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Projective Arithmetic Functional Encryption and Indistinguishability Obfuscation from Degree-5 Multilinear Maps [chapter]

Prabhanjan Ananth, Amit Sahai
<span title="">2017</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this work, we propose a variant of functional encryption called projective arithmetic functional encryption (PAFE).  ...  . iO from degree-5 multilinear maps.  ...  multilinear maps. iO from degree-5 multilinear maps.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-56620-7_6">doi:10.1007/978-3-319-56620-7_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/57btx65zkvcadfnleohwevgovq">fatcat:57btx65zkvcadfnleohwevgovq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170710165301/http://eprint.iacr.org/2016/1097.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1c/f4/1cf4f34f6060d1f398c8235679b97a2a989f7861.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-56620-7_6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Constraining Pseudorandom Functions Privately [chapter]

Dan Boneh, Kevin Lewi, David J. Wu
<span title="">2017</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Our first construction uses indistinguishability obfuscation and achieves our strongest notions of functionality and privacy.  ...  We also give two constructions based on concrete assumptions on multilinear maps which achieve slightly weaker notions of privacy and for more limited classes of constraints: namely, for the class of bit-fixing  ...  Acknowledgments This work was funded by NSF, DARPA, a grant from ONR, the Simons Foundation, and an NSF Graduate Research Fellowship.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-54388-7_17">doi:10.1007/978-3-662-54388-7_17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lu5msiz6pvcg7cudife5adpr4a">fatcat:lu5msiz6pvcg7cudife5adpr4a</a> </span>
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How to Obfuscate Programs Directly [chapter]

Joe Zimmerman
<span title="">2015</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
From "clean" multilinear maps, on the other hand (whose existence is still open), we present the first approach that would achieve obfuscation for P/poly directly, without FHE.  ...  Our scheme works either with "noisy" multilinear maps, which can only evaluate expressions of degree λ c for pre-specified constant c; or with "clean" multilinear maps, which can evaluate arbitrary expressions  ...  [GLSW14] constructs indistinguishability obfuscation (iO) from composite-order multilinear maps.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-46803-6_15">doi:10.1007/978-3-662-46803-6_15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6wnoonhj6feblo65oi4xwkxlpu">fatcat:6wnoonhj6feblo65oi4xwkxlpu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160309215024/http://eprint.iacr.org/2014/776.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/93/7793fac0ec69cbe036cd3085c83a18b305e407cb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-46803-6_15"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Indistinguishability Obfuscation from SXDH on 5-Linear Maps and Locality-5 PRGs [chapter]

Huijia Lin
<span title="">2017</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Two recent works [Lin, EUROCRYPT 2016, Lin and Vaikuntanathan, FOCS 2016] showed how to construct Indistinguishability Obfuscation (IO) from constant degree multilinear maps.  ...  In this work, we reduce the degree of multilinear maps needed to 5, by giving a new construction of IO from asymmetric L-linear maps and a pseudo-random generator (PRG) with output locality L and polynomial  ...  The author thanks Benny Applebaum, Nir Bitansky, Stefano Tessaro, and Vinod Vaikuntanathan for many helpful and insightful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-63688-7_20">doi:10.1007/978-3-319-63688-7_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zyatiaqpqrfgffjt6xfff55twi">fatcat:zyatiaqpqrfgffjt6xfff55twi</a> </span>
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Indistinguishability Obfuscation from DDH-Like Assumptions on Constant-Degree Graded Encodings

Huijia Lin, Vinod Vaikuntanathan
<span title="">2016</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v4uclqixrrhlnk5pbw4wii6cfq" style="color: black;">2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)</a> </i> &nbsp;
This narrows the gap between the mathematical objects that exist (bilinear maps, from elliptic curve groups) and ones that suffice to construct general purpose indistinguishability obfuscation.  ...  and Lin, EUROCRYPT 2016), or polynomial families of assumptions on graded encoding schemes with a high polynomial degree/multilinearity (e.g., Gentry, Lewko, Sahai and Waters, FOCS 2014).  ...  Huijia Lin was partially supported by NSF grants CNS-1528178 and CNS-1514526. Vinod Vaikuntanathan was supported by NSF Grants CNS-1350619 and CNS-1414119 and by the U.S.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/focs.2016.11">doi:10.1109/focs.2016.11</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/focs/LinV16.html">dblp:conf/focs/LinV16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4ht5vc7b55ehphb2vrc24xkneq">fatcat:4ht5vc7b55ehphb2vrc24xkneq</a> </span>
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Pairing for Greenhorn: Survey and Future Perspective [article]

