Filters








17 Hits in 3.6 sec

Improvements of Algebraic Attacks for solving the Rank Decoding and MinRank problems [article]

Magali Bardet, Maxime Bros, Daniel Cabarcas, Philippe Gaborit, Ray Perlner, Daniel Smith-Tone, Jean-Pierre Tillich, Javier Verbel
2020 arXiv   pre-print
Rank Decoding (RD) is the main underlying problem in rank-based cryptography.  ...  Two main approaches have been studied to solve RD: combinatorial ones and algebraic ones.  ...  Javier Verbel was supported for this work by Colciencias scholarship 757 for PhD studies and the University of Louisville facilities.  ... 
arXiv:2002.08322v3 fatcat:qt3zmk5imjc6neytawezi7j6vq

On the Complexity of the Rank Syndrome Decoding Problem

Philippe Gaborit, Olivier Ruatta, Julien Schrek
2016 IEEE Transactions on Information Theory  
The Rank Syndrome Decoding (RSD) problem is the analagous for rank metric of the Syndrome Decoding problem for Hamming distance.  ...  In this paper we propose two new generic attacks on the Rank Syndrome Decoding (RSD) problem.  ...  Algebraic attacks aim at caracterizing the notion of rank through algebraic settings, which give equations that one tries to solve with classical solving tools like Grobner basis.  ... 
doi:10.1109/tit.2015.2511786 fatcat:quynxesm5vfsvpwkfgdw73bfyi

On the complexity of the Rank Syndrome Decoding problem [article]

Philippe Gaborit and Olivier Ruatta and Julien Schrek
2013 arXiv   pre-print
In this paper we propose two new generic attacks on the Rank Syndrome Decoding (RSD) problem Let C be a random [n,k] rank code over GF(q^m) and let y=x+e be a received word such that x ∈ C and the Rank  ...  The second attack is based on a algebraic attacks: based on the theory of q-polynomials introduced by Ore we propose a new algebraic setting for the RSD problem that permits to consider equations and  ...  The Rank Syndrome Decoding (RSD) problem is the analagous for rank metric of the Syndrome Decoding problem for Hamming distance.  ... 
arXiv:1301.1026v1 fatcat:gw4zl7fytragplpv5gmmyzcbmm

An Algebraic Attack on Rank Metric Code-Based Cryptosystems [article]

Magali Bardet, Pierre Briaud, Maxime Bros, Philippe Gaborit, Vincent Neiger, Olivier Ruatta, Jean-Pierre Tillich
2020 arXiv   pre-print
The Rank metric decoding problem is the main problem considered in cryptography based on codes in the rank metric.  ...  (PQCrypto 2019) on systems arising from the MinRank problem; with target rank r, Verbel et al. lower the solving degree to r+2, and even less for some favorable instances that they call superdetermined  ...  The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, as well as Ray Perlner and Daniel Smith for useful discussions.  ... 
arXiv:1910.00810v2 fatcat:bzlesnkjkfatpets6oi4u6gxte

Improvement of algebraic attacks for solving superdetermined MinRank instances [article]

Magali Bardet, Manon Bertin
2022 arXiv   pre-print
We show that the algebraic attack from Barelli and Couvreur (Asiacrypt 2018), improved in Bardet et al.  ...  In this paper, we give a complete algebraic explanation of the link between the (KS) and (SM) modelings (for any instance).  ...  In code-based cryptography, the MinRank problem is exactly the decoding problem for matrix codes in rank metric.  ... 
arXiv:2208.01442v1 fatcat:hdgnajo5wnbs5pkzxwaqq4u56m

Multivariate Public Key Cryptosystem from Sidon Spaces [article]

Netanel Raviv, Ben Langton, Itzhak Tamo
2022 arXiv   pre-print
In particular, it is proved that the two popular attacks on the MinRank problem, the kernel attack, and the minor attack, succeed only with exponentially small probability.  ...  This system, whose security relies on the hardness of the well-known MinRank problem, is shown to be resilient to several straightforward algebraic attacks.  ...  In all of these attacks, it is shown that breaking the system requires solving some special case of MinRank, and the feasibility of success is discussed. The MinRank problem.  ... 
arXiv:2106.07785v3 fatcat:bnv5npc6wnb4hobv2ddplcxhhi

An algebraic approach to the Rank Support Learning problem [article]

Magali Bardet
2021 arXiv   pre-print
This problem is for instance used in the Durandal signature scheme. In this paper, we propose an algebraic attack on RSL which clearly outperforms the previous attacks to solve this problem.  ...  The Rank Support Learning problem (RSL) is a variant where an attacker has access to N decoding instances whose errors have the same support and wants to solve one of them.  ...  (Rank Decoding problem (RD)) Input: an F q m -basis (c 1 , . . . , c k ) of a subspace C of F n q m , an integer r ∈ N, and a vector y ∈ F n q m such that |y − c| RANK ≤ r for some c ∈ C.  ... 
arXiv:2103.03558v1 fatcat:poczjy22zvhltgqbxs2f6ihg6a

Algebraic Cryptanalysis of McEliece Variants with Compact Keys [chapter]

Jean-Charles Faugère, Ayoub Otmani, Ludovic Perret, Jean-Pierre Tillich
2010 Lecture Notes in Computer Science  
An implementation of our algebraic attack in the computer algebra system MAGMA allows to find the secret-key in a negligible time (less than one second) for almost all the proposed challenges.  ...  We have used these highly structured algebraic equations to mount an efficient key-recovery attack against two recent variants of the McEliece cryptosystems that aim at reducing public key sizes.  ...  As pointed in [2] , promising candidates include: the problem of solving multivariate equations over a finite field, the problem of finding a short vector in a lattice and the problem of decoding a linear  ... 
doi:10.1007/978-3-642-13190-5_14 fatcat:ji7gr6vfojfllaj7deubxau2hm

