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《Studies in Complexity and Cryptography (Miscellanea on the Interplay between Randomness and Computation) _Oded Goldreich》介绍
SprngerispartofSpnger Science+Busi tess Media(www.sprnger.com)This volume contains acoll ction of studies in the areas of complexity theory andfoundations of cryptography.These studies were conducted at different timesduring the last couple of decades.Although many of these studies have beenrc ferred to by other works， none of them was formally published beforeIndeed， this volume is quite unusual， and it raises two opposite questionsregarding the publication of the foregoing studies：(1) why were these studiesnot pub ished(formally) before， and(2) why are they being pub ished now?Let me start with the second question.In the years that have elapsed sino ethe completion of many of these individual studies， I have occasionally looked atthem for some reason.On these ncca sions， I felt that it is somewhat inappropriatethat these works were never published formally(although many of them wereposted on forums such as ECCC) .The current vol urn eisai me data mn endingthis situations or new hat.
Turning to the first question， the answer varies according to the case.Re-garding the surveys and the programmatic and/or re fective articles.the answerisquitestraightforward：Thestandardpublicationvenuesforresearchincom-plexity and/or cryptography do not welcome such articles.which muay reflect theunfortunate fact that our community does not hold such articles in high esteem.Regarding the articles that describe research contributions， the answer variesfrom the non-existence of an adequate venue{atleast at the relevant time) ， tounjustified(in retrospect) timid ness regard iug the work.The late publication of some of these articles also raises questions regardingthe relation of the current versions to the original ones.These questions areaddressed at the beginning of each individual article， where the original postingis stated and the nature of the revision is outlined.Ingen ct al， all articles wererevised(based on their last posted version) ， but the revision attempts to preservethe spirit of the original work.In the few cases that later developments sugges sta different perspective and/or technical imn provements， this is stated explicitlywhile comparing the original perspective and/or results with the current oneThe compilation of this volume led me to complete the writing of a couple ofsurveys.In addition， I decided to also include in this volumn ea few rather recentresearch contributions.
The studies in this volume are arranged in three part a.Part I contains 20research contributions， Part II contain 12 surveys(and one overview essay on“Random bess and Computation) ， and Part III contains three progra tn maticand/or reflective articles.Most studies in Part I(and a couple of the studies inPart II) were conducted by me in collaboration with other researchersThe topics addressed in the various studies include average-cae complexity，complexity of approximation， de randomization， expander graphs， hashing func-tions， locally test abl coo des， m nach itcs that take advice， NP-completeness， one-
Prefaceway functions， probabil s tically chock able proofs(PCPs) ， proofs of know lod gr，property testing pseudo randomness， randomness extractors， sampling， trapdoorper in u tations， zero-knowledge and non-interative zero-knowledge(NIZ K) .In-deed， one may say that most of these works belong to the interplay betweenrandomness and computation.Part I：Re sen rch Contributionsl.The Shortest Move-Sequence in the Generalized 15-Puzzle Is NP-Hard2.Proofs of Computational Ability3.On Constructing l-1One-way Functions4.On the Circuit Complexity of Perfect Hashing5.Collision-Free Hashing from Lattice Problems6.Another Proof that BPP I：Contained in PH(and More)7.Strong Proofs of Knowledge8.Simplified De randomization of BPP Using a Hitting