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Cryptanalysis of the Ajtai-Dwork cryptosystem [chapter]

Phong Nguyen, Jacques Stern
<span title="">1998</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 particular, this settles the open question regarding the NP-hardness of the Ajtai-Dwork cryptosystem: from a recent result of Goldreich and Goldwasser, our result shows that breaking the Ajtai-Dwork  ...  We also adopt a theoretical point of view: we show that there is a converse to the Ajtai-Dwork security result, by reducing the question of distinguishing encryptions of one from encryptions of zero to  ...  We would like to thank the anonymous referees for their helpful comments.  ... 
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Page 6572 of Mathematical Reviews Vol. , Issue 99i [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
; Stern, Jacques (F-ENS-I; Paris) Cryptanalysis of the Ajtai-Dwork cryptosystem.  ...  In particular, this settles the open question regarding the NP-hardness of the Ajtai-Dwork cryptosystem: from a recent result of Goldreich and Goldwasser, our result shows that break- ing the Ajtai-Dwork  ... 
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Lattice-Based Cryptography [chapter]

Oded Regev
<span title="">2006</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;
We describe some of the recent progress on lattice-based cryptography, starting from the seminal work of Ajtai, and ending with some recent constructions of very efficient cryptographic schemes.  ...  -Improved cryptosystems: As we have seen in Section 4, the situation with lattice-based cryptosystems is not entirely satisfactory: The original construction of Ajtai and Dwork, as well as some of the  ...  A result along these lines is known for the Ajtai-Dwork cryptosystem [34] , but it is still open if the same can be shown for newer cryptosystems such as the ones in [31, 32] .  ... 
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Lattice-Based Cryptography [chapter]

Johannes Gehrke, Daniel Kifer, Ashwin Machanavajjhala, Arjen K. Lenstra, Phong Nguyen, Phong Nguyen, Daniele Micciancio, Scott Contini, Sabrina De Capitani diVimercati, Burt Kaliski, Stephen M Papa, William D. Casper (+13 others)
<span title="">2011</span> <i title="Springer US"> Encyclopedia of Cryptography and Security </i> &nbsp;
In 1997 Ajtai and Dwork [2] also proposed a cryptosystem with similar average-case/worst-case connection properties: decrypting random challenges is at least as hard as solving the worst-case instance  ...  Cryptanalysis applications are usually based on lattice reduction techniques.  ...  See also lattice reduction for information about the use of lattices in cryptanalysis.  ... 
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TECHNIQUES OF LATTICE BASED CRYPTOGRAPHY STUDIED ON A PERVASIVE COMPUTING ENVIRONMENT

Divyajyothi M G, Rachappa, D H Rao
<span title="2020-08-31">2020</span> <i title="Zenodo"> Zenodo </i> &nbsp;
We discuss about a cryptosystem whose security relies on high lattice dimension.  ...  Most of the existing cryptographic solutions widely in use rely on the hardness of factorization and number theory problems.  ...  In cooperation with Cynthia Dwork, Ajtai published the Ajtai-Dwork cryptosystem a short time later in 1997. Its security is based on the hardness of SVP.  ... 
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Proof of Plaintext Knowledge for the Ajtai-Dwork Cryptosystem [chapter]

Shafi Goldwasser, Dmitriy Kharchenko
<span title="">2005</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;
We then show a interactive zero-knowledge proof of plaintext knowledge (PPK) for the Ajtai-Dwork cryptosystem, based directly on the security of the cryptosystem rather than resorting to general interactive  ...  In this paper, we show statistical zero-knowledge protocols for statements of the form "plaintext m corresponds to ciphertext c" and "ciphertext c and c' decrypt to the same value" for the Ajtai-Dwork  ...  For the Ajtai-Dwork cryptosystem, these general completeness constructions of PPK were the only one knows prior to our work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30576-7_29">doi:10.1007/978-3-540-30576-7_29</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fa75f7m6enadpehgrx6wqi62le">fatcat:fa75f7m6enadpehgrx6wqi62le</a> </span>
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Page 726 of Mathematical Reviews Vol. , Issue 99a [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
de- cryption errors in the Ajtai-Dwork cryptosystem (105-111); Oded Goldreich, Shafi Goldwasser and Shai Halevi, Public-key cryp- tosystems from lattice reduction problems (112-131); Rosario Gennaro, Hugo  ...  of the Qu-Vanstone cryptosystem based on group factorizations (198-212); Thomas A.  ... 
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Cryptographic Functions from Worst-Case Complexity Assumptions [chapter]

Daniele Micciancio
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsmcy3rqifaqpn7ibccavehimi" style="color: black;">The LLL Algorithm</a> </i> &nbsp;
discuss how this affects the traditional approach to cryptanalysis based on random challenges.  ...  In this paper we give a survey of the constructions and proof techniques used in this area, explain the importance of basing cryptographic functions on the worst-case complexity of lattice problems, and  ...  Another problem with Ajtai-Dwork cryptosystem is that it relies on the hardness of uSVP γ for a fairly large value of γ.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02295-1_13">doi:10.1007/978-3-642-02295-1_13</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/series/isc/Micciancio10.html">dblp:series/isc/Micciancio10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2nvkrtnrnbg6fhriq5wiybvnwy">fatcat:2nvkrtnrnbg6fhriq5wiybvnwy</a> </span>
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A Practical View of the State-of-the-Art of Lattice-Based Cryptanalysis

