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172 results on '"Thomé, Emmanuel"'

1. Refined Analysis of the Asymptotic Complexity of the Number Field Sieve

Author

Gluher, Aude Le, Spaenlehauer, Pierre-Jean, and Thomé, Emmanuel

Subjects
Computer Science - Cryptography and Security, Computer Science - Computational Complexity, Mathematics - Number Theory
Abstract

The classical heuristic complexity of the Number Field Sieve (NFS) is the solution of an optimization problem that involves an unknown function, usually noted $o(1)$ and called $\xi(N)$ throughout this paper, which tends to zero as the entry $N$ grows. The aim of this paper is to find optimal asymptotic choices of the parameters of NFS as $N$ grows, in order to minimize its heuristic asymptotic computational cost. This amounts to minimizing a function of the parameters of NFS bound together by a non-linear constraint. We provide precise asymptotic estimates of the minimizers of this optimization problem, which yield refined formulas for the asymptotic complexity of NFS. One of the main outcomes of this analysis is that $\xi(N)$ has a very slow rate of convergence: We prove that it is equivalent to $4{\log}{\log}{\log}\,N/(3{\log}{\log}\,N)$. Moreover, $\xi(N)$ has an unpredictable behavior for practical estimates of the complexity. Indeed, we provide an asymptotic series expansion of $\xi$ and numerical experiments indicate that this series starts converging only for $N>\exp(\exp(25))$, far beyond the practical range of NFS. This raises doubts on the relevance of NFS running time estimates that are based on setting $\xi=0$ in the asymptotic formula., Comment: Accepted for publication in Mathematical Cryptology

Published
2020

2. Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment

Author

Boudot, Fabrice, Gaudry, Pierrick, Guillevic, Aurore, Heninger, Nadia, Thomé, Emmanuel, and Zimmermann, Paul

Subjects
Computer Science - Cryptography and Security
Abstract

We report on two new records: the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a 795-bit prime field. Previous records were the factorization of RSA-768 in 2009 and a 768-bit discrete logarithm computation in 2016. Our two computations at the 795-bit level were done using the same hardware and software, and show that computing a discrete logarithm is not much harder than a factorization of the same size. Moreover, thanks to algorithmic variants and well-chosen parameters, our computations were significantly less expensive than anticipated based on previous records.The last page of this paper also reports on the factorization of RSA-250.

Published
2020

3. A kilobit hidden SNFS discrete logarithm computation

Author

Fried, Joshua, Gaudry, Pierrick, Heninger, Nadia, and Thomé, Emmanuel

Subjects
Computer Science - Cryptography and Security
Abstract

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.

Published
2016
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4. Solving discrete logarithms on a 170-bit MNT curve by pairing reduction

Author

Guillevic, Aurore, Morain, François, and Thomé, Emmanuel

Subjects
Computer Science - Cryptography and Security, Mathematics - Number Theory
Abstract

Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and their security relies on the fact that the embedding field of the underlying curve is relatively large. How large is debatable. The aim of our work is to sustain the claim that the combination of degree 3 embedding and too small finite fields obviously does not provide enough security. As a computational example, we solve the DLP on a 170-bit MNT curve, by exploiting the pairing embedding to a 508-bit, degree-3 extension of the base field., Comment: to appear in the Lecture Notes in Computer Science (LNCS)

Published
2016

5. A modified block Lanczos algorithm with fewer vectors

Author

Thomé, Emmanuel

Subjects
Computer Science - Cryptography and Security, Computer Science - Symbolic Computation
Abstract

