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LPN Decoded [chapter]

Andre Esser, Robert Kübler, Alexander May
2017 Lecture Notes in Computer Science  
Our new algorithms are modifications and extensions of the simple Gaussian elimination algorithm with recent advanced techniques for decoding random linear codes.  ...  To the best of our knowledge, we provide the first quantum algorithms for LPN.  ...  LPN and its Relation to Decoding Let us slightly modify the Gauss algorithm from Section 3.2.  ... 
doi:10.1007/978-3-319-63715-0_17 fatcat:oqpz2rj5yvh5roebxapns7ygpi

Decoding Linear Codes with High Error Rate and Its Impact for LPN Security [chapter]

Leif Both, Alexander May
2018 Lecture Notes in Computer Science  
Since cryptographic instances of LPN usually work in the high error regime, our algorithm has implications for LPN security.  ...  We propose a new algorithm for the decoding of random binary linear codes of dimension n that is superior to previous algorithms for high error rates.  ...  LPN 512 , 1 4 5121 LPN 117, 255 log(T ) log(S) log(T ) log(S) Fig. 7: Complexities of different decoding algorithms for LPN instances. 512 Prange [Pra62] 213 - 117 - BJMM [BJMM12] 190 114 117 62  ... 
doi:10.1007/978-3-319-79063-3_2 fatcat:u5je5dunh5dx7k2keouxfcyvhq

Control with minimum communication cost per symbol

Justin Pearson, Joao P. Hespanha, Daniel Liberzon
2014 53rd IEEE Conference on Decision and Control  
This paper explores how the imposition of limits on an encoder's bit-rate and average resource consumption affect the encoder/decoder/controller's ability to keep the process bounded.  ...  assume that the sensor that measures the state is connected to the actuator through a finite capacity communication channel over which an encoder at the sensor sends symbols from a finite alphabet to a decoder  ...  Theorem 2 from [2] guarantees the existence of a stabilizing encoder/decoder/controller triple with bit-rate log 2 LpN, M, Sq{N T .  ... 
doi:10.1109/cdc.2014.7040336 dblp:conf/cdc/PearsonHL14 fatcat:kp23bsf3ebgv3ekchl4353lski

A Post-Quantum Biometric Template Protection Scheme based on Learning Parity With Noise (LPN) Commitments

Rosario Arjona, Iluminada Baturone
2020 IEEE Access  
In biometric LPN Commitments this attack is not possible since and ′ should be equal to decode the system of linear equations.  ...  Nowadays, the best algorithms for decoding random binary linear codes formulated as a syndrome decoding problem are based on Information Set Decoding (ISD) [23] , a probabilistic decoding strategy that  ... 
doi:10.1109/access.2020.3028703 fatcat:f4wobq3jv5dl5f7oh5u4p7gzm4

Designing an asynchronous processor using Petri nets

A. Semenov, A.M. Koelmans, L. Lloyd, A. Yakovlev
1997 IEEE Micro  
If \Store" has been decoded, and its request loses competition for the mutual exclusion token to the request coming from PC, the LPN will deadlock.  ...  PC), Address Decoder (AD) and Memory (Mem).  ... 
doi:10.1109/40.592316 fatcat:v3pgz6ensnhx7hvnbrobflauj4

Optimization of $$\mathsf {LPN}$$ Solving Algorithms [chapter]

Sonia Bogos, Serge Vaudenay
2016 Lecture Notes in Computer Science  
When searching for an algorithm to solve an LPN instance, we make use of the existing techniques and optimize their use.  ...  We formalize an LPN algorithm as a path in a graph G and our algorithm is searching for the optimal paths in this graph.  ...  Let decode be an optimal deterministic decoding algorithm.  ... 
doi:10.1007/978-3-662-53887-6_26 fatcat:v2zu34pumjfhthdnzjlibgkpmq

An Algorithm for Solving the LPN Problem and Its Application to Security Evaluation of the HB Protocols for RFID Authentication [chapter]

Marc P. C. Fossorier, Miodrag J. Mihaljević, Hideki Imai, Yang Cui, Kanta Matsuura
2006 Lecture Notes in Computer Science  
A novel algorithm for solving the LPN problem is proposed and analyzed.  ...  The algorithm originates from the recently proposed advanced fast correlation attacks, and it employs the concepts of decimation, linear combining, hypothesizing and minimum distance decoding.  ...  Particularly note that the LPN problem can be formulated also as the problem of decoding a random linear block code [1, 14] and has been shown to be NPcomplete [1] .  ... 
doi:10.1007/11941378_5 fatcat:uz4svaf7fvbvnb22nhp2zdyhhy

Computational Limitations in Robust Classification and Win-Win Results [article]

Akshay Degwekar, Preetum Nakkiran, Vinod Vaikuntanathan
2019 arXiv   pre-print
Because E is a sparse matrix, it can be used to solve the problem of distinguishing LPN samples from random and decoding noisy codewords. Proof.  ...  Traditionally this problem is studied as the problem of decoding linear codes with preprocessing (for LPN) and closest vector problem with preprocessing (for LWE).  ... 
arXiv:1902.01086v2 fatcat:7o2osvqcmbckpkc7xznpmujkny

