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Simplifying algebraic attacks with univariate analysis

2011
*
2011 Information Theory and Applications Workshop
*

Such a view

doi:10.1109/ita.2011.5743578
dblp:conf/ita/HellesethR11
fatcat:37elv3fpdzg4tgdbn5hm2tmv7e
*simplifies*theory on*algebraic**attacks*on such ciphers and provides an alternative view of the Rønjom-Helleseth*attack*. ...*With*this view, one can show that, 1) the problem of estimating*algebraic*immunity and spectral immunity is closely connected to determining low-weight codewords in cyclic codes, and 2) the least number ... This paper shows that considering the nonlinear Boolean function as an equivalent*univariate*polynomial mapping from GF(2 n ) to GF (2) can*simplify*and generalize some cryptographic*attacks*on certain ...##
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Using SAT Solving to Improve Differential Fault Analysis of Trivium
[chapter]

2011
*
Communications in Computer and Information Science
*

In particular,

doi:10.1007/978-3-642-23141-4_7
fatcat:tqkwtijj5zcm5n65snm2mre4de
*algebraic*methods in side channel and differential fault*analysis*(DFA) attracted a lot of attention recently. ... For this*attack*, they required 3.2 one-bit fault injections on average and 800 keystream bits. In this paper, we give an example of combining DFA*attacks*and*algebraic**attacks*. ... Instead of*attacking*Trivium*with*only one method, an*attacker*can gain more power by combining di_erential fault*analysis**with**algebraic*techniques. ...##
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Mutant Differential Fault Analysis of Trivium MDFA
[chapter]

2015
*
Lecture Notes in Computer Science
*

We study the efficiency of our improved

doi:10.1007/978-3-319-15943-0_26
fatcat:bqj4wiqe7bf5dorkes6j5zfcmm
*attack*by comparing the size of gathered DFA information*with*previous*attacks*. ... Therefore, we introduce a new*algebraic*framework that combines the power of different*algebraic*techniques for handling additional information received from a physical*attack*. ... In fact, this is the first*attack*combining differential fault*analysis**with*an advanced*algebraic*technique. ...##
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Using LLL-Reduction for Solving RSA and Factorization Problems
[chapter]

2009
*
The LLL Algorithm
*

mod q − 1
A Coppersmith-type

doi:10.1007/978-3-642-02295-1_10
dblp:series/isc/May10
fatcat:4osx6ny2w5gqfdjls3uon6dsh4
*analysis*results in a heuristic polynomial time*attack*that works for d p , d q ≤ N 0.073 . ... Whereas the choice of the*algebraic*multiples is quite straightforward for*univariate*polynomials, for multivariate polynomial equations the choice of the*algebraic*multiples appears to be a complex optimization ...##
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Some Algebraic Aspects of the Advanced Encryption Standard
[chapter]

2005
*
Lecture Notes in Computer Science
*

Rijndael is a cipher

doi:10.1007/11506447_6
fatcat:fflppp4cabblbgwcfhpxatmp6u
*with*a simple, elegant and highly*algebraic*structure. ... In these notes we will examine some*algebraic*aspects of the AES and consider a number of*algebraic*techniques that could be used in the*analysis*of the cipher. ... Solve: Assume that step 2 yields at least one*univariate*equation. Solve this equation; 4. Repeat:*Simplify*the equations and repeat the process to find the values of the other variables. ...##
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Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
[chapter]

1999
*
Lecture Notes in Computer Science
*

The new type of

doi:10.1007/3-540-48405-1_2
fatcat:5rzw5u5nm5et7ohvl3zja644pu
*attack*is quite general, and in a companion paper we use it to*attack*other multivariate*algebraic*schemes, such as the Dragon encryption and signature schemes. ... We represent the published system of multivariate polynomials by a single*univariate*polynomial of a special form over an extension field, and use it to reduce the cryptanalytic problem to a system of ... To*simplify*the asymptotic*analysis*, we assume that r is a constant and n grows to infinity, and argue that the*attack*should run in expected polynomial time (even though we cannot formally prove this ...##
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Algorithm 959

