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On error distributions in ring-based LWE

Wouter Castryck, Ilia Iliashenko, Frederik Vercauteren
<span title="">2016</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xbreg5du4raqhmwsc3tbnxzgmu" style="color: black;">LMS Journal of Computation and Mathematics</a> </i> &nbsp;
We give a comparison of these versions, and revisit some unfortunate choices that have been made in the recent literature, one of which is scaling up by${|\unicode[STIX]{x1D6E5}_{K}|}^{1/2n}$with$\unicode  ...  This has led to various non-dual variants of ring-LWE, in which one compensates for the non-duality by scaling up the errors.  ...  The following example, introduced in [11] and revisited in [4] , illustrates this.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1112/s1461157016000280">doi:10.1112/s1461157016000280</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/haypgf6brfa4dkravdpfmvitlq">fatcat:haypgf6brfa4dkravdpfmvitlq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180727012224/https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C852C8D1C2F84DA398EA07D2B2F3E4CB/S1461157016000280a.pdf/div-class-title-on-error-distributions-in-ring-based-lwe-div.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/5a/31/5a31f411cbcc0928a64117fef2937493f271e900.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1112/s1461157016000280"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Polly Cracker, Revisited [chapter]

Martin R. Albrecht, Pooya Farshim, Jean-Charles Faugère, Ludovic Perret
<span title="">2011</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;
Furthermore, we show that a large class of algebraic transformations cannot convert this scheme to a fully secure Polly-Cracker-style scheme.  ...  These problems can be seen as natural generalisations of the LWE problem and the approximate GCD problem over polynomial rings.  ...  structured) non-linear noise-free systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-25385-0_10">doi:10.1007/978-3-642-25385-0_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/osym22c3arcmjiqrdmebsmpuym">fatcat:osym22c3arcmjiqrdmebsmpuym</a> </span>
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Decentralized Ciphertext-Policy Attribute-Based Encryption: A Post-Quantum Construction

Mohammad Shahriar Rahman, Anirban Basu, Shinsaku Kiyomoto
<span title="">2017</span> <i title="Innovative Information Science &amp; Technology Research Group (ISYOU)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7hlkkmw3qjhrnliyaattoye5ty" style="color: black;">Journal of Internet Services and Information Security</a> </i> &nbsp;
We utilize Learning With Errors over Rings (R-LWE) as the underlying hardness assumption for te protocol.  ...  Any user can encrypt data in terms of any monotone access structure over attributes issued from any chosen set of authorities. Hence the protocol does not depend on any central authority.  ...  It is also more efficient than the LWE-based schemes due to the algebraic structure of R-LWE. • The protocol supports any monotone access policy (both AND and OR) that can be expressed as a Linear Secret  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22667/jisis.2017.08.31.001">doi:10.22667/jisis.2017.08.31.001</a> <a target="_blank" rel="external noopener" href="https://doaj.org/article/04cc0011b8de4a709591897a6ebf317a">doaj:04cc0011b8de4a709591897a6ebf317a</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4z72aw6vencxbjs3m54u2udas4">fatcat:4z72aw6vencxbjs3m54u2udas4</a> </span>
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Cryptography Core Technology [chapter]

Chen-Mou Cheng, Kenta Kodera, Atsuko Miyaji, Shinya Okumura
<span title="">2020</span> <i title="Springer Singapore"> Security Infrastructure Technology for Integrated Utilization of Big Data </i> &nbsp;
Another is analysis to learning with error (LWE), which is a postquantum cryptosystem and has the functionality of homomorphic encryption.  ...  That is, E is a plane algebraic curve defined by the equation y 2 = x 3 + ax + b for a, b ∈ F p n such that = −16(4a 3 + 27b 2 ) = 0.  ...  The main difference between K and Z is the algebraic structures of their rings of integers modulo p.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-981-15-3654-0_2">doi:10.1007/978-981-15-3654-0_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l5avyfoh6vgwffotnijyxauwq4">fatcat:l5avyfoh6vgwffotnijyxauwq4</a> </span>
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LWR-Based Fully Homomorphic Encryption, Revisited

Fucai Luo, Fuqun Wang, Kunpeng Wang, Jie Li, Kefei Chen
<span title="">2018</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sdme5pnua5auzcsjgqmqefb66m" style="color: black;">Security and Communication Networks</a> </i> &nbsp;
Furthermore, we also extend the LWR-based FHE scheme to the multikey setting using the tricks used to construct LWE-based multikey FHE by Mukherjee and Wichs at Eurocrypt 2016.  ...  the simple algebraic structure of the well-studied LWE [14] and classical (quantum) reduction from some apparently intractable lattice problems (e.g., GapSVP) to LWE [14, 15] .  ...  The search problem of LWE , , , is aim to find secret s given independent samples from LWE , , , (s) (for s ∈ Z ). The LWE , , , assumption is that the LWE , , , problem is infeasible.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2018/5967635">doi:10.1155/2018/5967635</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z3v6d7gsonbsvbrtkek66v7yym">fatcat:z3v6d7gsonbsvbrtkek66v7yym</a> </span>
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Practical Cryptanalysis of a Public-Key Encryption Scheme Based on New Multivariate Quadratic Assumptions [chapter]

