Statistical Decoding 2.0: Reducing Decoding to LPN

International audienceThe security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoders (ISD). A while ago, a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-checks of moderate weight, and uses some kind of majority voting on these equations to recover the error. This algorithm was long forgotten because even the best variants of it performed poorly when compared to the simplest ISD algorithm. We revisit this old algorithm by using parity-check equations in a more general way. Here the parity-checks are used to get LPN samples with a secret which is part of the error and the LPN noise is related to the weight of the parity-checks we produce. The corresponding LPN problem is then solved by standard Fourier techniques. By properly choosing the method of producing these low weight equations and the size of the LPN problem, we are able to outperform in this way significantly information set decoders at code rates smaller than 0.3. It gives for the first time after 60 years, a better decoding algorithm for a significant range which does not belong to the ISD family

Reduction from sparse LPN to LPN, Dual Attack 3.0

The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders ($\mathsf{ISD}$). However, recently a new algorithm called RLPN-decoding which relies on a completely different approach was introduced and it has been shown that RLPN outperforms significantly $\mathsf{ISD}$ decoders for a rather large range of rates. This RLPN decoder relies on two ingredients, first reducing decoding to some underlying LPN problem, and then computing efficiently many parity-checks of small weight when restricted to some positions. We revisit RLPN-decoding by noticing that, in this algorithm, decoding is in fact reduced to a sparse-LPN problem, namely with a secret whose Hamming weight is small. Our new approach consists this time in making an additional reduction from sparse-LPN to plain-LPN with a coding approach inspired by $\mathsf{coded}$-$\mathsf{BKW}$. It outperforms significantly the $\mathsf{ISD}$\u27s and RLPN for code rates smaller than $0.42$. This algorithm can be viewed as the code-based cryptography cousin of recent dual attacks in lattice-based cryptography. We depart completely from the traditional analysis of this kind of algorithm which uses a certain number of independence assumptions that have been strongly questioned recently in the latter domain. We give instead a formula for the LPN noise relying on duality which allows to analyze the behavior of the algorithm by relying only on the analysis of a certain weight distribution. By using only a minimal assumption whose validity has been verified experimentally we are able to justify the correctness of our algorithm. This key tool, namely the duality formula, can be readily adapted to the lattice setting and is shown to give a simple explanation for some phenomena observed on dual attacks in lattices in [DP23]

COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study

Background: The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms. Methods: International, prospective observational study of 60 109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms. Results: ‘Typical’ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (≤ 18 years: 69, 48, 23; 85%), older adults (≥ 70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each P < 0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country. Interpretation: This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men

Security Analysis of SDiTH

International audienceWe show that here standard decoding algorithms for generic linear codes over a finite field can speeded up by a factor which is essentially the size of the finite fieldby reducing it to a low weight codeword problem and by working in the relevant projective space. We apply this technique to SDiTH and show that the parameters of both the original submission and the updated version fall short of meeting the security requirements asked by the NIST

Reduction from Sparse LPN to LPN, Dual Attack 3.0

The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders (ISD). However, recently a new algorithm called RLPNdecoding which relies on a completely different approach was introduced and it has been shown that RLPN outperforms significantly ISD decoders for a rather large range of rates. This RLPN decoder relies on two ingredients, first reducing decoding to some underlying LPN problem, and then computing efficiently many parity-checks of small weight when restricted to some positions. We revisit RLPN-decoding by noticing that, in this algorithm, decoding is in fact reduced to a sparse-LPN problem, namely with a secret whose Hamming weight is small. Our new approach consists this time in making an additional reduction from sparse-LPN to plain-LPN with a coding approach inspired by coded-BKW. It outperforms significantly the ISD's and RLPN for code rates smaller than 0.42. This algorithm can be viewed as the code-based cryptography cousin of recent dual attacks in lattice-based cryptography. We depart completely from the traditional analysis of this kind of algorithm which uses a certain number of independence assumptions that have been strongly questioned recently in the latter domain. We give instead a formula for the LPN noise relying on duality which allows to analyze the behavior of the algorithm by relying only on the analysis of a certain weight distribution. By using only a minimal assumption whose validity has been verified experimentally we are able to justify the correctness of our algorithm. This key tool, namely the duality formula, can be readily adapted to the lattice setting and is shown to give a simple explanation for some phenomena observed on dual attacks in lattices in [DP23b]

