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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
2021 Mathematics  
The "Multivariate Ring 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.  ...  Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable.  ... 
doi:10.3390/math9080858 fatcat:b3vbn777wjb5texfvbuedcnaui

Revisiting Multivariate Ring Learning with Errors and its Applications on Lattice-based Cryptography [article]

Alberto Pedrouzo-Ulloa, Juan Ramón Troncoso-Pastoriza, Nicolas Gama, Mariya Georgieva, Fernando Pérez-González
2019 IACR Cryptology ePrint Archive  
The "Multivariate Ring 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.  ...  , packing, unpacking and homomorphic slot manipulation, and, consequently, bootstrapping, and optimization of high level applications in encrypted approximate arithmetic, complex processing, and efficient  ... 
dblp:journals/iacr/Pedrouzo-UlloaT19 fatcat:y45ql43vfvgljnjchl22riej5e

Efficient Implementation of Password-Based Authenticated Key Exchange from RLWE and Post-Quantum TLS [article]

Xinwei Gao, Jintai Ding, Lin Li, Saraswathy RV, Jiqiang Liu
2017 IACR Cryptology ePrint Archive  
Compared with original implementation, we achieve 21.5x and 18.5x speedup for RLWE-PAK and RLWE-PPK respectively. Compare with quantum-vulnerable J-PAKE protocol, we achieve nearly 8x speedup.  ...  Two post-quantum password-based authenticated key exchange (PAKE) protocols were proposed at CT-RSA 2017.  ...  Learning with Errors and Ring Variant In 2005, Oded Regev showed a problem called Learning with Errors (LWE) [25] .  ... 
dblp:journals/iacr/GaoDLRL17 fatcat:6mlhpycnwfcutpy5z2qrmvpst4

Multivariate Cryptosystems for Secure Processing of Multidimensional Signals [article]

Alberto Pedrouzo-Ulloa, Juan Ramón Troncoso-Pastoriza, Fernando Pérez-González
2017 arXiv   pre-print
This work introduces a new cryptographic hard problem denoted m-RLWE (multivariate Ring Learning with Errors) which generalizes RLWE, and proposes several relinearization-based techniques to efficiently  ...  and we exemplify some of the proposed transformation techniques in critical and ubiquitous block-based processing applications  ...  PRELIMINARIES The state of the art in FHE is based on the Learning with Errors (LWE) [17] and Ring Learning with Errors (RLWE) problems [18] , which have proven security reductions from hard lattice  ... 
arXiv:1712.00848v1 fatcat:qvwgu44yeffyxf3p46k6jruzsa

Post-Quantum Era Privacy Protection for Intelligent Infrastructures

Lukas Malina, Petr Dzurenda, Sara Ricci, Jan Hajny, Gautam Srivastava, Raimundas Matulevicius, Abasi-amefon O. Affia, Maryline Laurent, Nazatul Haque Sultan, Qiang Tang
2021 IEEE Access  
(2) the increase of IoT/II applications and digital services with growing data collection capabilities are introducing new threats and risks on citizens' privacy.  ...  Particularly, we emphasize on post-quantum cryptography techniques that may (or must when quantum computers become a reality) be used in the future through concrete products, pilots, and projects.  ...  [228] introduced a new lattice-based group signature that is probably based on the hardness of the Small Integer Solutions (SIS) and Learning with Errors (LWE) problems in the random oracle model.  ... 
doi:10.1109/access.2021.3062201 fatcat:kqcwwqjfjnds7bzlrid7r6gjlu

On Ring Learning with Errors over the Tensor Product of Number Fields [article]

Alberto Pedrouzo-Ulloa, Juan Ramón Troncoso-Pastoriza, Fernando Pérez-González
2018 arXiv   pre-print
This hardness problem is denoted as "Multivariate Ring Learning with Errors" (m-RLWE or multivariate RLWE) and we show its relation to hardness problems over the tensor product of ideal lattices.  ...  underlying considered lattices; this enables improvements on the efficiency and cipher expansion on those cryptographic applications which were previously based on the LWE problem.  ...  Introduction In recent years, a high number of cryptographic schemes and applications have been proposed based on the LWE (Learning with Errors) problem.  ... 
arXiv:1607.05244v3 fatcat:3555h2k6wzdvpg6ylauyyedauu

Will quantum computers be the end of public key encryption?

William Buchanan, Alan Woodward
2016 Journal of Cyber Security Technology  
One of the earliest public key encryption schemes, RSA, named after Ron Rivest, Adi Shamir, and Leonard Adleman [4], was based upon the mathematics of prime numbers.  ...  However, it was when Diffie and Hellman published their seminal paper entitled 'New Directions in Cryptography' [2] that, as far as the general public was concerned, public key encryption was born.  ...  The mathematical problems that are most actively being investigated are (1) Lattice-based cryptography (2) Multivariate-based cryptography (3) Hash-based signatures (4) Code-based cryptography (5) Supersingular  ... 
doi:10.1080/23742917.2016.1226650 fatcat:sfcvw3en6jho3jg5bvt5q2fpri

The Hardness of LWE and Ring-LWE: A Survey [article]

David Balbás
2021 IACR Cryptology ePrint Archive  
The Learning with Errors (LWE) problem consists of distinguishing linear equations with noise from uniformly sampled values.  ...  We start by introducing both Ring-LWE and LWE and their mathematical foundations, focusing on lattices and algebraic number theory.  ...  I also want to thank Per Austrin, Phillip Gajland, and Maribel González-Vasco for helpful comments on the draft.  ... 
dblp:journals/iacr/Balbas21 fatcat:uy5rswilzjfqldjuufgsqeibxy

