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How to Meet Ternary LWE Keys [article]

Alexander May
2021 IACR Cryptology ePrint Archive  
The presumably best attack on these schemes is a hybrid attack that combines lattice reduction techniques with Odlyzko's Meet-in-the-Middle approach.  ...  We leave it is an open question whether our new Meetin-the-Middle attack in combination with lattice reduction can be used to speed up the hybrid attack.  ...  Acknowledgements: The author wants to thank Elena Kirshanova, John Schank and Andre Esser for discussions and estimations concerning lattice reduction and the Hybrid attack, and the anonymous reviewers  ... 
dblp:journals/iacr/May21 fatcat:zk3r7kpzvjdy5dhy7bzqbpf5si

Reduced memory meet-in-the-middle attack against the NTRU private key

Christine van Vredendaal
2016 LMS Journal of Computation and Mathematics  
The two most used techniques in attacking the NTRU private key are meet-in-the-middle attacks and lattice-basis reduction attacks.  ...  Howgrave-Graham combined both techniques in 2007 and pointed out that the largest obstacle to attacks is the memory capacity that is required for the meet-in-the-middle phase.  ...  Hybrid Attack The hybrid lattice-basis reduction and meet-in-the-middle attack [14] mentioned in the introduction works by taking the NTRU lattice and applying lattice-basis reduction to part of the  ... 
doi:10.1112/s1461157016000206 fatcat:pmmtofcvd5gs7p4jt5w54ylgau

Efficient FPGA Implementation of Modular Multiplication and Exponentiation

M Issad, M Anane, B Boudraa, A M Bellemou, N Anane
2020 Malaysian Journal of Computing and Applied Mathematics  
Efficient parallel and pipeline strategies are developed at the digit level for the optimization of the execution time.  ...  The application for 1024-bits data length shows that the MMM run in 6.24 µs and requires 647 slices. The ME is executed in 6.75 ms, using 2881 slices.  ...  Related Works The most attacks used to check the robustness of Lattice-Based Cryptosystems are the Reduction algorithms attack and Meet-In-the-Middle (MIM) attack developed by (Oldgz) (Vredendaal, 2016  ... 
doi:10.37231/myjcam.2020.3.1.37 fatcat:2dfcacmq7rahpbmw5ja7unbptu

ETRU: NTRU over the Eisenstein integers

Katherine Jarvis, Monica Nevins
2013 Designs, Codes and Cryptography  
Moreover, because its security is conjectured to rely on the hardness of certain lattice problems, which are not known to be susceptible to quantum attack, NTRU is viewed as a quantum-resistant cryptosystem  ...  The NTRU Cryptosystem The NTRU public key cryptosystem as described in [8] depends on three integer parameters N , p and q, such that N > 1, p and q are relatively prime and q is much larger than p.  ...  The authors would like to thank the anonymous referees for several  ... 
doi:10.1007/s10623-013-9850-3 fatcat:qxdwhb7te5a3bat2e7phhzehg4

High-Speed Key Encapsulation from NTRU [chapter]

Andreas Hülsing, Joost Rijneveld, John Schanck, Peter Schwabe
2017 Lecture Notes in Computer Science  
It is, to the best of our knowledge, the rst NTRU software with full protection against timing attacks.  ...  This paper presents software demonstrating that the 20year-old NTRU cryptosystem is competitive with more recent latticebased cryptosystems in terms of speed, key size, and ciphertext size.  ...  In 2007, Howgrave-Graham recognized that sparsity could be exploited by a hybrid lattice reduction and combinatorial attack based on Schnorr's RSR and Odlyzko's meet-in-the-middle strategy [31] .  ... 
doi:10.1007/978-3-319-66787-4_12 fatcat:rq7slwi2ajduzkbngdbc5oajmy

Round2: KEM and PKE based on GLWR [article]

Hayo Baan, Sauvik Bhattacharya, Óscar García-Morchón, Ronald Rietman, Ludo Tolhuizen, Jose Luis Torre-Arce, Zhenfei Zhang
2017 IACR Cryptology ePrint Archive  
Lattice-based cryptography is one of the families in post-quantum cryptography, demonstrating desirable features such as well-understood security, efficient performance, and versatility.  ...  Finally, Round2 includes various approaches of refreshing the system public parameter A, allowing efficient ways of preventing precomputation and back-door attacks.  ...  Hybrid Attack In this section, we consider a hybrid lattice reduction and meet-in-the-middle attack (henceforth called hybrid attack ) originally due to [28] that targeted the NTRU [27] cryptosystem  ... 
dblp:journals/iacr/BaanBGRTTZ17 fatcat:66nz47rubnfx3lt55a3owiatpq

New Bleichenbacher Records: Fault Attacks on qDSA Signatures

Akira Takahashi, Mehdi Tibouchi, Masayuki Abe
2018 Transactions on Cryptographic Hardware and Embedded Systems  
Using a hybrid parallelization model relying on both shared and distributed memory, we achieve a very efficient implementation of our highly scalable range reduction algorithm.  ...  Both of these computations, and particularly the latter, set new records in the implementation of Bleichenbacher's attack.  ...  Acknowledgements We are indebted to Adi Shamir for suggesting crucial ideas for this work, including, in particular, the application of the Schroeppel-Shamir algorithm.  ... 
doi:10.13154/tches.v2018.i3.331-371 dblp:journals/tches/TakahashiTA18 fatcat:y72kdfhb6fgpvgchzzl4j26d74

SoK: On the Security of Cryptographic Problems from Linear Algebra [article]