Mahender Kumar, Satish Chand
<span title="2021-08-27">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Additionally, we discuss the extension of bilinear pairing to tri-linear and multilinear pairing and discuss a few assumptions to check their feasibility to implement multilinear pairing.  ...  Pairing is the most powerful tool in cryptography that maps two points on the elliptic curve to the group over the finite field.  ...  One could say that multilinear maps are at the heart of indistinguishability obfuscation, witness encryption, multiparty key exchanges, among many other applications.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.12392v1">arXiv:2108.12392v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lpwnif5f5vaxzcapdtqda76aca">fatcat:lpwnif5f5vaxzcapdtqda76aca</a> </span>
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Garbled Circuits as Randomized Encodings of Functions: a Primer [chapter]

Benny Applebaum
<span title="">2017</span> <i title="Springer International Publishing"> Tutorials on the Foundations of Cryptography </i> &nbsp;
In this tutorial, we study garbled circuits from a foundational point of view under the framework of randomized encoding (RE) of Functions.  ...  We review old and new constructions of REs, present some lower-bounds, and describe some applications.  ...  [46, 14] , software protection [55, 58, 25] , functional encryption [83, 56] , key-dependent message security [19, 2] , code obfuscation [5, 38] , and others.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-57048-8_1">doi:10.1007/978-3-319-57048-8_1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hb2wsmjvvbgx7i62r6ibpv6jiu">fatcat:hb2wsmjvvbgx7i62r6ibpv6jiu</a> </span>
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Implementing Conjunction Obfuscation Under Entropic Ring LWE

David Bruce Cousins, Giovanni Di Crescenzo, Kamil Doruk Gur, Kevin King, Yuriy Polyakov, Kurt Rohloff, Gerard W. Ryan, Erkay Savas
<span title="">2018</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/inod5dqjxfdj3bnjykkklcg7d4" style="color: black;">2018 IEEE Symposium on Security and Privacy (SP)</a> </i> &nbsp;
satisfy Indistinguishability Obfuscation (IO), a weaker security model.  ...  Conjunction programs evaluate functions f (x1, . . . , xL) = i∈I yi, where yi is either xi or ¬xi and I ⊆ [L], and can be used as classifiers.  ...  of non-trivial obfuscators based on IO via multilinear maps [25] , [26] , [27] or the heuristic techniques not derived from the computational hardness of mathematical problems [2] , [3] , [4] ,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sp.2018.00007">doi:10.1109/sp.2018.00007</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/sp/CousinsCGKPRRS18.html">dblp:conf/sp/CousinsCGKPRRS18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tokd33t7xnbbvp2jwooksxrqce">fatcat:tokd33t7xnbbvp2jwooksxrqce</a> </span>
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Function-Hiding Inner Product Encryption Is Practical [chapter]

Sam Kim, Kevin Lewi, Avradip Mandal, Hart Montgomery, Arnab Roy, David J. Wu
<span title="">2018</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In a functional encryption scheme, secret keys are associated with functions and ciphertexts are associated with messages.  ...  We then show that function privacy enables a number of applications in biometric authentication, nearest-neighbor search on encrypted data, and single-key two-input functional encryption for functions  ...  Acknowledgments This work was supported by NSF, DARPA, the Simons foundation, a grant from ONR, and an NSF Graduate Research Fellowship.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-98113-0_29">doi:10.1007/978-3-319-98113-0_29</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3f6jf3igaza23nid3qgnzblbgq">fatcat:3f6jf3igaza23nid3qgnzblbgq</a> </span>
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Dual System Framework in Multilinear Settings and Applications to Fully Secure (Compact) ABE for Unbounded-Size Circuits [chapter]

Nuttapong Attrapadung
<span title="">2017</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Unbounded-size Circuits and Succinctness. It is desirable for new fully secure schemes to preserve functionalities and efficiency from previous selectively secure systems.  ...  We propose a new generic framework for constructing fully secure attribute based encryption (ABE) in multilinear settings. It is applicable in a generic manner to any predicates.  ...  Unfortunately, these candidates (and their variants, notably CLT15 [22] ) were later shown to be broken [17, 21, 18] . 5 As an alternative approach, multilinear maps based on indistinguishability obfuscation  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-54388-7_1">doi:10.1007/978-3-662-54388-7_1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x767dmtlmnbgbbkxumoyujjtga">fatcat:x767dmtlmnbgbbkxumoyujjtga</a> </span>
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Pseudorandom Functions: Three Decades Later [chapter]

