are local; a PRG is called local if its output bit strings, when viewed as the truth table of a Boolean function ... Lemma 21 ( 21*Pseudorandom**shrinkage*lemma, Lemma 4.8 of [10] 4 ). There exists a constant c 0 > 0 such that the following holds. ...##
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Small Bias Requires Large Formulas

2018
*
International Colloquium on Automata, Languages and Programming
*

ACM Subject Classification Theory of computation → Circuit complexity, Theory of computation →

doi:10.4230/lipics.icalp.2018.22
dblp:conf/icalp/Bogdanov18
fatcat:avdco4psyjanznkhnbutx73wui
*Pseudorandomness*and derandomization Keywords and phrases formula lower bounds, natural proofs,*pseudorandomness*... The following*shrinkage*property of formulas follows immediately*from*linearity of expectation: Claim 2. Assume f : {0, 1} n → {0, 1} has formula size s. ... The proofs of [10, 18, 28] rely on*shrinkage*of a random restriction, the one of [8] on simultaneous*shrinkage*of multiple restrictions, while [13, 14, 27] use high probability*shrinkage*. ...##
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Mining Circuit Lower Bound Proofs for Meta-Algorithms

2015
*
Computational Complexity
*

We show that circuit lower bound proofs based on the method of random restrictions yield non-trivial compression algorithms for "easy" Boolean functions

doi:10.1007/s00037-015-0100-0
fatcat:r625fgu375arxokmoistrnflgu
*from*the corresponding circuit classes. ... We use this*shrinkage*result to get both compression and #SAT algorithms for (de Morgan) formulas of size about n 2 . ... [26] proved a version of*shrinkage*result with respect to certain*pseudorandom*restrictions, in order to construct a non-trivial*pseudorandom*generator for small de Morgan formulas. ...##
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Mining Circuit Lower Bound Proofs for Meta-algorithms

2014
*
2014 IEEE 29th Conference on Computational Complexity (CCC)
*

We show that circuit lower bound proofs based on the method of random restrictions yield non-trivial compression algorithms for "easy" Boolean functions

doi:10.1109/ccc.2014.34
dblp:conf/coco/ChenKKSZ14
fatcat:7sv5lgqvh5he7h2x7k4i67auj4
*from*the corresponding circuit classes. ... We use this*shrinkage*result to get both compression and #SAT algorithms for (de Morgan) formulas of size about n 2 . ... [26] proved a version of*shrinkage*result with respect to certain*pseudorandom*restrictions, in order to construct a non-trivial*pseudorandom*generator for small de Morgan formulas. ...##
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Cryptographic Hardness of Random Local Functions–Survey
[chapter]

2013
*
Lecture Notes in Computer Science
*

In particular, we will survey known attacks and hardness results, discuss different flavors of hardness (one-wayness,

doi:10.1007/978-3-642-36594-2_33
fatcat:cnghkimszra2ljkp7ersxiwgoq
*pseudorandomness*, collision resistance, public-key encryption), and mention applications ... Acknowledgement This survey originates*from*two talks given at Oberwolfach Workshop for Computational Complexity (2012) and at The Tenth Theory of Cryptography Conference (TCC 2013). ...*Pseudorandomness**from*One-wayness The work of [7] relates the*pseudorandomness*of random local functions to the difficulty of inverting them. ...##
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The exact complexity of pseudorandom functions and the black-box natural proof barrier for bootstrapping results in computational complexity

2022
*
Symposium on the Theory of Computing
*

This paper provides answers to this problem on

doi:10.1145/3519935.3520010
dblp:conf/stoc/FanL022
fatcat:axkbbap6tbf3bd7456k7lgsahq
*pseudorandom*functions (PRFs). ... We note that the*pseudorandom*generator in [29] essentially follows*from*the*shrinkage*exponent of 𝑈 2 formulas [25, 53] . ... lower bound*from*polynomial method [48, 50] and Andreev's function lower bounds*from**shrinkage*exponent [3, 25, 53] ) do not induce such efficient PRF distinguishers. ...##
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Collision Resistant Hashing from Learning Parity with Noise
[article]

2017
*
IACR Cryptology ePrint Archive
*

(ITCS 2017), we introduce a general construction of CRH

dblp:journals/iacr/0001ZWGL17
fatcat:g4xhcnglkbaxbdkznvvntfxhs4
*from*LPN for various parameter choices. ... The Learning Parity with Noise (LPN) problem has recently found many cryptographic applications such as authentication protocols,*pseudorandom*generators/functions and even asymmetric tasks including public-key ... That is, LPN-based PKE uses*pseudorandom*public keys (so that one can efficiently fake random public keys that are computationally indistinguishable*from*real ones) and in this scenario Gertner et al. ...##
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Data Randomization Scheme for Endurance Enhancement and Interference Mitigation of Multilevel Flash Memory Devices

2013
*
ETRI Journal
*

Accordingly, the endurance phenomenon can be mitigated through analysis of interference that causes tech

doi:10.4218/etrij.13.0212.0273
fatcat:tt6l5bv4gfbxtoq2pscqpqlnp4
*shrinkage*. ... An on-chip*pseudorandom*generator composed of an address-based seed location decoder is developed and evaluated with respect to uniformity. ... Conclusion Lack of endurance for flash memory is a serious problem that causes tech*shrinkage*. ...##
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Front Matter

2010
*
Journal of Modern Applied Statistical Methods
*

Mundfrom
Exploratory Factor Analysis on
Dichotomous Data
369 -378
Marcelo Angelo Cirillo,
Generalized Variances Ratio Test for
Daniel Furtado Ferreira, Comparing k Covariance Matrices

doi:10.22237/jmasm/1288584000
fatcat:metuga5wtncadp253kb2wp6eda
*from*Thelma ... Factors 536 -546 Anton Abdulbasah Kamil, Maximum Downside Semi Deviation Adli Mustafa, Stochastic Programming for Portfolio Khilpah Ibrahim Optimization Problem 547 -557 Gyan Prakash On Bayesian*Shrinkage*... exact, and approximate randomization methods, and (3) applications of computer programming, preferably in Fortran (all other programming environments are welcome), related to statistical algorithms,*pseudorandom*...##
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Shrinkage of Decision Lists and DNF Formulas
[article]

2020
*
arXiv
*
pre-print

We establish nearly tight bounds on the expected

arXiv:2012.05132v2
fatcat:a7cxvfjit5ca3dqq75c3mpgeny
*shrinkage*of decision lists and DNF formulas under the p-random restriction 𝐑_p for all values of p ∈ [0,1]. ... For Boolean functions f, we obtain the same*shrinkage*bound with respect to DNF formula size plus 1 (i.e., replacing DL(·) with DNF(·)+1 on both sides of the inequality). ... Very interesting recent work of Filmus, Meir and Tal [6] extends the technique of Håstad [11] to obtain p 2−o(1) factor*shrinkage*bounds for DeMorgan formulas under a family of*pseudorandom*projections ...
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