HELEN: A Public-Key Cryptosystem Based on the LPN and the Decisional Minimal Distance Problems [chapter]

Alexandre Duc, Serge Vaudenay
2013 Lecture Notes in Computer Science  
We propose HELEN, a code-based public-key cryptosystem whose security is based on the hardness of the Learning from Parity with Noise problem (LPN) and the decisional minimum distance problem.  ...  The complexity of decryption is O (µn + T Decode ), where T Decode is the complexity of the decoding algorithm. Let ρ be the maximum number of errors the errorcorrecting code can correct.  ...  Let also Decode be an efficient decoding algorithm corresponding to this code. Encryption: We encrypt a plaintext m ∈ {0, 1} κ in two steps. First we compute b 1 . . . b µ := Encode(m).  ... 
doi:10.1007/978-3-642-38553-7_6 fatcat:p7nozvdntjbylnkfxqoyng2wnq

Neurons in primary auditory cortex represent sound source location in a cue-invariant manner

Katherine C. Wood, Stephen M. Town, Jennifer K. Bizley
2019 Nature Communications  
Furthermore, neural firing pattern decoders outperformed two-channel model decoders using population activity.  ...  tested on LPN responses (top right), trained and tested on LPN (lower left) and trained and tested on HPN (lower right). b Root-mean squared error (RMSE) of the decoder (coloured symbols) was lower than  ...  We trained the distributed decoder with responses to one condition (e.g., LPN) and tested the decoder using responses from the same neurons to another condition (e.g., HPN).  ... 
doi:10.1038/s41467-019-10868-9 pmid:31289272 pmcid:PMC6616358 fatcat:7rrdve2rdfgyjlfhfo4vilt4fm

A New Algorithm for Solving Ring-LPN with a Reducible Polynomial [article]

Qian Guo, Thomas Johansson, Carl Löndahl
2014 arXiv   pre-print
The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology.  ...  A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic primitive.  ...  Attacks 1) Attacks on Standard LPN: The LPN problem can be viewed as a general decoding problem in coding theory.  ... 
arXiv:1409.0472v1 fatcat:ou3fll4ysbakzeguk337im3jia

Solving LPN Using Covering Codes [chapter]

Qian Guo, Thomas Johansson, Carl Löndahl
2014 Lecture Notes in Computer Science  
We present a new algorithm for solving the LPN problem.  ...  In particular, we can now solve the (512, 1 8 ) LPN instance with complexity less than 2 80 operations in expectation, indicating that cryptographic schemes like HB variants and LPN-C should increase their  ...  The two major threats against LPN-based cryptographic constructions are generic algorithms that decode random linear codes (information-set decoding (ISD)) and variants of the BKW algorithm, originally  ... 
doi:10.1007/978-3-662-45611-8_1 fatcat:visiw2fcofctji3kolmxkzzw5y

On the Security of Non-Linear HB (NLHB) Protocol against Passive Attack

Mohammad Reza Sohizadeh Abyaneh
2010 2010 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing  
In contrast to HB, NLHB relies on the complexity of decoding a class of non-linear codes to render the passive attacks proposed against HB ineffective.  ...  As a variant of the HB authentication protocol for RFID systems, which relies on the complexity of decoding linear codes against passive attacks, Madhavan et al. presented Non-Linear HB(NLHB) protocol.  ...  Phase I: Linearization Our objective in this phase is to find a relatively good linear approximation for non-linear part of NLHB to convert the problem of decoding a non-linear random code to LPN problem  ... 
doi:10.1109/euc.2010.86 dblp:conf/euc/Abyaneh10 fatcat:pfyu3kroxzhc5lcearxe4er2z4

Chosen-Ciphertext Secure Key Encapsulation Mechanism in the Standard Model

Shengfeng Xu, Xiangxue Li
2021 IEEE Access  
The encapsulated key is determined by a special LPN problem (with no random oracle required).  ...  In this work, we propose the first direct construction of LPN-based KEM, which is secure in the standard model.  ...  We can decode the correct s from c 1 − S T 0 c 0 by using the decoding algorithm ECC −1 , where the error term satisfies |(S 0 − S 0 ) T e + (E 0 − E 0 ) T s| ≤ αm.  ... 
doi:10.1109/access.2021.3051047 fatcat:aehcc7pdknbd3evcj3tlpjo3be

Simple Chosen-Ciphertext Security from Low-Noise LPN [chapter]

Eike Kiltz, Daniel Masny, Krzysztof Pietrzak
2014 Lecture Notes in Computer Science  
CCA-secure encryption from low-noise LPN.  ...  This raises the question, whether it's possible to shorten the keys in the LPN setting by using the techniques from [9] .  ...  The LPN problem is very attractive, because of its similarity to the well-studied syndrome decoding problem and its assumed hardness in a post-quantum world.  ... 
doi:10.1007/978-3-642-54631-0_1 fatcat:bjiug4evvbberjckm6gcyw76ky
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