Martin R. Albrecht, Jean-Charles Faugére, Robert Fitzpatrick, Ludovic Perret, Yosuke Todo, Keita Xagawa
<span title="">2014</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;
To this end, we exploit the fact that the new problem proposed by Huang, Liu and Yang reduces to an easy instance of the Learning With Errors (LWE) problem.  ...  Acknowledgement Jean-Charles Faugère and Ludovic Perret have been partially supported supported by the Computer Algebra and Cryptography (CAC) project (ANR-09-JCJCJ-0064-01) and the HPAC grant (ANR ANR  ...  We will revisit the fact that the hardness of this new problem is related to the difficulty of solving a LWE-style problem for a very small secret.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-54631-0_26">doi:10.1007/978-3-642-54631-0_26</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mjdk7cepujgannhxhx45353sz4">fatcat:mjdk7cepujgannhxhx45353sz4</a> </span>
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CHIMERA: Combining Ring-LWE-based Fully Homomorphic Encryption Schemes

Christina Boura, Nicolas Gama, Mariya Georgieva, Dimitar Jetchev
<span title="2020-08-07">2020</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/assei3huevd3bfn4hgcs7we3ji" style="color: black;">Journal of Mathematical Cryptology</a> </i> &nbsp;
This is achieved by first mapping the different plaintext spaces to a common algebraic structure and then by applying efficient switching algorithms. This approach has many practical applications.  ...  AbstractThis paper proposes a practical hybrid solution for combining and switching between three popular Ring-LWE-based FHE schemes: TFHE, B/FV and HEAAN.  ...  TFHE Here, we revisit the TFHE scheme using the definition of the FHE module structure. In practice, the definition of the FHE module structure does not directly apply to TFHE.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/jmc-2019-0026">doi:10.1515/jmc-2019-0026</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4w5cmb4o2zgsrm6dti457ft2jq">fatcat:4w5cmb4o2zgsrm6dti457ft2jq</a> </span>
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Revisiting Multivariate Ring Learning with Errors and Its Applications on Lattice-Based Cryptography

Alberto Pedrouzo-Ulloa, Juan Ramón Troncoso-Pastoriza, Nicolas Gama, Mariya Georgieva, Fernando Pérez-González
<span title="2021-04-14">2021</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ye33srllvnanjouxn4tmrfgjsq" style="color: black;">Mathematics</a> </i> &nbsp;
In this work, we revisit the security of multivariate RLWE and propose new alternative instantiations of the problem that avoid the attack while still preserving the advantages of the multivariate structure  ...  Learning with Errors" problem was presented as a generalization of Ring Learning with Errors (RLWE), introducing efficiency improvements with respect to the RLWE counterpart thanks to its multivariate structure  ...  Division Algebras and Non-Norm Condition In [41] , the authors propose an alternative variant of LWE over cyclic algebras, which they denote as CLWE (Cyclic Algebra LWE).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/math9080858">doi:10.3390/math9080858</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b3vbn777wjb5texfvbuedcnaui">fatcat:b3vbn777wjb5texfvbuedcnaui</a> </span>
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Towards Efficient Arithmetic for Lattice-Based Cryptography on Reconfigurable Hardware [chapter]

Thomas Pöppelmann, Tim Güneysu
<span title="">2012</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;
This problem can be mitigated by introducing algebraic structure into the previously completely randomly generated lattice.  ...  ., with a computer algebra system) and its square root.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-33481-8_8">doi:10.1007/978-3-642-33481-8_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/53fo5qtatbe4nifvlaku7nxlvm">fatcat:53fo5qtatbe4nifvlaku7nxlvm</a> </span>
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Multivariate lattices for encrypted image processing

Alberto Pedrouzo-Ulloa, Juan Ramon Troncoso-Pastoriza, Fernando Perez-Gonzalez
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rc5jnc4ldvhs3dswicq5wk3vsq" style="color: black;">2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</a> </i> &nbsp;
are inherently sensitive signals that require privacypreserving solutions when processed in an untrusted environment, but their efficient encrypted processing is particularly challenging due to their structure  ...  LWE-based cryptosystems are computationally demanding, reason why RLWE was defined as an algebraic version of LWE, trading subspace dimensionality by polynomial ring order (using an ideal ring), achieving  ...  Notation and structure: We represent vectors by boldface lowercase letters.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icassp.2015.7178262">doi:10.1109/icassp.2015.7178262</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icassp/Pedrouzo-UlloaT15.html">dblp:conf/icassp/Pedrouzo-UlloaT15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e5yj6ijonffbhizk7e5xh4ciy4">fatcat:e5yj6ijonffbhizk7e5xh4ciy4</a> </span>
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High-Speed Signatures from Standard Lattices [chapter]