The block Lanczos algorithm proposed by Peter Montgomery is an efficient means to tackle the sparse linear algebra problem which arises in the context of the number field sieve factoring algorithm and its predecessors. We present here a modified version of the algorithm, which incorporates several improvements: we discuss how to efficiently handle homogeneous systems and how to reduce the number of vectors stored in the course of the computation. We also provide heuristic justification for the success probability of our modified algorithm. While the overall complexity and expected number of steps of the block Lanczos is not changed by the modifications presented in this article, we expect these to be useful for implementations of the block Lanczos algorithm where the storage of auxiliary vectors sometimes has a non-negligible cost. 1 Linear systems for integer factoring For factoring a composite integer N, algorithms based on the technique of combination of congruences look for several pairs of integers (x, y) such that x 2 $\not\equiv$ y 2 mod N. This equality is hoped to be non trivial for at least one of the obtained pairs, letting gcd(x -- y, N) unveil a factor of the integer N. Several algorithms use this strategy: the CFRAC algorithm, the quadratic sieve and its variants, and the number field sieve. Pairs (x, y) as above are obtained by combining relations which have been collected as a step of these algorithms. Relations are written multiplicatively as a set of valuations. All the algorithms considered seek a multiplicative combination of these relations which can be rewritten as an equality of squares. This is achieved by solving a system of linear equations defined over F 2, where equations are parity constraints on, Comment: Topics in Computational Number Theory inspired by Peter L. Montgomery, Cambridge University Press, 2016

Published
2016

6. Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix

Author

Dumas, Jean-Guillaume, Kaltofen, Erich, Thomé, Emmanuel, and Villard, Gilles

Subjects
Computer Science - Symbolic Computation
Abstract

Computational problem certificates are additional data structures for each output, which can be used by a-possibly randomized-verification algorithm that proves the correctness of each output. In this paper, we give an algorithm that computes a certificate for the minimal polynomial of sparse or structured nxn matrices over an abstract field, of sufficiently large cardinality, whose Monte Carlo verification complexity requires a single matrix-vector multiplication and a linear number of extra field operations. We also propose a novel preconditioner that ensures irreducibility of the characteristic polynomial of the generically preconditioned matrix. This preconditioner takes linear time to be applied and uses only two random entries. We then combine these two techniques to give algorithms that compute certificates for the determinant, and thus for the characteristic polynomial, whose Monte Carlo verification complexity is therefore also linear.

Published
2016

7. Interactive certificate for the verification of Wiedemann's Krylov sequence: application to the certification of the determinant, the minimal and the characteristic polynomials of sparse matrices

Author

Dumas, Jean-Guillaume, Kaltofen, Erich, and Thomé, Emmanuel

Subjects
Computer Science - Symbolic Computation, Computer Science - Computational Complexity, Computer Science - Cryptography and Security
Abstract

Certificates to a linear algebra computation are additional data structures for each output, which can be used by a-possibly randomized- verification algorithm that proves the correctness of each output. Wiede-mann's algorithm projects the Krylov sequence obtained by repeatedly multiplying a vector by a matrix to obtain a linearly recurrent sequence. The minimal polynomial of this sequence divides the minimal polynomial of the matrix. For instance, if the $n\times n$ input matrix is sparse with n 1+o(1) non-zero entries, the computation of the sequence is quadratic in the dimension of the matrix while the computation of the minimal polynomial is n 1+o(1), once that projected Krylov sequence is obtained. In this paper we give algorithms that compute certificates for the Krylov sequence of sparse or structured $n\times n$ matrices over an abstract field, whose Monte Carlo verification complexity can be made essentially linear. As an application this gives certificates for the determinant, the minimal and characteristic polynomials of sparse or structured matrices at the same cost.

Published
2015

8. Fast integer multiplication using generalized Fermat primes

Author

Covanov, Svyatoslav and Thomé, Emmanuel

Subjects
Computer Science - Symbolic Computation, Computer Science - Computational Complexity, Computer Science - Discrete Mathematics, Computer Science - Data Structures and Algorithms
Abstract

For almost 35 years, Sch{\"o}nhage-Strassen's algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n $\times$ log n $\times$ log log n) for multiplying n-bit inputs. In 2007, F{\"u}rer proved that there exists K > 1 and an algorithm performing this operation in O(n $\times$ log n $\times$ K log n). Recent work by Harvey, van der Hoeven, and Lecerf showed that this complexity estimate can be improved in order to get K = 8, and conjecturally K = 4. Using an alternative algorithm, which relies on arithmetic modulo generalized Fermat primes, we obtain conjecturally the same result K = 4 via a careful complexity analysis in the deterministic multitape Turing model.

