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Efficient polynomial algorithms for distributive lattices

Jean-Paul Bordat
1991 Discrete Applied Mathematics  
., Efficient polynomial algorithms for distributive lattices, Discrete Applied Mathematics 32 (1991) 31-50.  ...  A rather efficient and combinatorial algorithm is produced for each of these problems.  ...  As an application, efficient algorithms for polynomial problems such as -canonical decomposition, -computation of transitive closure, random generation, -recognition, orientability, can be designed.  ... 
doi:10.1016/0166-218x(91)90022-o fatcat:odjfjgbzxjdhpbj6uvzea2guoe

2.3 An Energy-Efficient Configurable Lattice Cryptography Processor for the Quantum-Secure Internet of Things

Utsav Banerjee, Abhishek Pathak, Anantha P. Chandrakasan
2019 2019 IEEE International Solid- State Circuits Conference - (ISSCC)  
This paper presents a configurable lattice cryptography processor which enables quantum-resistant security protocols for IoT.  ...  This is the first ASIC implementation which demonstrates multiple lattice-based protocols proposed for NIST post-quantum standardization.  ...  Acknowledgements: The authors would like to thank Texas Instruments for funding this work, and the TSMC University Shuttle Program for chip fabrication support.  ... 
doi:10.1109/isscc.2019.8662528 dblp:conf/isscc/BanerjeePC19 fatcat:vb3vp7o7n5f3riofdxpee6bkci

Memory‐constrained implementation of lattice‐based encryption scheme on standard Java Card platform

Ye Yuan, Kazuhide Fukushima, Junting Xiao, Shinsaku Kiyomoto, Tsuyoshi Takagi
2021 IET Information Security  
Two efficient discrete Gaussian sampling approaches, known at the discrete Ziggurat sampling algorithm and Knuth-Yao algorithm, were implemented on the Java Card and resulted in a reduction in running  ...  More important, polynomial modular multiplication is shown to perform efficiently on a standard Java Card platform even when the big integers and floating-point number operations are not supported.  ...  In some lattice-based cryptosystems, we need efficient algorithms that produce distributions that are close to the desired discrete Gaussian distribution statistically.  ... 
doi:10.1049/ise2.12012 fatcat:zhp7s7q6snd7bllne334u4nlyu

A New Provably Secure Cryptosystem Using Dedekind Domain Direct Product Approach

Amir Hassani Karbasi
2018 Ratio Mathematica  
We prove the security of our main algorithm from the R-SIS and R-LWE problems as NP-hard problems.  ...  We show that our cryptosystem has security stronger than that of ETRU, over cartesian product of dedekind domains and extended cyclotomic polynomials.  ...  derive a key generation algorithm for the ETRU for each component in vectors, where the generated public key follows a distribution for which Ideal-SVP reduces to R-LWE.  ... 
doi:10.23755/rm.v34i0.404 doaj:83ab2c7b067f4eb89c721357d721aa95 fatcat:fdf6dduxabgrlcakxf4at6kmhm

Physical-Layer Cryptography Through Massive MIMO

Thomas R. Dean, Andrea J. Goldsmith
2017 IEEE Transactions on Information Theory  
We show that the eavesdropper's decoder for the MIMO system with M-PAM modulation is equivalent to solving standard lattice problems that are conjectured to be of exponential complexity for both classical  ...  The decoding complexity is analyzed by mapping the massive MIMO system to a lattice.  ...  regarding information-theoretic secrecy in the context of our model, and Mainak Chowdhury for discussions on algorithms for MIMO decoding and linear codes.  ... 
doi:10.1109/tit.2017.2715187 fatcat:meod6hf75rcdhis4swcocijq4e

A Practical Implementation of Identity-Based Encryption Over NTRU Lattices [chapter]

Sarah McCarthy, Neil Smyth, Elizabeth O'Sullivan
2017 Lecture Notes in Computer Science  
An identity-based encryption scheme enables the efficient distribution of keys in a multi-user system.  ...  This research examines the first pragmatic lattice-based IBE scheme presented by Ducas, Lyubashevsky and Prest in 2014 and brings it into the realm of practicality for use on small devices.  ...  Acknowledgements The authors would like to thank the anonymous reviewers of SAC 2017 and IMACC 2017 for their careful reading of the paper and their diligent comments.  ... 
doi:10.1007/978-3-319-71045-7_12 fatcat:6sl6mpecijdldazju3ankwqlrq

Discrete Gaussian Sampling Reduces to CVP and SVP [article]

Noah Stephens-Davidowitz
2016 arXiv   pre-print
In particular, polynomial-time algorithms for DGS with very high parameters s have found many uses in cryptography and in reductions between lattice problems.  ...  It has long been an important tool in the study of lattices. More recently, algorithms for discrete Gaussian sampling (DGS) have found many applications in computer science.  ...  Acknowledgments I would like to thank Divesh Aggarwal, Daniel Dadush, and Oded Regev for many enlightening discussions and for their helpful comments on early drafts of this work; Daniele Micciancio for  ... 
arXiv:1506.07490v4 fatcat:kpxdpcpsfzdcjpedbtehgczrse