Reduction from Sparse LPN to LPN, Dual Attack 3.0

The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders (ISD). However, recently a new algorithm called RLPNdecoding which relies on a completely different approach was introduced and it has been shown that RLPN outperforms significantly ISD decoders for a rather large range of rates. This RLPN decoder relies on two ingredients, first reducing decoding to some underlying LPN problem, and then computing efficiently many parity-checks of small weight when restricted to some positions. We revisit RLPN-decoding by noticing that, in this algorithm, decoding is in fact reduced to a sparse-LPN problem, namely with a secret whose Hamming weight is small. Our new approach consists this time in making an additional reduction from sparse-LPN to plain-LPN with a coding approach inspired by coded-BKW. It outperforms significantly the ISD's and RLPN for code rates smaller than 0.42. This algorithm can be viewed as the code-based cryptography cousin of recent dual attacks in lattice-based cryptography. We depart completely from the traditional analysis of this kind of algorithm which uses a certain number of independence assumptions that have been strongly questioned recently in the latter domain. We give instead a formula for the LPN noise relying on duality which allows to analyze the behavior of the algorithm by relying only on the analysis of a certain weight distribution. By using only a minimal assumption whose validity has been verified experimentally we are able to justify the correctness of our algorithm. This key tool, namely the duality formula, can be readily adapted to the lattice setting and is shown to give a simple explanation for some phenomena observed on dual attacks in lattices in [DP23b]

Statistical Decoding 2.0: Reducing Decoding to LPN

International audienceThe security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoders (ISD). A while ago, a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-checks of moderate weight, and uses some kind of majority voting on these equations to recover the error. This algorithm was long forgotten because even the best variants of it performed poorly when compared to the simplest ISD algorithm. We revisit this old algorithm by using parity-check equations in a more general way. Here the parity-checks are used to get LPN samples with a secret which is part of the error and the LPN noise is related to the weight of the parity-checks we produce. The corresponding LPN problem is then solved by standard Fourier techniques. By properly choosing the method of producing these low weight equations and the size of the LPN problem, we are able to outperform in this way significantly information set decoders at code rates smaller than 0.3. It gives for the first time after 60 years, a better decoding algorithm for a significant range which does not belong to the ISD family

Transfer of a miniaturized method for high-throughput screening of biomass pretreatment and saccharification and application on poplar and miscanthus clones

CT2 ; Département BAPTransfer of a miniaturized method for high-throughput screening of biomass pretreatment and saccharification and application on poplar and miscanthus clones. Exploring lignocellulosic biomas

Paediatric COVID-19 mortality: a database analysis of the impact of health resource disparity

Background The impact of the COVID-19 pandemic on paediatric populations varied between high-income countries (HICs) versus low-income to middle-income countries (LMICs). We sought to investigate differences in paediatric clinical outcomes and identify factors contributing to disparity between countries.Methods The International Severe Acute Respiratory and Emerging Infections Consortium (ISARIC) COVID-19 database was queried to include children under 19 years of age admitted to hospital from January 2020 to April 2021 with suspected or confirmed COVID-19 diagnosis. Univariate and multivariable analysis of contributing factors for mortality were assessed by country group (HICs vs LMICs) as defined by the World Bank criteria.Results A total of 12 860 children (3819 from 21 HICs and 9041 from 15 LMICs) participated in this study. Of these, 8961 were laboratory-confirmed and 3899 suspected COVID-19 cases. About 52% of LMICs children were black, and more than 40% were infants and adolescent. Overall in-hospital mortality rate (95% CI) was 3.3% [=(3.0% to 3.6%), higher in LMICs than HICs (4.0% (3.6% to 4.4%) and 1.7% (1.3% to 2.1%), respectively). There were significant differences between country income groups in intervention profile, with higher use of antibiotics, antivirals, corticosteroids, prone positioning, high flow nasal cannula, non-invasive and invasive mechanical ventilation in HICs. Out of the 439 mechanically ventilated children, mortality occurred in 106 (24.1%) subjects, which was higher in LMICs than HICs (89 (43.6%) vs 17 (7.2%) respectively). Pre-existing infectious comorbidities (tuberculosis and HIV) and some complications (bacterial pneumonia, acute respiratory distress syndrome and myocarditis) were significantly higher in LMICs compared with HICs. On multivariable analysis, LMIC as country income group was associated with increased risk of mortality (adjusted HR 4.73 (3.16 to 7.10)).Conclusion Mortality and morbidities were higher in LMICs than HICs, and it may be attributable to differences in patient demographics, complications and access to supportive and treatment modalities