A Novel Niederreiter-like cryptosystem based on the (u|u + υ)-construction codes

Roumaissa Mahdjoubi, Pierre Louis Cayrel, Sedat Akleylek, Guenda Kenza
2021 RAIRO - Theoretical Informatics and Applications  
The security is based on the hardness of the Rank Syndrome Decoding (RSD) problem and it presents a (u|u + υ)-construction code using two different types of codes: Ideal Low Rank Parity Check (ILRPC) codes  ...  The proposed encryption scheme benefits are a larger minimum distance, a new efficient decoding algorithm and a smaller ciphertext and public key size compared to the Loidreau's variants and to its IND-CCA  ...  s attack (2020) [5] The authors in [5] provided an improvement of algebraic attacks for solving MinRank and Rank Decoding problems without using Gröbner basis and breaks rank based parameters proposed  ... 
doi:10.1051/ita/2021010 fatcat:b7z4ngmt4nhvrcbmlie7xdiz2m

A polynomial attack on a NIST proposal: RankSign, a code-based signature in rank metric [article]

Thomas Debris-Alazard, Jean-Pierre Tillich
2018 IACR Cryptology ePrint Archive  
This signature scheme is based on the rank metric and enjoys remarkably small key sizes, about 10KBytes for an intended level of security of 128 bits.  ...  As a second contribution we will show that the problem is deeper than finding a new signature in rank-based cryptography, we also found an attack on the generic problem upon which its security reduction  ...  Restricting the number of solutions. We have solved the bilinear system (17) with Gröbner basis techniques that are implemented in Magma.  ... 
dblp:journals/iacr/Debris-AlazardT18 fatcat:k7hiki5i5ra4ramacbwirxxvvm

RankSign: an efficient signature algorithm based on the rank metric [article]

Philippe Gaborit, Olivier Ruatta, Julien Schrek, Gilles Zémor
2017 arXiv   pre-print
The paper describes RankSign: a new signature algorithm for the rank metric based on a new mixed algorithm for decoding erasures and errors for the recently introduced Low Rank Parity Check (LRPC) codes  ...  When the classical approach consists in finding the unique preimage of a syndrome through a decoding algorithm, we propose to introduce the notion of mixed decoding of erasures and errors for building  ...  of the GPT cryposystem. algebraic attacks and Levy-Perret attack: the particular nature of the rank metric makes it a natural field for algebraic attacks and solving by Groebner basis, since these attack  ... 
arXiv:1606.00629v2 fatcat:4r3pcnwlqfczdpx3y7bad7oiue

Two attacks on rank metric code-based schemes: RankSign and an Identity-Based-Encryption scheme [article]

Thomas Debris-Alazard, Jean-Pierre Tillich
2018 arXiv   pre-print
This signature scheme is based on the rank metric and enjoys remarkably small key sizes, about 10KBytes for an intended level of security of 128 bits.  ...  As a second contribution we will show that the problem is deeper than finding a new signature in rank-based cryptography, we also found an attack on the generic problem upon which its security reduction  ...  We have solved the bilinear system (17) with Gröbner basis techniques that are implemented in Magma.  ... 
arXiv:1804.02556v2 fatcat:bypwdkfv5zhizgigg7lir574fq

Two Attacks on Rank Metric Code-Based Schemes: RankSign and an IBE Scheme [chapter]

Thomas Debris-Alazard, Jean-Pierre Tillich
2018 Lecture Notes in Computer Science  
This signature scheme is based on the rank metric and enjoys remarkably small key sizes, about 10KBytes for an intended level of security of 128 bits.  ...  Unfortunately we will show that all the parameters proposed for this scheme in [5] can be broken by an algebraic attack that exploits the fact that the augmented LRPC codes used in this scheme have very  ...  We have solved the bilinear system (17) with Gröbner basis techniques that are implemented in Magma.  ... 
doi:10.1007/978-3-030-03326-2_3 fatcat:zh2tgmo7ivhkto3omjcmkulfke

Coding Theory

Joachim Rosenthal, Mohammad Amin Shokrollahi
2007 Oberwolfach Reports  
Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete  ...  The workshop on coding theory covered many facets of the recent research advances.  ...  MinRank and Rank Decoding: similarity and cryptographic relevance Françoise Levy-dit-Vehel In this talk, we study a very natural problem in linear algebra called MinRank (MR), that was originally introduced  ... 
doi:10.4171/owr/2007/56 fatcat:ac2rttsrn5g2rn5la72nudiyum

Post Quantum Cryptography: Techniques, Challenges, Standardization, and Directions for Future Research [article]

Ritik Bavdekar, Eashan Jayant Chopde, Ashutosh Bhatia, Kamlesh Tiwari, Sandeep Joshua Daniel, Atul
2022 arXiv   pre-print
The best classical algorithms available take exponential time. Shor's factoring algorithm can solve the problems in polynomial time.  ...  Grover's search algorithm gives a square root time boost for the searching of the key in symmetric schemes like AES and 3DES.  ...  This problem is considered a hard problem even for quantum computers. There are methods like the Grobner basis that help solve the problem.  ... 
arXiv:2202.02826v1 fatcat:ghq4lqiu4rf5vpuv6gbk7ws4jm
« Previous Showing results 1 — 15 out of 17 results