Set Generator9.On Testing Expansion in Bounded-Degree Graphs10.A Candidate One Way Functions Based on Expander Graphsll.The FG LSS-Reduction and Minimum Vertex Cover in Hypergraphs12.The GGM Construction Docs NOT Yi cld Correlation In tract ablity13.On Logarithmic Versus Single-Bit Advice14.On Prn of s Of Knowledge：Probabil tic Versus Deter mn in stic Provers15.On the Average Case Complexity of Property Testing16.A Candidate Counterexample to the Easy Cylinders Conjecture17.From Absolute Distinguish ability to Positive Distinguish ability18.Testing Graph Blow-Up19.Proximity Oblivious Testing and the Role of In variances20.In a World of P=BPPPart II：Sure ys1.On Levin's Theory of Average-Case Complexity2.On Three X OR-Lemmas3.On Yao'sX OR-Lemma4.A Sample of Samplers-A Computational Perspective on Sampling5.Short Locally Testable Codes and Pra of：6.Bravely， Moderately：A Common Theme in Four Recent Results7.On the Complexity of Computational Problems Regarding Distributions8.On Basing Non-Interactive Zero-Knowledge on Trapdoor Permutations9.Average Case Complexity， Revisited10.Basic Farts Ah out Expander Graphs11.A Brief Introduction to Property Testing12.Introduction to Testing Graph PropertiesPart IIi：Progr mnn atic and Reflective Articles1.On Security Preserving Reductions-A Suggested Terminology2.Contemplations on Testing Graph Properties3.Another Motivation for Reducing the Rau dom ness Complexity of AlgorithmsI am grateful to all of my co-authors of the papers included in the currentvolume：Lido rAvi gad， Mihir Bell are.Z vika Braker ski.Shaf Goldwasser.ShaiHalevi， Tali Kaufman， Leonid Levin， Noam Nisan， Dana Ron， MadhuSudan，Luca Trevisan.Salil V adhan， Avi Wig der a on.and David Zuckerman.In add i-tion.I wish to thank all resc archers who have contributed to the rc search beingsurveyed in this volume.
《Studies in Complexity and Cryptography (Miscellanea on the Interplay between Randomness and Computation) _Oded Goldreich》目录
Simpli fed De randmizatin f BPP Using a Hitting Set Generatr.
ded Gldreich.Sull V adhan， and Aui Wigdersn
n Test ig Expansin in Bunded-Degree Graphs.68
ded Gldreich and Dana Rn
Candidate ne-Way Functins Based n Expander Graph 8.76
de il Gldreich
Using the FG LSS-Reductin t Prve In apprx im ablity Results fr
Minimum Vertex Cver in Hypergraphs-.88
ded Gldreich
The GGM Cnstructin Des NT Yield Crrelatin Intractable
Functin Ensembles，98
ded Gldreich
Frm Lg art hmic Advice t Single-Bit Advice.109
ded Gldreich， MadhuSudan， and Luca Trec is an
n Prbabilistic yers us Deterministic Prvers in the De initin f
Prfs f Knw lei lge.
MshirBelareanddnlGl reich
n the Average-Case Cmplexity f Prperty Testing.
ded Gldreich
A Candidate Cunterexample t the Easy CyideraCujecture.
ded Gldreich
Frm AbslteDistinguih ability t Psitive Ds tinguish abit y.
Z vika Braker ski and ded Gldreich
Testing Graph Blw-Up：-
Lid r Arg ad and ded Gldreich
Prximity blivius Testing and the Rle f In variances.
ded Gldreich and TaliKa ufm un
In a Wrld f P=BPP
ded Gld ry ich
Surveys
Ntes n Levins Thery f Average-Case Cmplexity，
ded Gldreich
Three X R-Lemmas—An Expsitin.
ded Gld rich
n Ya sX R-Lemma.
ded Gldreich， Nam Na sun， and Az i Wigdersn
A Sample f Samplers.A Cmputatinal Perspective n Sampling.
ded Gldreich
Shrt Lcally Testable Cdes and Prfs.
ded Gldreich
Bravely， Mde rat cly：A Cmmn Theme in Fur Recent Wrks.
ded Gldreich
n the Cmplexity f Cmputatinal Prblems Regarding
Distributins.
ded Gldreich undSulilVadhan
Basing Nn-Interactive Zer-Knwledge n(Enhanced) Trapdr
Permutatins：The State f the Art.
ded Gldreich
Average Case Cmplexity， Revisited.
ded Gldreich
Basic Facts abut Expander Graphs.
ded Gldreich
A Brief Intrductin t Prperty Testing.
ded Gldreich
Intrductin t Test ig Graph Prperties
ded Gldreich
Randmness and Cmputatin.
ded Gldreich
Prgrammatic and Reflective Articles
n Security Preserving Reductins-Revised Terminlgy.
ded Gldreich
Cntemplatins n Testing Graph Prper tics.
ded Gld rich
Anthe