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Complexity of the homomorphism extension problem in the random case
[article]

2012
*
arXiv
*
pre-print

We prove that if A is a large

arXiv:1106.0663v5
fatcat:o5gpi467rzfobdw2zathkg552e
*random*relational structure with at least one relation*of*arity at least 2 then*the**problem*EXT(A) is almost surely NP-complete. ...*The*author would like to thank Libor Barto for suggesting this*problem*. ... Acknowledgments*The*research was supported by*the*GAČR project GAČR 201/09/H012, by*the*Charles University project GA UK 67410 and by*the*grant SVV-2011-263317. ...##
###
Algorithmic aspects of M-Lipschitz mappings of graphs
[article]

2018
*
arXiv
*
pre-print

Furthermore, our

arXiv:1801.05496v3
fatcat:sijafagz6ngmjmyhtzxk7xwow4
*problem**of*extending partial mappings is connected to*the**problem**of*list*homomorphism*and yields a better run-time*complexity*for a specific family*of*its instances. ... We study two natural*problems*regarding graph-indexed*random*walks. - Computing*the*maximum range*of*a graph-indexed*random*walk for a given graph. - Deciding if we can extend a partial GI*random*walk ... Acknowledgments This research was supported by*the*Charles University Grant Agency, project GA UK 1158216 and by*the*Center*of*Excellence -ITI (P202/12/G061*of*GAČR). ...##
###
Quantum Query Complexity of Subgraph Isomorphism and Homomorphism
[article]

2015
*
arXiv
*
pre-print

Interestingly,

arXiv:1509.06361v2
fatcat:eydgqkabuvhbhdxdxrwarfnqcu
*the**randomized*bound*of*Ω(α_H · n) for f_H still remains open. We also study*the*Subgraph*Homomorphism**Problem*, denoted by f_[H], and show that Q(f_[H]) = Ω(n). ...*In*this paper we show: Q(f_H) = Ω(√(α_H · n)), where Q(f_H) denotes*the*quantum query*complexity**of*f_H. ...*The*authors also thank Biswaroop Maiti for*the*discussion*in**the*beginning phase*of*this work. ...##
###
Approximation Algorithms for Graph Homomorphism Problems
[chapter]

2006
*
Lecture Notes in Computer Science
*

Multiway uncut can be viewed as a special

doi:10.1007/11830924_18
fatcat:xr642moslnckxjndlgpimcryte
*case**of*prelabeled MGH where one is also given a prelabeling ϕ : U → VH , U ⊆ VG, and*the*output has to be an*extension**of*ϕ . ... We introduce*the*maximum graph*homomorphism*(MGH)*problem*: given a graph G, and a target graph H, find a mapping ϕ : VG → VH that maximizes*the*number*of*edges*of*G that are mapped to edges*of*H. ... Feige gave*the*first inapproximability results for various NP-hard optimization*problems*assuming*the**complexity**of*refuting*random*-3CNF formulas. ...##
###
Efficient and Secure Evaluation of Multivariate Polynomials and Applications
[chapter]

2010
*
Lecture Notes in Computer Science
*

This includes

doi:10.1007/978-3-642-13708-2_15
fatcat:zrp7qxsdgbdsxmzmylxhfzdzum
*the*variants*of*Yao's garbled circuit protocol*in**the*malicious model such as [22, 13]*in**the*twoparty*case*and works such as [17] [18] [19]*in**the*multi-party*case*. ...*in**the*computational*complexity**of**the*original semi-honest protocol. ...*In**case**of*GM encryption we show a simple way*of*extending it to work over any*extension*field*of*GF(2) while preserving its*homomorphic*properties. ...##
###
Page 4273 of Mathematical Reviews Vol. , Issue 83j
[page]

1983
*
Mathematical Reviews
*

From

*the*summary: “We consider*the**case**of*automata operating within*random*environments. ... Frances 83):68056 On*the*average-*case**complexity**of*selecting*the*k th best. SIAM J. Comput. 11 (1982), no. 3, 428-447. ...##
###
Somewhat homomorphic encryption scheme for arithmetic operations on large integers

2012
*
2012 Global Information Infrastructure and Networking Symposium (GIIS)
*

Even though

doi:10.1109/giis.2012.6466769
dblp:conf/giis/PisaAD12
fatcat:qd2v53zpijbcdofnfu22s5ft3a
*the*total number*of*allowed*homomorphic*operations is limited*in*our scheme, our results show that*the*new*extension*is more efficient*in*terms*of*processing and that*the*ratio between*the*...*In*this paper, we propose a new encryption scheme oriented for calculating arithmetic functions*of*large integer numbers. Our proposal is an*extension**of**the*encryption scheme proposed*in*[1]. ... Indeed,*in*our*extension*,*the*noise size is log 2 B times larger, which increases*the**complexity**of**the**problem*. ...##
###
Algebraic and model theoretic methods in constraint satisfaction
[article]

2015
*
arXiv
*
pre-print

This text is related to

arXiv:1507.00931v1
fatcat:gdiqkrt7sbhjfjke4mtqx75uua
*the*tutorials I gave at*the*Banff International Research Station and within a "Doc-course" at Charles University Prague*in**the*fall*of*2014. ... It describes my current research and some*of**the*most important open questions related to it. ... Classify*the**complexity**of*CSP(Γ), for all finite language reducts Γ*of**the**random*partial order.*In*other words, classify*the**complexity**of*Poset-SAT*problems*. ...##
###
Homomorphic Encryption: Theory & Applications
[article]

2013
*
arXiv
*
pre-print

*The*chapter then provides a survey

*of*some

*of*

*the*classical

*homomorphic*encryption schemes existing

*in*

*the*current literature. ...