Published
2015

10. Isogeny graphs with maximal real multiplication

Author

Ionica, Sorina and Thomé, Emmanuel

Subjects
Mathematics - Number Theory
Abstract

An isogeny graph is a graph whose vertices are principally polarized abelian varieties and whose edges are isogenies between these varieties. In his thesis, Kohel described the structure of isogeny graphs for elliptic curves and showed that one may compute the endomorphism ring of an elliptic curve defined over a finite field by using a depth first search algorithm in the graph. In dimension 2, the structure of isogeny graphs is less understood and existing algorithms for computing endomorphism rings are very expensive. Our setting considers genus 2 jacobians with complex multiplication, with the assumptions that the real multiplication subring is maximal and has class number one. We fully describe the isogeny graphs in that case. Over finite fields, we derive a depth first search algorithm for computing endomorphism rings locally at prime numbers, if the real multiplication is maximal. To the best of our knowledge, this is the first DFS-based algorithm in genus 2.

Published
2014

12. Computation with No Memory, and Rearrangeable Multicast Networks

Author

Burckel, Serge, Gioan, Emeric, and Thomé, Emmanuel

Subjects
Computer Science - Discrete Mathematics
Abstract

We investigate the computation of mappings from a set S^n to itself with "in situ programs", that is using no extra variables than the input, and performing modifications of one component at a time, hence using no memory. In this paper, we survey this problem introduced in previous papers by the authors, we detail its close relation with rearrangeable multicast networks, and we provide new results for both viewpoints. A bijective mapping can be computed by 2n - 1 component modifications, that is by a program of length 2n - 1, a result equivalent to the rearrangeability of the concatenation of two reversed butterfly networks. For a general arbitrary mapping, we give two methods to build a program with maximal length 4n-3. Equivalently, this yields rearrangeable multicast routing methods for the network formed by four successive butterflies with alternating reversions. The first method is available for any set S and practically equivalent to a known method in network theory. The second method, a refinement of the first, described when |S| is a power of 2, is new and allows more flexibility than the known method. For a linear mapping, when S is any field, or a quotient of an Euclidean domain (e.g. Z/sZ for any integer s), we build a program with maximal length 2n - 1. In this case the assignments are also linear, thereby particularly efficient from the algorithmic viewpoint, and giving moreover directly a program for the inverse when it exists. This yields also a new result on matrix decompositions, and a new result on the multicast properties of two successive reversed butterflies. Results of this flavour were known only for the boolean field Z/2Z.

Published
2013

13. A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic

Author

Barbulescu, Razvan, Gaudry, Pierrick, Joux, Antoine, and Thomé, Emmanuel

Subjects
Computer Science - Cryptography and Security, Mathematics - Number Theory
Abstract

In the present work, we present a new discrete logarithm algorithm, in the same vein as in recent works by Joux, using an asymptotically more efficient descent approach. The main result gives a quasi-polynomial heuristic complexity for the discrete logarithm problem in finite field of small characteristic. By quasi-polynomial, we mean a complexity of type $n^{O(\log n)}$ where $n$ is the bit-size of the cardinality of the finite field. Such a complexity is smaller than any $L(\varepsilon)$ for $\epsilon>0$. It remains super-polynomial in the size of the input, but offers a major asymptotic improvement compared to $L(1/4+o(1))$.

Published
2013

14. Computing class polynomials for abelian surfaces

Author

Enge, Andreas and Thomé, Emmanuel

Subjects
Computer Science - Cryptography and Security, Mathematics - Number Theory
Abstract

We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating $\theta$- constants in quasi-linear time using Newton iterations on the Borchardt mean. We report on experiments with our implementation and present an example with class number 17608.

Published
2013

15. Computing Discrete Logarithms in

Author

Grémy, Laurent, Guillevic, Aurore, Morain, François, Thomé, Emmanuel, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Adams, Carlisle, editor, and Camenisch, Jan, editor

Published
2018
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16. Root optimization of polynomials in the number field sieve

Author

Bai, Shi, Brent, Richard P., and Thomé, Emmanuel

Subjects
Mathematics - Number Theory, Computer Science - Data Structures and Algorithms, 11A51 (Primary) 11R09 (Secondary)
Abstract

The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties., Comment: 16 pages, 18 references

Published
2012
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17. An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves

Author

Enge, Andreas, Gaudry, Pierrick, and Thomé, Emmanuel

Subjects
Computer Science - Cryptography and Security, Mathematics - Algebraic Geometry
Abstract

We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in $X$ and $Y$ are low with respect to their genera. The finite base fields $\FF_q$ are arbitrary, but their sizes should not grow too fast compared to the genus. For such families, the group structure and discrete logarithms can be computed in subexponential time of $L_{q^g}(1/3, O(1))$. The runtime bounds rely on heuristics similar to the ones used in the number field sieve or the function field sieve.

