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SALSA: Attacking Lattice Cryptography with Transformers [article]

Emily Wenger, Mingjie Chen, François Charton, Kristin Lauter
2022 arXiv   pre-print
SALSA can fully recover secrets for small-to-mid size LWE instances with sparse binary secrets, and may scale to attack real-world LWE-based cryptosystems.  ...  Consequently, "quantum resistant" cryptosystems are in high demand, and lattice-based cryptosystems, based on a hard problem known as Learning With Errors (LWE), have emerged as strong contenders for standardization  ...  In [14] and [46] , both papers give reductions of binary-LWE to hard lattice problems, implying the hardness of binary-LWE.  ... 
arXiv:2207.04785v1 fatcat:zz7yt2g3xrh4bmptfrok2fsbsy

On the Hardness of Module Learning With Errors with Short Distributions [article]

Katharina Boudgoust, Corentin Jeudy, Adeline Roux-Langlois, Weiqiang Wen
2022 IACR Cryptology ePrint Archive  
We also prove that the search version of M-LWE with large uniform secret and uniform η-bounded error is at least as hard as the standard M-LWE problem, if the number of samples m is close to the module  ...  The latter result can be extended to provide the hardness of M-LWE with uniform η-bounded secret and error under specific parameter conditions.  ...  We thank our anonymous referees of Asiacrypt 2020, Indocrypt 2020 and CT-RSA 2021 for their throrough proof reading and constructive feedback on the original papers.  ... 
dblp:journals/iacr/BoudgoustJRW22a fatcat:pbj4bnzb6bbjtmy24guqnp6uzu

A Mathematical Perspective on Post-Quantum Cryptography

Maximilian Richter, Magdalena Bertram, Jasper Seidensticker, Alexander Tschache
2022 Mathematics  
Therefore, the main focus is put on the algorithms' corresponding algebraic foundations, in particular LWE problems, NTRU lattices, linear codes and multivariate equation systems with the aim of fostering  ...  In 2016, the National Institute of Standards and Technology (NIST) announced an open competition with the goal of finding and standardizing suitable algorithms for quantum-resistant cryptography.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math10152579 fatcat:rem4jnuxubcjpja35ovdgsmkhu

Lattice PUF: A Strong Physical Unclonable Function Provably Secure against Machine Learning Attacks [article]

Ye Wang, Xiaodan Xi, Michael Orshansky
2020 arXiv   pre-print
The POK provides the secret key of the LWE decryption function; its stability is ensured by a fuzzy extractor (FE).  ...  Our design compactly realizes the decryption function of the learning-with-errors (LWE) cryptosystem.  ...  Aydin Aysu for his insightful advice on idea presentation, assistance with FPGA implementation of repetition code, and comments that greatly improved the manuscript.  ... 
arXiv:1909.13441v2 fatcat:cwbdqurzmva6peqdri7jvxouhi

Entropic Hardness of Module-LWE from Module-NTRU [article]

Katharina Boudgoust, Corentin Jeudy, Adeline Roux-Langlois, Weiqiang Wen
2022 IACR Cryptology ePrint Archive  
In this paper, we focus on proving the hardness of (search) M-LWE for general secret distributions, provided they carry sufficient min-entropy. This is called entropic hardness of M-LWE.  ...  Then, we provide one such distribution whose required properties rely on the hardness of the decisional Module-NTRU problem.  ...  We also thank our anonymous referees of Eurocrypt 2022 for their thorough proof reading and constructive feedback.  ... 
dblp:journals/iacr/BoudgoustJRW22 fatcat:sc3ytpxvtfdmjhexzxs6prhvmq

Compact Lattice Signatures

Dipayan Das, Vishal Saraswat
2018 Proceedings of the 15th International Joint Conference on e-Business and Telecommunications  
We propose a compact lattice-based signature scheme with key-size and signatures of order n, where n is the dimension of the lattice.  ...  The proposed scheme is simple and is competitive with the other post-quantum signature schemes.  ...  Part of the work was carried out while visiting the R.C.Bose Centre for Cryptology and Security, Indian Statistical Institute, Kolkata. We are thankful to Kajla Basu for her support.  ... 
doi:10.5220/0006861606560661 dblp:conf/icete/DasS18 fatcat:eawydz6lkzax3azbovor4p5ujm

Lattice-based Key Sharing Schemes - A Survey [article]

Prasanna Ravi, James Howe, Anupam Chattopadhyay, Shivam Bhasin
2020 IACR Cryptology ePrint Archive  
However, most if not all of it is predominantly built upon hardness guarantees of number theoretic problems that can be broken by large scale quantum computers in the future.  ...  general algorithmic frameworks, practical implementation aspects and physical attack security, with special focus on lattice-based key sharing schemes competing in the NIST's standardization process.  ...  There are other proven variants of the LWE problem based on binary secrets by Brakerski et al. [44] and sparse fixed weight ternary secrets by Cheon et al. [53] .  ... 
dblp:journals/iacr/RaviHCB20 fatcat:gwfp7xfzbbgxnldzbngfc4ru7q

Time-independent discrete Gaussian sampling for post-quantum cryptography

A. Khalid, J. Howe, C. Rafferty, M. O'Neill
2016 2016 International Conference on Field-Programmable Technology (FPT)  
Lattice-based cryptosystems, based on the hardness of the LWE problem are as hard to solve as Definition 1.  ...  It is a synchronous, binary stream cipher with a 288-bit internal state. To achieve a large number of uniformly random bits per clock cycle, the Trivium modules are unrolled.  ... 
doi:10.1109/fpt.2016.7929543 dblp:conf/fpt/KhalidHRO16 fatcat:sgjzijgzx5bcrfk5cczyu24wpi