Artur Mariano, Thijs Laarhoven, Fabio Correia, Manuel Rodrigues, Gabriel Falcao
<span title="">2017</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q7qi7j4ckfac7ehf3mjbso4hne" style="color: black;">IEEE Access</a> </i> &nbsp;
ACKNOWLEDGMENTS Artur Mariano thanks HiPEAC network for a collaboration grant awarded to visit Gabriel Falcão in late 2016, when the write up of this paper started.  ...  As an example, the Ajtai-Dwork cryptosystem, one of the earliest cryptosystems based on lattices, bases its security on the γ -Unique SVP, a problem that derives from the SVP [7] .  ...  While cryptography is the process of creating new systems, cryptanalysis, on the one hand, enables the analysis of existing cryptosystems, so that we either trust them or find out that these schemes are  ... 
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Broadcast Attacks against Lattice-Based Cryptosystems [chapter]

Thomas Plantard, Willy Susilo
<span title="">2009</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 1988, Håstad proposed the classical broadcast attack against public key cryptosystems. The scenario of a broadcast attack is as follows.  ...  As a result, our attacks have many security implications on most of the lattice-based or knapsack cryptosystems.  ...  Lattice-based cryptosystems In 1997, Ajtai and Dwork [19] proposed the first lattice cryptosystem where its security is based on a variant of the Shortest Vector Problem (SVP).  ... 
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Efficient FPGA Implementation of Modular Multiplication and Exponentiation

M Issad, M Anane, B Boudraa, A M Bellemou, N Anane
<span title="2020-06-30">2020</span> <i title="Universiti Sultan Zainal Abidin"> Malaysian Journal of Computing and Applied Mathematics </i> &nbsp;
This paper presents an FPGA implementation of the most critical operations of Public Key Cryptography (PKC), namely the Modular Exponentiation (ME) and the Modular Multiplication (MM).  ...  Efficient parallel and pipeline strategies are developed at the digit level for the optimization of the execution time.  ...  LBC Cryptosystems There are different cryptosystems based on LBC the first construction was created by AJTAI-DWORK [10] in 1996 but in 2001 Nguyen and Stern broke this cryptosystem by solving the SVP  ... 
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A Review of Sieve Algorithms in Solving the Shortest Lattice Vector Problem

Zedong Sun, Zedong Sun, Chunxiang Gu, Chunxiang Gu, Yonghui Zheng, Yonghui Zheng
<span title="">2020</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q7qi7j4ckfac7ehf3mjbso4hne" style="color: black;">IEEE Access</a> </i> &nbsp;
ACKNOWLEDGMENT The authors thank anonymous reviewers for their comments and helping us improve this paper.  ...  Furthermore, Ajtai and Dwork [3] presented the first worst-case to average-case reduction for hard lattice problems, which furnishes latticebased cryptosystems with provable security.  ...  Either cryptanalysis using lattice algorithms or the design of lattice-based cryptosystem, hard lattice problems are of vital importance.  ... 
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Techniques in Lattice Basis Reduction [article]

Bal K. Khadka, Spyros M. Magliveras
<span title="2017-02-11">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The first technique relies on the sensitivity of LLL to permutations of the input basis B, and optimization ideas over the symmetric group S_m viewed as a metric space.  ...  The credit on reduction theory goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H.  ...  Their cryptosystem is quite impractical because of the massive data expansion, as it encrypts data bit-by-bit. Inspired by the Ajtai-Dwork cryptosystem, O.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1702.03364v1">arXiv:1702.03364v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yytfi4x4evcrvjcpa5gknzj74u">fatcat:yytfi4x4evcrvjcpa5gknzj74u</a> </span>
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The Two Faces of Lattices in Cryptology [chapter]

Phong Q. Nguyen
<span title="">2001</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;
Paradoxically, several positive cryptographic applications of lattices have emerged in the past ve years: there now exist public-key cryptosystems based on the hardness of lattice problems, and lattices  ...  We survey the main examples of the two faces of lattices in cryptology.  ...  This shows that unless major improvements 3 are found, the Ajtai-Dwork cryptosystem is only of theoretical importance. Cryptanalysis overview.  ... 
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Classical Cryptosystems In A Quantum Setting [article]

Michael Stephen Brown
<span title="2004-04-09">2004</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
of several of the most popular classical public key cryptosystems.  ...  However, developments in the area of quantum computing indicate that many of the public key cryptosystems currently in use could easily be broken if large-scale quantum computers become technologically  ...  Further suppose that we are given a function f : S → {0, 1} such that: Chapter 8 1. f (x) = 1 if x is The Ajtai-Dwork Cryptosystem The Ajtai-Dwork cryptosystem [AD97] was one of the first proposed cryptosystems  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/0404061v1">arXiv:quant-ph/0404061v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tjicssumpbfwfo76h2pckotcqy">fatcat:tjicssumpbfwfo76h2pckotcqy</a> </span>
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