Özgür Dagdelen, Rachid El Bansarkhani, Florian Göpfert, Tim Güneysu, Tobias Oder, Thomas Pöppelmann, Ana Helena Sánchez, Peter Schwabe
<span title="">2015</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;
The use of more structured codes, such as quasi-dyadic Goppa codes [31] , has been the target of an algebraic attack [15] which is eective against certain (but not all) proposed parameters.  ...  The security analysis is revisited and appropriate parameters are selected in Section 4.  ...  This work Intel Core i7-4770K A Decoding Attack An approach for solving LWE that has not been considered in the original work [6] is the decoding attack.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-16295-9_5">doi:10.1007/978-3-319-16295-9_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nxoz27xzcjdtjhuzk3qwj5nxoa">fatcat:nxoz27xzcjdtjhuzk3qwj5nxoa</a> </span>
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Polly Cracker, revisited

Martin R. Albrecht, Jean-Charles Faugère, Pooya Farshim, Gottfried Herold, Ludovic Perret
<span title="2015-03-20">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c45m6ttnaje4xbjsq7m2c6df2a" style="color: black;">Designs, Codes and Cryptography</a> </i> &nbsp;
Furthermore, we show that a large class of algebraic transformations cannot convert this scheme to a fully secure Polly Cracker-style scheme.  ...  These problems can be seen as natural generalisations of the learning with errors (LWE) and the approximate GCD problems over polynomial rings.  ...  The advantage of a PPT algorithm A in solving LWE is Adv lwe n,q,χ,A (λ) := Pr LWE A n,q,χ (λ) ⇒ T .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10623-015-0048-8">doi:10.1007/s10623-015-0048-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k6pvlxzdhfgkjedo7pyjgmtne4">fatcat:k6pvlxzdhfgkjedo7pyjgmtne4</a> </span>
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On Ring Learning with Errors over the Tensor Product of Number Fields [article]

Alberto Pedrouzo-Ulloa, Juan Ramón Troncoso-Pastoriza, Fernando Pérez-González
<span title="2018-02-01">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The "Ring Learning with Errors" (RLWE) problem was formulated as a variant of the "Learning with Errors" (LWE) problem, with the purpose of taking advantage of an additional algebraic structure in the  ...  underlying considered lattices; this enables improvements on the efficiency and cipher expansion on those cryptographic applications which were previously based on the LWE problem.  ...  In order to alleviate this issue, an algebraic version of the LWE problem was proposed by Lyubashevsky et al. [15, 16] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1607.05244v3">arXiv:1607.05244v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3555h2k6wzdvpg6ylauyyedauu">fatcat:3555h2k6wzdvpg6ylauyyedauu</a> </span>
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Compact Ring-LWE Cryptoprocessor [chapter]

Sujoy Sinha Roy, Frederik Vercauteren, Nele Mentens, Donald Donglong Chen, Ingrid Verbauwhede
<span title="">2014</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;
In this paper we propose an efficient and compact processor for a ring-LWE based encryption scheme.  ...  We use these computational optimizations along with several architectural optimizations to design an instruction-set ring-LWE cryptoprocessor.  ...  To achieve computational efficiency and to reduce the key size, an algebraic variant of the LWE called ring-LWE [17] uses special structured ideal lattices.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-44709-3_21">doi:10.1007/978-3-662-44709-3_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/53y5rxhpkvhbponi44is6c2c3m">fatcat:53y5rxhpkvhbponi44is6c2c3m</a> </span>
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Making NTRU as Secure as Worst-Case Problems over Ideal Lattices [chapter]

Damien Stehlé, Ron Steinfeld
<span title="">2011</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;
In 2009, Stehlé et al. [35] introduced a structured variant of LWE, which they proved as hard as Ideal-SIS (under a quantum reduction), and allowed for the design of an asymptotically ecient CPA-secure  ...  In 2002, Micciancio [23] succeeded in restricting SIS to structured matrices while preserving a worst-case to average-case reduction.  ...  Variants of R-LWE.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-20465-4_4">doi:10.1007/978-3-642-20465-4_4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lhry2ibwe5fc3gh53jkhha3grq">fatcat:lhry2ibwe5fc3gh53jkhha3grq</a> </span>
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