Published
2009

19. Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

Author

Cheng, Howard, Hanrot, Guillaume, Thomé, Emmanuel, Zima, Eugene, and Zimmermann, Paul

Subjects
Computer Science - Symbolic Computation
Abstract

The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves slightly over existing programs for the computation of $\pi$, and we announce a new record of 2 billion digits for $\zeta(3)$.

Published
2007

20. Solving Discrete Logarithms on a 170-Bit MNT Curve by Pairing Reduction

Author

Guillevic, Aurore, Morain, François, Thomé, Emmanuel, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Avanzi, Roberto, editor, and Heys, Howard, editor

Published
2017
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21. A Kilobit Hidden SNFS Discrete Logarithm Computation

Author

Fried, Joshua, Gaudry, Pierrick, Heninger, Nadia, Thomé, Emmanuel, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Coron, Jean-Sébastien, editor, and Nielsen, Jesper Buus, editor

Published
2017
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22. Discrete Logarithm Factory

Author

Al Aswad, Haetham, Pierrot, Cécile, Thomé, Emmanuel, Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Discrete Logarithm, Discrete Logarithm Factory, Tower NFS, Number Field Sieve, Public Key Cryptography, [INFO]Computer Science [cs], Special NFS, Finite Fields
Abstract

The Number Field Sieve and its variants are the best algorithms to solve the discrete logarithm problem in finite fields. The Factory variant accelerates the computation when several prime fields are targeted. This article adapts the Factory variant to non-prime finite fields of medium and large characteristic. We combine this idea with two other variants of NFS, namely the tower and special variant. This combination leads to improvements in the asymptotic complexity. Besides, we lay out estimates of the practicality of this method for 1024-bit targets and extension degree 6.

Published
2023

23. A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic

Author

Barbulescu, Razvan, Gaudry, Pierrick, Joux, Antoine, Thomé, Emmanuel, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Kobsa, Alfred, editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Weikum, Gerhard, editor, Nguyen, Phong Q., editor, and Oswald, Elisabeth, editor

Published
2014
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24. Discrete Logarithm in GF(2809) with FFS

Author

Barbulescu, Razvan, Bouvier, Cyril, Detrey, Jérémie, Gaudry, Pierrick, Jeljeli, Hamza, Thomé, Emmanuel, Videau, Marion, Zimmermann, Paul, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, and Krawczyk, Hugo, editor

Published
2014
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25. The State of the Art in Integer Factoring and Breaking Public-Key Cryptography

Author

Boudot, Fabrice, Gaudry, Pierrick, Guillevic, Aurore, Heninger, Nadia, Thomé, Emmanuel, Zimmermann, Paul, XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Computer Science and Engineering [Univ California San Diego] (CSE - UC San Diego), University of California [San Diego] (UC San Diego), and University of California (UC)-University of California (UC)

Subjects
[INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], Computer Networks and Communications, Electrical and Electronic Engineering, Law, Computer Science::Cryptography and Security
Abstract

International audience; The security of essentially all public-key cryptography currently in common use today is based on the presumed computational hardness of three number-theoretic problems: integer factoring (required for the security of RSA encryption and digital signatures), discrete logarithms in finite fields (required for Diffie-Hellman key exchange and the DSA digital signature algorithm), and discrete logarithms over elliptic curves (required for elliptic curve Diffie-Hellman and ECDSA, Ed25519, and other elliptic curve digital signature algorithms).In this column, we will review the current state of the art of cryptanalysis for these problems using classical (non-quantum) computers, including in particular our most recent computational records for integer factoring and prime field discrete logarithms.

