A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On the complexity of the generalized MinRank problem

2013
*
Journal of symbolic computation
*

We study

doi:10.1016/j.jsc.2013.03.004
fatcat:neopu3qjx5eb5pqxreyuebbmam
*the**complexity**of*solving*the**generalized**MinRank**problem*, i.e. computing*the*set*of*points where*the*evaluation*of*a polynomial matrix has rank at most r. ... We show that its*complexity*can be bounded by using*the**complexity*bounds for*the**generalized**MinRank**problem*. ... Acknowledgments This work was supported in part by*the*HPAC grant and*the*GeoLMI grant (ANR 2011 BS03 011 06)*of**the*French National Research Agency. ...##
###
On the Complexity of the Generalized MinRank Problem
[article]

2013
*
arXiv
*
pre-print

We study

arXiv:1112.4411v2
fatcat:n7bs3yofpzanfjlqvnuswghevu
*the**complexity**of*solving*the**generalized**MinRank**problem*, i.e. computing*the*set*of*points where*the*evaluation*of*a polynomial matrix has rank at most r. ... We show that its*complexity*can be bounded by using*the**complexity*bounds for*the**generalized**MinRank**problem*. ... Acknowledgments This work was supported in part by*the*HPAC grant and*the*GeoLMI grant (ANR 2011 BS03 011 06)*of**the*French National Research Agency. ...##
###
The complexity of MinRank
[article]

2022
*
arXiv
*
pre-print

In this note, we leverage some

arXiv:1905.02682v3
fatcat:u4f2zpwbyffv5lz62bp7jqn6rm
*of*our results from arXiv:1706.06319 to produce a concise and rigorous proof for*the**complexity**of**the**generalized**MinRank**Problem*in*the*under-defined and well-defined case ... Acknowledgements We are grateful to an anonymous referee for a detailed reading and comments which helped us improve*the*clarity*of**the*proof*of**the*main theorem. ... In this paper, we take another look at*the**complexity**of*solving*the**generalized**MinRank**Problem*with*the*minors modeling. ...##
###
Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology

2010
*
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation - ISSAC '10
*

In both cases, under

doi:10.1145/1837934.1837984
dblp:conf/issac/FaugereDS10
fatcat:44jtyqxqyrbrnai5oadnffoqw4
*genericity*assumptions*on**the*entries*of**the*considered matrix, we give new bounds*on**the*degree*of*regularity*of**the*considered ideal which allows us to estimate*the**complexity**of*... For instance,*the*exact degree*of*regularity*of**the*determinantal ideal formulation*of*a*generic*well-defined*MinRank**problem*is r(n − r) + 1. ... When k = 1*the**MinRank**problem*can be reduced to*the*well known EigenValue*problem*. Therefore,*the**MinRank**problem*can be seen as a*generalized*nonlinear eigenvalue*problem*. ...##
###
Efficient Zero-Knowledge Authentication Based on a Linear Algebra Problem MinRank
[chapter]

2001
*
Lecture Notes in Computer Science
*

*MinRank*is

*one*

*of*

*the*most efficient schemes based

*on*NP-complete

*problems*. It can be used to prove in Zero-knowledge a solution to any

*problem*described by multivariate equations. ... We study a more

*general*

*problem*called

*MinRank*that

*generalizes*SD and contains also other well known hard

*problems*. ... Related

*Problems*This version

*of*

*the*

*MinRank*, is a

*generalized*version

*of*

*one*among many NPcomplete rank

*problems*studied in [23] and [10] . In our scheme R will be a finite field GF (q). ...

##
###
HybridRAM: The first quantum approach for key recovery attacks on Rainbow
[article]

2022
*
arXiv
*
pre-print

We also design a Grover oracle quantum circuit suitable for

arXiv:2206.10898v1
fatcat:emtqi2p7dvgrbervdp72jb3w6i
*the*rectangular*MinRank*attack and then propose a Hybrid Rectangular*MinRank*attack that recovers*the*keys*of*Rainbow using*the*designed quantum ... A rectangular*MinRank*attack, proposed by Ward Beullens in 2021, reduced*the*security*of*Rainbow below*the*security requirements set out by NIST. ... reduced*the**complexity**of**the**MinRank*attacks*on**the*Rainbow to 1/3*of*existing attacks in*the*parameter sets III and V*of*Rainbow [8] . ...##
###
Improvements of Algebraic Attacks for solving the Rank Decoding and MinRank problems
[article]

2020
*
arXiv
*
pre-print

Based

arXiv:2002.08322v3
fatcat:qt3zmk5imjc6neytawezi7j6vq
*on*this*problem*and quasi-cyclic versions*of*it, very efficient schemes have been proposed recently, such as those in*the*ROLLO and RQC submissions, which have reached*the*second round*of**the*NIST ... For*the*other case, called underdetermined, we also improve*the*results from*the*previous attack by combining*the*Ourivski-Johansson modeling together with a new modeling for a*generic**MinRank*instance ... We thank*the*Facultad de Ciencias*of**the*Universidad Nacional de Colombia sede Medelln for granting us access to*the*Enlace server, where we ran some*of**the*experiments. ...##
###
Analysis on the MinRank Attack using Kipnis-Shamir Method Against Rainbow
[article]

