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Pseudorandomness from Shrinkage

Russell Impagliazzo, Raghu Meka, David Zuckerman
2012 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science  
One powerful theme in complexity theory and 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.  ... 
doi:10.1109/focs.2012.78 dblp:conf/focs/ImpagliazzoMZ12 fatcat:qnmowrrq2vbq7h3g2gnemdfrxa

Negation-limited formulas

Siyao Guo, Ilan Komargodski
2017 Theoretical Computer Science  
As a result, the 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.  ... 
doi:10.1016/j.tcs.2016.11.027 fatcat:lvawujcwtbegxkixyxuhy3tzzy

Locally Computable UOWHF with Linear Shrinkage

Benny Applebaum, Yoni Moses
2016 Journal of Cryptology  
However, this construction suffers 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  ... 
doi:10.1007/s00145-016-9232-x fatcat:o6n6pjucuremla3d2csjrnihty

Locally Computable UOWHF with Linear Shrinkage [chapter]

Benny Applebaum, Yoni Moses
2013 Lecture Notes in Computer Science  
However, this construction suffers 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  ... 
doi:10.1007/978-3-642-38348-9_29 fatcat:zhgfefzzyjdela747zuhtzr46e

A Remark on One-Wayness versus Pseudorandomness [chapter]

Periklis A. Papakonstantinou, Guang Yang
2012 Lecture Notes in Computer Science  
to be tight for 1-1 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 .  ... 
doi:10.1007/978-3-642-32241-9_41 fatcat:7vaynrvfbrfvbfandixyymo2k4

Circuit Lower Bounds for MCSP from Local Pseudorandom Generators

Mahdi Cheraghchi, Valentine Kabanets, Zhenjian Lu, Dimitrios Myrisiotis
2020 ACM Transactions on Computation Theory  
ACM Subject Classification Theory of computation → Circuit complexity; Theory of computation → 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.  ... 
doi:10.1145/3404860 fatcat:eeqmy7heabbsxcosw7yb7kjq6u

Small Bias Requires Large Formulas

Andrej Bogdanov, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
ACM Subject Classification Theory of computation → Circuit complexity, Theory of computation → 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.  ... 
doi:10.4230/lipics.icalp.2018.22 dblp:conf/icalp/Bogdanov18 fatcat:avdco4psyjanznkhnbutx73wui

Mining Circuit Lower Bound Proofs for Meta-Algorithms

Ruiwen Chen, Valentine Kabanets, Antonina Kolokolova, Ronen Shaltiel, David Zuckerman
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 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.  ... 
doi:10.1007/s00037-015-0100-0 fatcat:r625fgu375arxokmoistrnflgu

Mining Circuit Lower Bound Proofs for Meta-algorithms

Ruiwen Chen, Valentine Kabanets, Antonina Kolokolova, Ronen Shaltiel, David Zuckerman
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 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.  ... 
doi:10.1109/ccc.2014.34 dblp:conf/coco/ChenKKSZ14 fatcat:7sv5lgqvh5he7h2x7k4i67auj4

Cryptographic Hardness of Random Local Functions–Survey [chapter]

Benny Applebaum
2013 Lecture Notes in Computer Science  
In particular, we will survey known attacks and hardness results, discuss different flavors of hardness (one-wayness, 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.  ... 
doi:10.1007/978-3-642-36594-2_33 fatcat:cnghkimszra2ljkp7ersxiwgoq

The exact complexity of pseudorandom functions and the black-box natural proof barrier for bootstrapping results in computational complexity

Zhiyuan Fan, Jiatu Li, Tianqi Yang
2022 Symposium on the Theory of Computing  
This paper provides answers to this problem on 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.  ... 
doi:10.1145/3519935.3520010 dblp:conf/stoc/FanL022 fatcat:axkbbap6tbf3bd7456k7lgsahq

Collision Resistant Hashing from Learning Parity with Noise [article]

Yu Yu, Jiang Zhang, Jian Weng, Chun Guo, Xiangxue Li
2017 IACR Cryptology ePrint Archive  
(ITCS 2017), we introduce a general construction of CRH 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.  ... 
dblp:journals/iacr/0001ZWGL17 fatcat:g4xhcnglkbaxbdkznvvntfxhs4

Data Randomization Scheme for Endurance Enhancement and Interference Mitigation of Multilevel Flash Memory Devices

Jaewon Cha, Sungho Kang
2013 ETRI Journal  
Accordingly, the endurance phenomenon can be mitigated through analysis of interference that causes tech 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.  ... 
doi:10.4218/etrij.13.0212.0273 fatcat:tt6l5bv4gfbxtoq2pscqpqlnp4

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 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  ... 
doi:10.22237/jmasm/1288584000 fatcat:metuga5wtncadp253kb2wp6eda

Shrinkage of Decision Lists and DNF Formulas [article]

Benjamin Rossman
2020 arXiv   pre-print
We establish nearly tight bounds on the expected 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  ... 
arXiv:2012.05132v2 fatcat:a7cxvfjit5ca3dqq75c3mpgeny
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