Published
2022

28. Universal Security : From Bits and Mips to Pools, Lakes – and Beyond

Author

Lenstra, Arjen K., Kleinjung, Thorsten, Thomé, Emmanuel, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Fischlin, Marc, editor, and Katzenbeisser, Stefan, editor

Published
2013
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29. Square Root Algorithms for the Number Field Sieve

Author

Thomé, Emmanuel, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Özbudak, Ferruh, editor, and Rodríguez-Henríquez, Francisco, editor

Published
2012
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30. Factorization of a 768-Bit RSA Modulus

Author

Kleinjung, Thorsten, Aoki, Kazumaro, Franke, Jens, Lenstra, Arjen K., Thomé, Emmanuel, Bos, Joppe W., Gaudry, Pierrick, Kruppa, Alexander, Montgomery, Peter L., Osvik, Dag Arne, te Riele, Herman, Timofeev, Andrey, Zimmermann, Paul, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and Rabin, Tal, editor

Published
2010
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31. Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms

Author

Joux, Antoine, Lercier, Reynald, Naccache, David, Thomé, Emmanuel, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and Parker, Matthew G., editor

Published
2009
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32. Mapping Computation with No Memory

Author

Burckel, Serge, Gioan, Emeric, Thomé, Emmanuel, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Calude, Cristian S., editor, Costa, José Félix, editor, Dershowitz, Nachum, editor, Freire, Elisabete, editor, and Rozenberg, Grzegorz, editor

Published
2009
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33. Faster Multiplication in GF(2)[x]

Author

Brent, Richard P., Gaudry, Pierrick, Thomé, Emmanuel, Zimmermann, Paul, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, van der Poorten, Alfred J., editor, and Stein, Andreas, editor

Published
2008
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34. When e-th Roots Become Easier Than Factoring

Author

Joux, Antoine, Naccache, David, Thomé, Emmanuel, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and Kurosawa, Kaoru, editor

Published
2007
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36. History of Cryptographic Key Sizes

Author

Smart, Nigel, Thomé, Emmanuel, IMEC (IMEC), Catholic University of Leuven - Katholieke Universiteit Leuven (KU Leuven), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Joppe Bos, and Martijn Stam

Subjects
[INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2022

38. Imperfect forward secrecy.

Author

Adrian, David, Bhargavan, Karthikeyan, Durumeric, Zakir, Gaudry, Pierrick, Green, Matthew, Halderman, J. Alex, Heninger, Nadia, Springall, Drew, Thomé, Emmanuel, Valenta, Luke, VanderSloot, Benjamin, Wustrow, Eric, Zanella-Béguelin, Santiago, and Zimmermann, Paul

Subjects
COMPUTER network protocols, PUBLIC key cryptography, CRYPTOGRAPHY, CRYPTOSYSTEMS, DATA encryption, COMPUTER network security, VIRTUAL private networks
Abstract

We investigate the security of Diffie-Hellman key exchange as used in popular Internet protocols and find it to be less secure than widely believed. First, we present Logjam, a novel flaw in TLS that lets a man-in-the-middle downgrade connections to "export-grade" Diffie-Hellman. To carry out this attack, we implement the number field sieve discrete logarithm algorithm. After a week-long precomputation for a specified 512-bit group, we can compute arbitrary discrete logarithms in that group in about a minute. We find that 82% of vulnerable servers use a single 512-bit group, and that 8.4% of Alexa Top Million HTTPS sites are vulnerable to the attack. In response, major browsers have changed to reject short groups. We go on to consider Diffie-Hellman with 768- and 1024-bit groups. We estimate that even in the 1024-bit case, the computations are plausible given nation-state resources. A small number of fixed or standardized groups are used by millions of servers; performing precomputation for a single 1024-bit group would allow passive eavesdropping on 18% of popular HTTPS sites, and a second group would allow decryption of traffic to 66% of IPsec VPNs and 26% of SSH servers. A close reading of published NSA leaks shows that the agency's attacks on VPNs are consistent with having achieved such a break. We conclude that moving to stronger key exchange methods should be a priority for the Internet community. [ABSTRACT FROM AUTHOR]

Published
2019
Full Text
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40. Discrete Logarithm in GF(2809) with FFS

Author

Barbulescu, Razvan, primary, Bouvier, Cyril, additional, Detrey, Jérémie, additional, Gaudry, Pierrick, additional, Jeljeli, Hamza, additional, Thomé, Emmanuel, additional, Videau, Marion, additional, and Zimmermann, Paul, additional