Andrej Bogdanov, Alon Rosen
<span title="">2017</span> <i title="Springer International Publishing"> Tutorials on the Foundations of Cryptography </i> &nbsp;
Puncturable PRFs have also been recently combined with indistinguishability obfuscation to exhibit hard on the average instances for the complexity classses PPAD [33, 60] and CLS [76] .  ...  The recently introduced notion of puncturable PRFs, in conjunction with indistinguishability obfuscation, has found applications for the construction of strong cryptographic primitives, and demonstrates  ...  Last but not least, thanks to Yehuda Lindell for this wonderful initiative and for confidently steering the project into safe harbor. Alon Rosen's work on this project was supported by ISF grant no.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-57048-8_3">doi:10.1007/978-3-319-57048-8_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dwdqcxanardkthw4oon7qn7aia">fatcat:dwdqcxanardkthw4oon7qn7aia</a> </span>
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Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves [article]

Dan Boneh and Darren Glass and Daniel Krashen and Kristin Lauter and Shahed Sharif and Alice Silverberg and Mehdi Tibouchi and Mark Zhandry
<span title="2018-08-31">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Nevertheless, we show that a cryptographic invariant map can be used to build several cryptographic primitives, including NIKE, that were previously constructed from multilinear maps and indistinguishability  ...  obfuscation.  ...  Acknowledgments We thank the American Institute of Mathematics (AIM) for supporting a workshop on multilinear maps where the initial seeds for this work were developed, and the Banff International Research  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.03038v3">arXiv:1807.03038v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/brihvmwo7jgrbih2br2dcqaz7u">fatcat:brihvmwo7jgrbih2br2dcqaz7u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200911081957/https://arxiv.org/pdf/1807.03038v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/69/51/695156d52b5229fbd72d4514dfdb5a76eebaa86e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.03038v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Order-preserving encryption using approximate common divisors

James Dyer, Martin Dyer, Karim Djemame
<span title="">2019</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ja4pgj75qbelfaa56antrp347a" style="color: black;">Journal of Information Security and Applications</a> </i> &nbsp;
In addition, recent work [22] on recovering the secret parameters of CLT2013 has indicated that encryption schemes based on multilinear maps may not be secure.  ...  s construction uses multilinear maps. However, as stated in Chenette et al. [18] , "The main drawback of the Boneh et al.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201107025920/http://eprints.whiterose.ac.uk/151516/1/order-jisa.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/12/61/1261d64017514aa7c2df02e35a6c8973ad35f805.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jisa.2019.102391"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

D2.3 - GDPR-compliant and Privacy-Preserving Analytics for Healthcare Providers

Suite5, SECURA BV, Tampere University
<span title="2020-05-31">2020</span> <i title="Zenodo"> Zenodo </i> &nbsp;
State of the art analysis on Functional Encryption and the provision of a set of GDPR-compliant analytics that can offer analytics services to providers that have access to encrypted data.  ...  The deliverable also reports on investigated and analytics techniques used by CSPs and Healthcare Providers in order to secure their infrastructures against cyber threats.  ...  [12] propose a candidate indistinguishability obfuscator iO for all polynomial-size log-depth circuits (NC 1 ), using a simplified variant of multilinear maps (i.e. Multilinear Jigsaw Puzzles).  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200928025003/https://zenodo.org/record/4022330/files/ASCLEPIOS%20D2.3%20-%20GDPR-compliant%20and%20Privacy-Preserving%20Analytics%20for%20Healthcare%20Providers.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2c/8d/2c8d892159f7a085763125406e8a1f8f023be96d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.4022329"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> zenodo.org </button> </a>

On the Statistical Leak of the GGH13 Multilinear Map and Some Variants [chapter]

Léo Ducas, Alice Pellet-Mary
<span title="">2018</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
At EUROCRYPT 2013, Garg, Gentry and Halevi proposed a candidate construction (later referred as GGH13) of cryptographic multilinear map (MMap).  ...  Despite weaknesses uncovered by Hu and Jia (EUROCRYPT 2016), this candidate is still used for designing obfuscators.  ...  The authors are grateful to Alex Davidson, Nico Döttling and Damien Stehlé for helpful discussions.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503082349/https://hal.archives-ouvertes.fr/hal-01895645/file/version_eprint.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/90/3c/903c56c0aa5a5a71b17147eac396f1299d956025.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-03326-2_16"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>
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