2020
*
IACR Cryptology ePrint Archive
*

As this method reduces

dblp:journals/iacr/NakamuraWI20
fatcat:vvwduwchajbczi4bsnhnbvmpxq
*the**problem*to*the*MQ*problem*that asks for a solution*of*a system*of*quadratic equations, its*complexity*depends*on**the*solving degree*of*a quadratic system deduced from*the*method ... Moreover,*the*termination*of**the*y-XL algorithm*on*an inhomogeneous system is not clear, and its*complexity*depends*on**the*existence*of*a non-trivial syzygy*on*each system and its discussion is delicate ...##
###
Improvement of algebraic attacks for solving superdetermined MinRank instances
[article]

2022
*
arXiv
*
pre-print

We give

arXiv:2208.01442v1
fatcat:hdgnajo5wnbs5pkzxwaqq4u56m
*complexity*estimates*of**the*attack for*generic*random instances.We apply those results to*the*DAGS cryptosystem, that was submitted to*the*first round*of**the*NIST standardization process. ...*The**MinRank*(MR)*problem*is a computational*problem*that arises in many cryptographic applications. In Verbel et al. ... Introduction*The**MinRank**Problem**The**MinRank**problem*was first mentioned in [12] where its NP-completeness was also proven. ...##
###
The computational complexity of some problems of linear algebra
[chapter]

1997
*
Lecture Notes in Computer Science
*

We consider

doi:10.1007/bfb0023480
fatcat:c2znq7yvbzfkninppzss3iffuy
*the*computational*complexity**of*some*problems*dealing with matrix rank. Let E, S be subsets*of*a commutative ring R. a 2 , . . .a t ) and*minrank*S (M ) = min (a 1 ,a 2 ,... ... Depending*on*E, S, and*on*which variant is studied,*the**complexity**of*these*problems*can range from polynomial-time solvable to random polynomial-time solvable to NP-complete to PSPACE-solvable to unsolvable ... We have good evidence that*the**MINRANK*and SING*problems*do not in*general*have*the*same*complexity*. ...##
###
The Computational Complexity of Some Problems of Linear Algebra

1996
*
BRICS Report Series
*

<br />Depending

doi:10.7146/brics.v3i33.20013
fatcat:mdqhjtrvf5fblhnjleitq7mspu
*on*E, S, and*on*which variant is studied,*the**complexity*<br />*of*these*problems*can range from polynomial-time solvable to random<br />polynomial-time solvable to NP-complete to PSPACE-solvable ... We consider*the*computational*complexity**of*some*problems*dealing with matrix rank.<br /> Let E, S be subsets*of*a commutative ring R.<br />Let x1, x2, ..., xt be variables. ... We have good evidence that*the**MINRANK*and SING*problems*do not in*general*have*the*same*complexity*. ...##
###
The Computational Complexity of Some Problems of Linear Algebra

1999
*
Journal of computer and system sciences (Print)
*

We consider

doi:10.1006/jcss.1998.1608
fatcat:4omziu6rcnfbvgbakda7dbwqam
*the*computational*complexity**of*some*problems*dealing with matrix rank. Let E, S be subsets*of*a commutative ring R. a 2 , . . .a t ) and*minrank*S (M ) = min (a 1 ,a 2 ,... ... Depending*on*E, S, and*on*which variant is studied,*the**complexity**of*these*problems*can range from polynomial-time solvable to random polynomial-time solvable to NP-complete to PSPACE-solvable to unsolvable ... We have good evidence that*the**MINRANK*and SING*problems*do not in*general*have*the*same*complexity*. ...##
###
The Complexity of Tensor Rank
[article]

2016
*
arXiv
*
pre-print

We show that determining

arXiv:1612.04338v1
fatcat:hswlqjlb6zdutiao2hyh6mkfcy
*the*rank*of*a tensor over a field has*the*same*complexity*as deciding*the*existential theory*of*that field. This implies earlier NP-hardness results by Håstad H90. ...*The*hardness proof also implies an algebraic universality result. ... Over*the**complex*numbers, Koiran's result places*the**problem*at*the*second level*of**the*polynomial hierarchy assuming*the**Generalized*Riemann hypothesis is true. ...##
###
Improved Cryptanalysis of UOV and Rainbow
[article]

2020
*
IACR Cryptology ePrint Archive
*

Secondly, we give two new attacks against

dblp:journals/iacr/Beullens20a
fatcat:fc65bfxhzrbj3aylxb7zpaqxaq
*the*UOV and Rainbow signature schemes;*the*intersection attack that applies to both UOV and Rainbow and*the*rectangular*MinRank*attack that applies only to Rainbow ...*The*contributions*of*this paper are twofold. ... to*the*solutions*of**the**MinRank**problem*. ...##
###
Breaking Rainbow Takes a Weekend on a Laptop
[article]

2022
*
IACR Cryptology ePrint Archive
*

Concretely, given a Rainbow public key for

dblp:journals/iacr/Beullens22
fatcat:vqicd74vifctvca4zmcqftzrsa
*the*SL 1 parameters*of**the*second-round submission, our attack returns*the*corresponding secret key after*on*average 53 hours (*one*weekend)*of*computation time ... This work introduces new key recovery attacks against*the*Rainbow signature scheme, which is*one**of**the*three finalist signature schemes still in*the*NIST Post-Quantum Cryptography standardization project ... Solving*MinRank**problems*. Our attacks will also make use*of*an algorithm to solve*the**MinRank**problem*. ...
« Previous

*Showing results 1 — 15 out of 302 results*