Published
2014
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41. Évaluation des Logiciels

Author

Canteaut, Anne, Fernández, Miguel Angel, Maranget, Luc, Perin, Sophie, Ricchiuto, Mario, Serrano, Manuel, Thomé, Emmanuel, Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Langages de programmation : systèmes de types, concurrence, preuve de programme (CAMBIUM), Collège de France (CdF (institution))-Inria de Paris, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Secure Diffuse Programming (INDES), Inria Sophia Antipolis - Méditerranée (CRISAM), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Inria, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
[INFO]Computer Science [cs]
Published
2021

42. Software Evaluation

Author

Canteaut, Anne, Fernández, Miguel Angel, Maranget, Luc, Perin, Sophie, Ricchiuto, Mario, Serrano, Manuel, Thomé, Emmanuel, Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Langages de programmation : systèmes de types, concurrence, preuve de programme (CAMBIUM), Collège de France (CdF (institution))-Inria de Paris, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Secure Diffuse Programming (INDES), Inria Sophia Antipolis - Méditerranée (CRISAM), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Inria, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
[INFO]Computer Science [cs]
Abstract

This document is intended for the members of Inria juries in order to assist them in their evaluation of software developed by the researchers. It results from the work carried out by the Software Evaluation working group from March to December 2020.

Published
2021

43. Refined Analysis of the Asymptotic Complexity of the Number Field Sieve

Author

Gluher, Aude Le, Spaenlehauer, Pierre-Jean, Thomé, Emmanuel, Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Computer Science - Cryptography and Security, Mathematics - Number Theory, Number Field Sieve, 68W40 (Analysis of algorithms), 11Y05 (Factorization), Complexity, Computational Complexity (cs.CC), Computer Science - Computational Complexity, [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], FOS: Mathematics, Number Theory (math.NT), Cryptography and Security (cs.CR), Computer Science::Operating Systems, Asymptotic optimization
Abstract

The classical heuristic complexity of the Number Field Sieve (NFS) is the solution of an optimization problem that involves an unknown function, usually noted $o(1)$ and called $\xi(N)$ throughout this paper, which tends to zero as the entry $N$ grows. The aim of this paper is to find optimal asymptotic choices of the parameters of NFS as $N$ grows, in order to minimize its heuristic asymptotic computational cost. This amounts to minimizing a function of the parameters of NFS bound together by a non-linear constraint. We provide precise asymptotic estimates of the minimizers of this optimization problem, which yield refined formulas for the asymptotic complexity of NFS. One of the main outcomes of this analysis is that $\xi(N)$ has a very slow rate of convergence: We prove that it is equivalent to $4{\log}{\log}{\log}\,N/(3{\log}{\log}\,N)$. Moreover, $\xi(N)$ has an unpredictable behavior for practical estimates of the complexity. Indeed, we provide an asymptotic series expansion of $\xi$ and numerical experiments indicate that this series starts converging only for $N>\exp(\exp(25))$, far beyond the practical range of NFS. This raises doubts on the relevance of NFS running time estimates that are based on setting $\xi=0$ in the asymptotic formula., Comment: Accepted for publication in Mathematical Cryptology

Published
2021

47. New factorization and discrete logarithm record computations

Author

Boudot, Fabrice, Gaudry, Pierrick, Guillevic, Aurore, Heninger, Nadia, Thomé, Emmanuel, Zimmermann, Paul, XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Computer Science and Engineering [San Diego] (CSE-UCSD), University of California [San Diego] (UC San Diego), and University of California-University of California

Subjects
[INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], factorisation d'entier, crible algébrique, discrete logarithm, logarithme discret, Integer factorization, cryptographie à clé publique, number field sieve, CADO-NFS, public-key cryptography, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Abstract

https://www.techniques-ingenieur.fr/; National audience; This article describes two new records established at the end of 2019 : an integer factorization record for thefactorization of RSA-240, and a discrete logarithm record of the same size. These two records correspond to 795-bit numbers, or 240 decimal digits, and were established with the same open-source CADO-NFS software, onthe same type of processors. These records serve as a reference for key size recommendations for cryptographic protocols.; Cet article décrit deux nouveaux records établis fin 2019 : un record de factorisation d'entier avec la factorisation du nombre RSA-240, et un record de calcul de logarithme discret de même taille. Ces deux records correspondent à des nombres de 795 bits, soit 240 chiffres décimaux, et ont été établis avec le même logiciel libre (CADO-NFS), sur le même type de processeurs. Ces records servent de référence pour les recommandations en termes de taille de clé pour les protocoles cryptographiques.

