A kilobit hidden SNFS discrete logarithm computation

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software. Our chosen prime $p$ looks random, and $p--1$ has a 160-bit prime factor, in line with recommended parameters for the Digital Signature Algorithm. However, our p has been trapdoored in such a way that the special number field sieve can be used to compute discrete logarithms in $\mathbb{F}\_p^*$ , yet detecting that p has this trapdoor seems out of reach. Twenty-five years ago, there was considerable controversy around the possibility of back-doored parameters for DSA. Our computations show that trapdoored primes are entirely feasible with current computing technology. We also describe special number field sieve discrete log computations carried out for multiple weak primes found in use in the wild. As can be expected from a trapdoor mechanism which we say is hard to detect, our research did not reveal any trapdoored prime in wide use. The only way for a user to defend against a hypothetical trapdoor of this kind is to require verifiably random primes

Improvements in the computation of ideal class groups of imaginary quadratic number fields

We investigate improvements to the algorithm for the computation of ideal class groups described by Jacobson in the imaginary quadratic case. These improvements rely on the large prime strategy and a new method for performing the linear algebra phase. We achieve a significant speed-up and are able to compute ideal class groups with discriminants of 110 decimal digits in less than a week.Comment: 14 pages, 5 figure

Practical improvements to class group and regulator computation of real quadratic fields

We present improvements to the index-calculus algorithm for the computation of the ideal class group and regulator of a real quadratic field. Our improvements consist of applying the double large prime strategy, an improved structured Gaussian elimination strategy, and the use of Bernstein's batch smoothness algorithm. We achieve a significant speed-up and are able to compute the ideal class group structure and the regulator corresponding to a number field with a 110-decimal digit discriminant

Protocol for soil functionality assessment in vineyards

Protocols used by Resolve partners during the project, to assess soil functionality on degraded aeras and evaluate soil restoration after applying recovering practices

Protocols for soil functionality assessment in vineyards

The purpose of this guideline is to describe the methods used during ReSolVe project for soil functionality assessment, so they can be implemented in similar studies. A brief introduction first underlines what are the main functions of soil and why maintaining an optimal soil functionality is particularly of major interest in viticulture. Then the different protocols selected for ReSolVe project and this guideline are presented according to the following classification: - Part I: assessment of soil physical and chemical features; - Part II: assessment of soil biological features (ecosystem service provision and providers); - Part III: assessment of rhizosphere biological features; - Part IV: assessment of grapevine quantitative and qualitative indicators reflecting soil functionality. In each part, global objectives of the monitoring are explained (what is it used for, in which cases…) and the parameters to evaluate are listed with their corresponding methodological sheet. In these sheets, instructions and information are given about: - Materials needed to perform the sampling and the measurement - Sampling procedure - Analysis procedure - Possible interpretations and conclusions that can be drawn (value and meaning of the results, indication of reference values when existing, potential limit of the protocol) - Bibliographic references related to the method described - Additional helpful information where appropriate (ex: template of sampling sheet

Protocol for soil functionality assessment in vineyards

Protocols used by Resolve partners during the project, to assess soil functionality on degraded aeras and evaluate soil restoration after applying recovering practices