Efficient Signature Schemes from R-LWE

2016 KSII Transactions on Internet and Information Systems  
The security of the above two schemes are reducible to the worst-case hardness of shortest vectors on ideal lattices.  ...  The security analyses indicate the proposed schemes are unforgeable under chosen message attack model, and the efficiency analyses also show that the above schemes are much more efficient than other correlative  ...  For a approximation factor 1 γ ≥ ( bounded by a fixed poly( ) n ), assume that it is hard for any polynomial-time even quantum algorithms to find an approximation of the shortest vector on ideal lattices  ... 
doi:10.3837/tiis.2016.08.026 fatcat:2uk7q7mtzzhldgryhfzkyxxara

Ring-LWE: Applications to Cryptography and Their Efficient Realization [chapter]

Sujoy Sinha Roy, Angshuman Karmakar, Ingrid Verbauwhede
2016 Lecture Notes in Computer Science  
Later for efficiency LWE was adapted for ring polynomials known as Ring-LWE. In this paper we discuss some of these ring-LWE based schemes that have been designed.  ...  The persistent progress of quantum computing with algorithms of Shor and Proos and Zalka has put our present RSA and ECC based public key cryptosystems at peril.  ...  For the generation of error polynomials from the discrete Gaussian distribution X , the implementations use one of the following sampling algorithms [8] : rejection sampling, inversion sampling and the  ... 
doi:10.1007/978-3-319-49445-6_18 fatcat:7y34eqtumvhexap5rusvgjzppy

Efficient Post-Quantum TLS Handshakes using Identity-Based Key Exchange from Lattices

Utsav Banerjee, Anantha P. Chandrakasan
2020 ICC 2020 - 2020 IEEE International Conference on Communications (ICC)  
We also propose concrete parameters for the underlying lattice computations and provide detailed implementation results.  ...  postquantum security levels, and show that our ID-based handshake is 3.7× more energy-efficient, thus highlighting the advantage of ID-based key exchange for post-quantum TLS.  ...  ACKNOWLEDGMENT The authors thank Texas Instruments for funding this work.  ... 
doi:10.1109/icc40277.2020.9148829 dblp:conf/icc/BanerjeeC20 fatcat:k4e5h4tfqrf4be3t3l2njgi2pe

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.  ...  In order to satisfy this constraint, Montgomery Power Ladder and Montgomery Modular Multiplication (MMM) algorithms are utilized for the ME and for the MM implementations as HW accelerators, respectively  ...  For the polynomials multiplication we not used the Karashuba algorithm as in NTRU_pke release submitted to NIST, we used our own polynomials multiplication XKwarizm algorithm in the ring Rq =Zq[X]/(X N  ... 
doi:10.37231/myjcam.2020.3.1.37 fatcat:2dfcacmq7rahpbmw5ja7unbptu

Generalized Compact Knapsacks Are Collision Resistant [chapter]

Vadim Lyubashevsky, Daniele Micciancio
2006 Lecture Notes in Computer Science  
lattices, even for almost constant values of m.  ...  In (Micciancio, FOCS 2002) it was proved that for appropriate choices of R and D, solving the generalized compact knapsack problem on the average is as hard as solving certain worst-case problems for cyclic  ...  Still, currently there appear to be no algorithms able to take advantage of the ring structure that these lattices possess (see [14] for a discussion of known algorithms for cyclic lattices).  ... 
doi:10.1007/11787006_13 fatcat:573vue5stbefrf6p44v5v4rkpu

NFLlib: NTT-Based Fast Lattice Library [chapter]

Carlos Aguilar-Melchor, Joris Barrier, Serge Guelton, Adrien Guinet, Marc-Olivier Killijian, Tancrède Lepoint
2016 Lecture Notes in Computer Science  
of overloaded operator; functions to sample polynomials in R p with different distributions for the coefficients (uniform distribution modulo p, uniformly bounded distribution, discrete Gaussian distribution  ...  To multiply polynomials efficiently, we use the quasi-linear polynomial multiplication algorithm called the NTT [34] .  ... 
doi:10.1007/978-3-319-29485-8_20 fatcat:el47i4l2vvbg7dheptw7dnl7yu

Cryptographic Functions from Worst-Case Complexity Assumptions [chapter]

Daniele Micciancio
2009 The LLL Algorithm  
A remarkable feature of lattice-based cryptographic functions is that they can be proved secure (that is, hard to break on the average) based on the assumption that the underlying lattice problems are  ...  Lattice problems have been suggested as a potential source of computational hardness to be used in the construction of cryptographic functions that are provably hard to break.  ...  For example, the lattice reduction algorithm of [23] for general norms is not even known to terminate in polynomial time for arbitrary dimension.  ... 
doi:10.1007/978-3-642-02295-1_13 dblp:series/isc/Micciancio10 fatcat:2nvkrtnrnbg6fhriq5wiybvnwy

Identity-Based Linkable Ring Signature on NTRU Lattice

Yongli Tang, Feifei Xia, Qing Ye, Mengyao Wang, Ruijie Mu, Xiaohang Zhang, Mohamed Amine Ferrag
2021 Security and Communication Networks  
The computational efficiency of signature has also been further improved since it only involves multiplication in the polynomial ring and modular operations of small integers.  ...  Finally, we implemented our scheme and other similar schemes, and it is shown that the time for the signature generation and verification of this scheme decreases roughly by 44.951% and 33.503%, respectively  ...  for any probabilistic polynomial time (PPT) algorithm.  ... 
doi:10.1155/2021/9992414 fatcat:to6bzowcezhh5n44mgplfk54ma
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