*The*chapter then introduces

*the*most important and recent research direction

*in*

*the*filed - fully

*homomorphic*encryption. ...

*In*

*case*

*of*symmetric schemes, we introduce a

*random*vector

*in*

*the*encryption process (e.g.,

*in*

*the*pseudo-

*random*generator for stream ciphers, or

*in*

*the*operating mode for block ciphers) -generally called ...

##
###
A Combinatorial Classic — Sparse Graphs with High Chromatic Number
[chapter]

2013
*
Bolyai Society Mathematical Studies
*

Acknowledgment: I thank to Martin Bálek and Andrew Goodall for

doi:10.1007/978-3-642-39286-3_15
fatcat:plrnkchibbdv5jm3jfap4dmk5u
*the*help when preparing this article. ... This is important for*the**complexity**of*algorithms, particularly*in**the*context*of*Constraint Satisfaction*Problems*-CSP: For a given a relational structure H, CSP (H) denotes*the*following decision*problem*...*The**problem**of**the*existence*of*uniquely k-colorable graphs with large girth has an interesting history:*the*triangle-free*case*(i.e. l = 3) was settled*in*[68] and this was improved*in*[31] to graphs ...##
###
Page 481 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

*The*investigation

*of*communication

*complexity*has proved to be very useful

*in*

*the*study

*of*

*complexity*

*of*computing prob- lems

*of*fundamental computing models as well as

*in*

*the*central topic

*of*

*the*

*complexity*... logn) messages, where n is

*the*number

*of*computers

*in*

*the*network. This paper presents a new distributed algorithm for

*the*same

*problem*using 2n? messages

*in*

*the*worst

*case*. ...

##
###
Extending Oblivious Transfer with Low Communication via Key-Homomorphic PRFs
[chapter]

2018
*
Lecture Notes in Computer Science
*

Our main technique is a novel twist on

doi:10.1007/978-3-319-76578-5_19
fatcat:dqrf37o2lrgxjarbhc47w2dvm4
*the*classic OT*extension**of*Ishai et al. (Crypto 2003), using an additively key-*homomorphic*PRF to reduce interaction. ... We present a new approach to extending oblivious transfer with communication*complexity*that is logarithmic*in**the*security parameter. ... I would like to thank Claudio Orlandi for*the*observation that an XOR-*homomorphic*PRG would imply non-interactive OT*extension*, which inspired this work. ...##
###
Polynomial AND homomorphic cryptosystem and applications

2019
*
Science China Information Sciences
*

To solve

doi:10.1007/s11432-018-9789-y
fatcat:qipqsltknbg2rgljcqqm42dq6m
*problems*such as these, we propose a polynomial AND*homomorphic*cryptosystem based on*the*ideal theory*of*abstract algebra;*the*scheme can be obtained from available multiplicatively*homomorphic*... Exploring new*homomorphic*cryptosystems to solve these*problems*is appealing, and is*of*high theoretical and practical significance. ... Acknowledgements This work was supported by National Natural Science Foundation*of*China (Grant No. 62172435). We are deeply grateful to all reviewers. ...##
###
Computational Counting (Dagstuhl Seminar 18341)

2018
*
Dagstuhl Reports
*

A total

doi:10.4230/dagrep.7.8.23
dblp:journals/dagstuhl-reports/BezakovaGJ17
fatcat:yp3oqvgo4fal5lbio5yeqt4uje
*of*43 researchers from all over*the*world, with interests and expertise*in*different aspects*of*computational counting, actively participated*in**the*meeting. ... This report documents*the*program and*the*outcomes*of*Dagstuhl Seminar 17341 "Computational Counting". ... Modular counting provides a rich setting*in*which to study*the*structure*of**homomorphism**problems*.*In*this talk we will discuss*the**complexity**of*counting graph*homomorphisms*modulo 2. ...##
###
Homomorphic Encryption — Theory and Application
[chapter]

2013
*
Theory and Practice of Cryptography and Network Security Protocols and Technologies
*

*In*

*case*

*of*symmetric schemes, we introduce a

*random*vector

*in*

*the*encryption process (e.g.,

*in*

*the*pseudo-

*random*generator for stream ciphers, or

*in*

*the*operating mode for block ciphers)generally called ...

*In*his security analysis

*of*BDD, Gentry has used

*the*best known

*complexity*bound for

*the*approximate shortest vector

*problem*(SVP)

*in*lattices. ... Author details Jaydip Sen * Department

*of*Computer Science, National Institute

*of*Science & Technology, Odisha, India ...

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