SCloud: Public Key Encryption and Key Encapsulation Mechanism Based on Learning with Errors [article]

Zhongxiang Zheng, Anyu Wang, Haining Fan, Chunhuan Zhao, Chao Liu, Xue Zhang
2020 IACR Cryptology ePrint Archive  
We propose a new family of public key encryption (PKE) and key encapsulation mechanism (KEM) schemes based on the plain learning with errors (LWE) problem.  ...  The new error-reconciliation mechanism is constructed by combining the binary linear codes and Gray codes.  ...  In 2005, Regev proves the hardness of the LWE problem by assuming the quantum hardness of the Shortest Independent Vectors Problem (SIVP) on random lattices.  ... 
dblp:journals/iacr/ZhengWFZLZ20 fatcat:eiw42fyaurd3tlp2whlkhh3bl4

AxRLWE: A Multilevel Approximate Ring-LWE Co-Processor for Lightweight IoT Applications

Dur-E-Shahwar Kundi, Ayesha Khalid, Song Bian, Chenghua Wang, Maire O'Neill, Weiqiang Liu
2022 IEEE Internet of Things Journal  
With 45nm CMOS technology, AxRLWE was bench-marked to fit well within the same area-budget of lightweight ECC processor and consume a third of energy compared to special class of R-Binary LWE (R-BLWE)  ...  To the best of our knowledge, this is the first endeavour exploring the inherent approximate nature of LWE problem to undertake a multi-level Approximate R-LWE (AxRLWE) architecture with respective security  ...  ACKNOWLEDGEMENT This work is supported by grants from the National Natural Science Foundation of China (62022041 and 61871216) and the Engineering and Physical Sciences Research Council of U.K.  ... 
doi:10.1109/jiot.2021.3122276 fatcat:tdufb6w6vrgcfaopsvxqmdzwp4

Hardness of Module-LWE and Ring-LWE on General Entropic Distributions [article]

Hao Lin, Yang Wang, Mingqiang Wang
2020 IACR Cryptology ePrint Archive  
We show an entropy bound that guarantees the security of arbitrary Entropic Module-LWE and Entropic Ring-LWE, these are the first results on the hardness of algebraically structured LWE with entropic secrets  ...  The hardness of Entropic LWE has been studied in a number of works. However, there is not work study the hardness of algebraically structured LWE with entropic secrets.  ...  To the best of our knowledge, these are the first results on the hardness of algebraically structured LWE with entropic secrets.  ... 
dblp:journals/iacr/LinWW20 fatcat:pjfmrlequrhk7jmu32u773nhmm

Post-Quantum Cryptographic Hardware Primitives [article]

Lake Bu, Rashmi Agrawal, Hai Cheng, Michel A. Kinsy
2019 arXiv   pre-print
The development and implementation of post-quantum cryptosystems have become a pressing issue in the design of secure computing systems, as general quantum computers have become more feasible in the last  ...  In this work, we introduce a set of hardware post-quantum cryptographic primitives (PCPs) consisting of four frequently used security components, i.e., public-key cryptosystem (PKC), key exchange (KEX)  ...  Among these techniques, designs based on Ring-learning with errors (Ring-LWE) [2] thus far have proven to be the most promising approach.  ... 
arXiv:1903.03735v1 fatcat:3iyrsygfxzb5xc6manhymqdmpq

Practical MP-LWE-based encryption balancing security-risk vs. efficiency [article]

Ron Steinfeld, Amin Sakzad, Raymond K. Zhao
2019 IACR Cryptology ePrint Archive  
Middle-Product Learning With Errors (MP-LWE) is a variant of the LWE problem introduced at CRYPTO 2017 by Rosca et al [RSSS17] .  ...  On the security side, we show how to obtain a nearly tight security proof for MP-LWE from the hardest Polynomial LWE problem over a large family of rings, improving on the loose reduction of [RSSS17] .  ...  from PLWE with a secret polynomial of dimension ≤ n, but the above 'generic' embedding attack against MP-LWE works on the MP-LWE secret in a larger dimension n = n + d − 1.  ... 
dblp:journals/iacr/SteinfeldSZ19 fatcat:x4mcq5rcjfg4ff3r322q2xakeq

A Decade of Lattice Cryptography

Chris Peikert
2016 Foundations and Trends® in Theoretical Computer Science  
The main focus is on the foundational short integer solution (SIS) and learning with errors (LWE) problems (and their more efficient ring-based variants), their provable hardness assuming the worst-case  ...  Lattice-based cryptography is the use of conjectured hard problems on point lattices in R n as the foundation for secure cryptographic systems.  ...  I warmly thank Vadim Lyubashevsky, Dieter van Melkebeek, Oded Regev, Noah Stephens-Davidowitz, Madhu Sudan, and an anonymous reviewer for many valuable comments on earlier drafts.  ... 
doi:10.1561/0400000074 fatcat:5orjj3lrufdalfufl7ju6rnz3e

Trend of Bootstrapping from 2009 to 2016

Paulin Boale Bomolo, Eugene Mbuyi Mukendi, Simon Ntumba Badibanga
2021 International Journal of Advanced Computer Science and Applications  
that to date the best bootstrapping on bits is that of the TFHE which executes this processing in 29 seconds improving that of the FHEW 30 times despite the multiplication algorithm used.  ...  The pedestal of fully homomorphic encryption is bootstrapping which allows unlimited processing on encrypted data. This technique is a bottleneck in the practicability of homomorphic encryption.  ...  Hard Problems of Homomorphic Encryption 1) The problem of learning with error: The Problem of Learning With Error (LWE) was introduced by Regev in 2005 [15] .  ... 
doi:10.14569/ijacsa.2021.0121212 fatcat:x44iblyiuzc5bfbdq23qt6f564
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