Post-Quantum Secure Remote Password Protocol from RLWE Problem [chapter]

Xinwei Gao, Jintai Ding, Jiqiang Liu, Lin Li
2018 Lecture Notes in Computer Science  
With the ground-breaking Diffie-Hellman key exchange proposed in 1976 [14] , public key cryptography came into reality and it has been widely deployed in real world applications.  ...  However, with the advent of quantum computer and Shor's algorithm, classic DLP-based public key cryptography algorithms are no longer secure, including SRP.  ...  Among all lattice-based constructions, Learning With Errors (LWE) and Ring-LWE based ones are more practical and outstanding due to much better efficiency, robust security and versatility.  ... 
doi:10.1007/978-3-319-75160-3_8 fatcat:aboktgxcmvghrmxaespm4wnpbe

Quantum Cryptanalysis (Dagstuhl Seminar 19421)

Michele Mosca, Maria Naya-Plasencia, Rainer Steinwandt, Michael Wagner
2020 Dagstuhl Reports  
Dagstuhl seminar on Quantum Cryptanalysis was heavily informed by NIST's ongoing standardization effort in post-quantum cryptography.  ...  Several NIST employees attended the seminar and lead a discussion session on the topic. As one would hope hoped for, many talks had an algorithmic focus.  ...  on rank-based cryptography, in particular recent submissions to NIST, based on problems with no masking.  ... 
doi:10.4230/dagrep.9.10.47 dblp:journals/dagstuhl-reports/MoscaNS19 fatcat:b4fbhk267zhsdch2lotalrzwoa

Cryptography Core Technology [chapter]

Chen-Mou Cheng, Kenta Kodera, Atsuko Miyaji, Shinya Okumura
2020 Security Infrastructure Technology for Integrated Utilization of Big Data  
Another is analysis to learning with error (LWE), which is a postquantum cryptosystem and has the functionality of homomorphic encryption.  ...  These two security bases have important roles in each protocol described in Sect. Analysis on ECDLP Introduction In recent years, elliptic curve cryptography is gaining momentum in deployment because  ...  Analysis on Ring-LWE over Decomposition Fields Introduction The ring variant of learning with errors (Ring-LWE) based cryptography [15, 16] is one of the most attractive research areas in cryptography  ... 
doi:10.1007/978-981-15-3654-0_2 fatcat:l5avyfoh6vgwffotnijyxauwq4

Reduction and decomposition of differential automata: Theory and applications [chapter]

Alexey S. Matveev, Andrey V. Savkin
1998 Lecture Notes in Computer Science  
Tang; Wavelet Analysis and its Applications.  ...  Wave lets on Z, Z_n, l^2(Z), Fourier series, transform and convolution on l*2. Wavelet Approximation and Algorithms: The Mallat Algorithm. Text: George J. Klir; Wavelet Analysis and its Applications.  ... 
doi:10.1007/3-540-64358-3_48 fatcat:hqwvar3zbfftdhg4cybpjwogde

Efficient implementation of ideal lattice-based cryptography

Thomas Pöppelmann
2017 it - Information Technology  
One alternative is lattice-based cryptography which allows the construction of asymmetric public-key encryption and signature schemes that offer a good balance between security, performance, and key as  ...  AbstractAlmost all practically relevant asymmetric cryptosystems like RSA or ECC are either based on the hardness of factoring or on the hardness of the discrete logarithm problem.  ...  ring learning with errors (RdLWE).  ... 
doi:10.1515/itit-2017-0030 fatcat:mpmamskk25h3lbyshy4rfd4y4y

Physical Security in the Post-quantum Era: A Survey on Side-channel Analysis, Random Number Generators, and Physically Unclonable Functions [article]

Sreeja Chowdhury, Ana Covic, Rabin Yu Acharya, Spencer Dupee, Fatemeh Ganji, Domenic Forte
2021 arXiv   pre-print
This survey aims to draw greater attention to the importance of physical security, with a focus on secure key generation and storage as well as secure execution.  ...  Physical security deals with the design and implementation of security measures fulfilling the practical requirements of cryptographic primitives, which are equally essential for classic and quantum ones  ...  Examples of Lattice-based algorithms are NTRU, BLISS, ring-TESLA, the GLP, and LAC [Bindel et al. 2016; D'Anvers et al. 2019; Espitau et al. 2017] , which are based on ring learning with errors (R-LWE  ... 
arXiv:2005.04344v2 fatcat:jstlhwebznfadf5g2zdri4sb6i

CRT-based fully homomorphic encryption over the integers

Jung Hee Cheon, Jinsu Kim, Moon Sung Lee, Aaram Yun
2015 Information Sciences  
In this paper, we revisit one of their proposals, in particular the third scheme which is based on the Chinese Remainder Theorem and is ring homomorphic.  ...  Our scheme can be used in applications requiring a large message space ZQ for log Q = O(λ 4 ) or SIMD style operations on Z k Q for log Q = O(λ), k = O(λ 3 ), with O(λ 5 ) ciphertext size as in the DGHV  ...  Acknowledgments We would like to thank Taekyoung Kwon and Hyung Tae Lee for valuable comments.  ... 
doi:10.1016/j.ins.2015.03.019 fatcat:4mv4ztkppvey3gqdw252rs3gaq
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