Published
2020

48. Nouveaux records de factorisation et de calcul de logarithme discret

Author

Boudot, Fabrice, Gaudry, Pierrick, Guillevic, Aurore, Heninger, Nadia, Thomé, Emmanuel, Zimmermann, Paul, XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Computer Science and Engineering [San Diego] (CSE-UCSD), University of California [San Diego] (UC San Diego), University of California-University of California, Department of Computer Science and Engineering [Univ California San Diego] (CSE - UC San Diego), and University of California (UC)-University of California (UC)

Subjects
[INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], factorisation d'entier, crible algébrique, discrete logarithm, logarithme discret, Integer factorization, cryptographie à clé publique, number field sieve, CADO-NFS, public-key cryptography, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Abstract

https://www.techniques-ingenieur.fr/; National audience; This article describes two new records established at the end of 2019 : an integer factorization record for thefactorization of RSA-240, and a discrete logarithm record of the same size. These two records correspond to 795-bit numbers, or 240 decimal digits, and were established with the same open-source CADO-NFS software, onthe same type of processors. These records serve as a reference for key size recommendations for cryptographic protocols.; Cet article décrit deux nouveaux records établis fin 2019 : un record de factorisation d'entier avec la factorisation du nombre RSA-240, et un record de calcul de logarithme discret de même taille. Ces deux records correspondent à des nombres de 795 bits, soit 240 chiffres décimaux, et ont été établis avec le même logiciel libre (CADO-NFS), sur le même type de processeurs. Ces records servent de référence pour les recommandations en termes de taille de clé pour les protocoles cryptographiques.

Published
2020

49. Indicateurs de suivi de l'activité scientifique de l'Inria

Author

Brotcorne, Luce, Canteaut, Anne, Viana, Aline, Grandmont, Céline, Guedj, Benjamin, Huot, Stéphane, Issarny, Valérie, Pallez, Guillaume, Perrier, Valérie, Quema, Vivien, Pomet, Jean-Baptiste, Rival, Xavier, Salvati, Sylvain, Thomé, Emmanuel, Integrated Optimization with Complex Structure (INOCS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), inTeRnet BEyond the usual (TRiBE ), Inria Saclay - Ile de France, COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Technology and knowledge for interaction (LOKI), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Middleware on the Move (MIMOVE), Topology-Aware System-Scale Data Management for High-Performance Computing (TADAAM), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Laboratoire d'Informatique de Grenoble (LIG), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Mathematics for Control, Transport and Applications (McTAO), Inria Sophia Antipolis - Méditerranée (CRISAM), Analyse Statique par Interprétation Abstraite (ANTIQUE), Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), Linking Dynamic Data (LINKS), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Inria, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-École polytechnique universitaire de Lille (Polytech Lille), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Inria Bordeaux - Sud-Ouest, Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris, Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Canteaut, Anne

Subjects
[MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO], [MATH.MATH-HO] Mathematics [math]/History and Overview [math.HO], [INFO.INFO-GL]Computer Science [cs]/General Literature [cs.GL], [INFO.INFO-GL] Computer Science [cs]/General Literature [cs.GL]
Abstract

La Commission d'Evaluation de l'Inria a mis en place début 2020, à la demande de la Direction Générale, un groupe de travail visant à réfléchir à des indicateurs pour l'analyse qualitative de l'activité scientifique de l'Institut. Ce document est le fruit des discussions de ce groupe, enrichies par les échanges avec la Direction Générale d'Inria et avec l'ensemble de la Commision d'Evaluation. Au-delà de cette « commande », il nous a semblé important de saisir cette opportunité pour mener une réflexion collective, qui dépasse le cadre de notre Institut, sur les indicateurs, et sur ce qu'ils peuvent ou ne peuvent pas dire de nos pratiques scientifiques.

Published
2020

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