Carl Bootland, Wouter Castryck, Alan Szepieniec, Frederik Vercauteren
2021 IACR Cryptology ePrint Archive  
In particular, we consider attacks against problems in the style of LWE, SIS and NTRU defined over rings of the form Z[X]/(f (X), g(X)), where classically g(X) = q is an integer modulus.  ...  Firstly, we survey the relevant existing attack strategies known to apply to the most commonly used lattice-based cryptographic problems as well as to a number of their variants.  ...  Acknowledgements The material in this work first appeared in various parts of the first author's PhD thesis [23] and has been reworked and reordered here.  ... 
dblp:journals/iacr/BootlandCSV21 fatcat:3q4lz2xzhraajovhwj6pa7djym

CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM

Joppe Bos, Leo Ducas, Eike Kiltz, T Lepoint, Vadim Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, Damien Stehle
2018 2018 IEEE European Symposium on Security and Privacy (EuroS&P)  
Recent advances in quantum computing and the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digital-signature, encryption, and keyestablishment protocols  ...  The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of post-quantum  ...  Resistance to hybrid attacks. Several schemes [12, 42] are potentially vulnerable to a hybrid attack [38, 45] , mixing lattice reduction techniques with Meet-in-the-Middle combinatorial search.  ... 
doi:10.1109/eurosp.2018.00032 dblp:conf/eurosp/BosDKLLSSSS18 fatcat:o7dl5wpwcndarjp3wtm2eqwycm

Quantum Cryptanalysis (Dagstuhl Seminar 19421)

Michele Mosca, Maria Naya-Plasencia, Rainer Steinwandt, Michael Wagner
2020 Dagstuhl Reports  
This seminar report documents the program and the outcomes of Dagstuhl Seminar 19421 Quantum Cryptanalysis, which took place in October 2019.  ...  Identifying new cryptanalytic improvements that make use of quantum algorithms and expanding the applicability of the best known cryptanalytic attacks by means of quantum technology.  ...  (CRYPTO 2012) improve the memory usage over a simple meet-in-the-middle. In this paper, we study quantum algorithms for the k-xor problem.  ... 
doi:10.4230/dagrep.9.10.47 dblp:journals/dagstuhl-reports/MoscaNS19 fatcat:b4fbhk267zhsdch2lotalrzwoa

Quantum Computing: A Taxonomy, Systematic Review and Future Directions [article]

Sukhpal Singh Gill, Adarsh Kumar, Harvinder Singh, Manmeet Singh, Kamalpreet Kaur, Muhammad Usman, Rajkumar Buyya
2021 arXiv   pre-print
As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ  ...  A detailed overview of quantum software tools and technologies, post-quantum cryptography and quantum computer hardware development to document the current state-of-the-art in the respective areas.  ...  Figure 11: Post-quantum Cryptography Protocols Langlois and Stehlé [289] compared the average-case reduction problems with module lattices in a lattice-based system.  ... 
arXiv:2010.15559v4 fatcat:y6cuttww5fd5jdmvcer352lh4e

Partial Key Exposure in Ring-LWE-Based Cryptosystems: Attacks and Resilience [article]

Dana Dachman-Soled, Huijing Gong, Mukul Kulkarni, Aria Shahverdi
2018 IACR Cryptology ePrint Archive  
We initiate the study of partial key exposure in ring-LWE-based cryptosystems.  ...  -Present and implement an efficient key exposure attack that, given certain 1/4-fraction of the coordinates of the NTT transform of the RLWE secret, along with RLWE instances, recovers the full RLWE secret  ...  In order to perform this enumeration efficiently, a meet-in-the-middle approach is used.  ... 
dblp:journals/iacr/Dachman-SoledGK18 fatcat:tw5ju3cgzzhgpddcjv43mvhzae

Post Quantum Cryptography: Techniques, Challenges, Standardization, and Directions for Future Research [article]

Ritik Bavdekar, Eashan Jayant Chopde, Ashutosh Bhatia, Kamlesh Tiwari, Sandeep Joshua Daniel, Atul
2022 arXiv   pre-print
Grover's search algorithm gives a square root time boost for the searching of the key in symmetric schemes like AES and 3DES.  ...  cryptography standardization process, and finally provides a couple of future research directions in this field.  ...  A major attack against them involves using lattice reduction algorithms like LLL.  ... 
arXiv:2202.02826v1 fatcat:ghq4lqiu4rf5vpuv6gbk7ws4jm

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Chithralekha Balamurugan, Kalpana Singh, Ganeshvani Ganesan, Muttukrishnan Rajarajan
2021 Cryptography  
This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks.  ...  This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have  ...  Acknowledgments: This research work has been carried out under the leadership of the Institute for Technological Research SystemX, and therefore granted within the scope of the program "Recherche Exploratoire  ... 
doi:10.3390/cryptography5040038 fatcat:wkb43zunwjagbnljc6brfou4ty

Unlimited potentials of carbon: different structures and uses (a Review)

Onyeka Stanislaus Okwundu, Emmanuel Uche Aniekwe, Chinaza Emmanuel Nwanno
2018 Metallurgical & Materials Engineering  
Structurally, carbon exists in the sp3 and sp2 hybridized state in the crystal lattice of its crystalline allotropes.  ...  It has been in use since antiquity and now, the possibility of manipulating the lattice structure of its crystalline allotropes, offers it unlimited advanced applications.  ...  Also, this review paper is a compilation of data, information, and extracts from a variety of sources, primarily web-based with critical sources identified in the references; the content and contribution  ... 
doi:10.30544/388 fatcat:tzo455fdb5ckhdssb7tqnoygqu
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