2016
*
ACM Transactions on Mathematical Software
*

The most relevant cryptographic criteria for both block and stream ciphers as well as for hash functions can be evaluated

doi:10.1145/2794077
fatcat:4tgey4sslzbxjfly4t3sra6hc4
*with*VBF: it obtains the nonlinearity linearity distance,*algebraic*degree, linear ... very high nonlinearity, a key property for robustness against linear*attacks*. the robustness against*attacks*) of Boolean and vector Boolean functions. ... Search for Vector Boolean Functions*with*Excellent Profiles Boolean functions*with*very high nonlinearity pose some of the most challenging problems in the area of symmetric cryptography and combinatorics ...##
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Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants
[chapter]

2011
*
Lecture Notes in Computer Science
*

First, we propose an improved version of the basic Kipnis-Shamir key recovery

doi:10.1007/978-3-642-19379-8_27
fatcat:gn3tb3322bdqbhnl3wpzbn5mie
*attack*against HFE. Second, we generalize the Kipnis-Shamir*attack*to Multi-HFE. ... Finally, adaptations of our*attack*overcome several variants (i.e. minus modifier and embedding). ... The authors were also supported in part by the french ANR under the Computer*Algebra*and Cryptography (CAC) project ANR-09-JCJCJ-0064-01. ...##
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Dynamic Anomaly Detection with High-fidelity Simulators: A Convex Optimization Approach
[article]

2020
*
arXiv
*
pre-print

The proposed diagnosis filter aims to achieve two desired features: (i) performance robustness

arXiv:2004.13927v3
fatcat:enoenvt5xje3lezk3op2wajoq4
*with*respect to model mismatch; (ii) high scalability. ... To validate the theoretical results, we implement the developed diagnosis filter in DIgSILENT PowerFactory to detect false data injection*attacks*on the Automatic Generation Control measurements in the ... For AGC*analysis*, as mentioned in Section II, we are interested in collective performance of all generators, and thus we can rely on certain levels of abstraction that*simplify*some elements of the initial ...##
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Cryptanalysis of a Theorem: Decomposing the Only Known Solution to the Big APN Problem
[chapter]

2016
*
Lecture Notes in Computer Science
*

Furthermore, we deduce a bitsliced implementation and significantly reduce the hardware cost of a 6-bit APN permutation using this decomposition, thus

doi:10.1007/978-3-662-53008-5_4
fatcat:cl6lv3qnqzbhdnsr42tuv4ylca
*simplifying*the use of such a permutation as building ... Such butterflies are 2 -bit mappings*with*two CCZ-equivalent representations: one is a quadratic non-bijective function and one is a degree + 1 permutation. ... In this proof, we rely a lot on the*univariate*degree of a polynomial of F 2 . It is different from the*algebraic*degree: the cube function has*univariate*degree 3 and*algebraic*degree 2. ...##
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Page 7896 of Mathematical Reviews Vol. , Issue 2000k
[page]

2000
*
Mathematical Reviews
*

The book has been used at the authors’ institution to teach a course to undergraduates

*with*only a linear*algebra*course under their belts. ... In addition, there are four appendices; one devoted to some linear*algebra*concepts, another devoted to MAPLE routines,*with*the other two covering answers and symbols. ...##
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Building Secure Public Key Encryption Scheme from Hidden Field Equations

2017
*
Security and Communication Networks
*

It is shown that the proposed public key encryption scheme is secure against known

doi:10.1155/2017/9289410
fatcat:x2vjeoyxo5ds7ipklq4i2ayzaa
*attacks*including the MinRank*attack*, the*algebraic**attacks*, and the linearization equations*attacks*. ... The proposal gains some advantages over the original HFE scheme*with*respect to the encryption speed and public key size. ... equation*attack*, the MinRank*attack*, and the*algebraic**attacks*. ...##
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Non-Linear Collision Analysis
[chapter]

2014
*
Lecture Notes in Computer Science
*

Such data dependency has usually been described

doi:10.1007/978-3-319-13066-8_13
fatcat:oqrgntkw5ngj5eny47rkx3kkou
*with*a particular leakage model by the classical Differential Power*Analysis*(DPA) [8] and Correlation Power*Analysis*(CPA) [4] . ... Motivation Side channel*attacks*(SCA) such as Power and EM*analysis*remain as a major concern for embedded cryptographic systems. ... showed in [21] that generic*univariate**attacks**with*a leakage model exist only for a very limited selection of target functions. ...##
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A New Second-Order Side Channel Attack Based on Linear Regression

2013
*
IEEE transactions on computers
*

In this paper, we propose a new

doi:10.1109/tc.2012.112
fatcat:irvp45dhw5fjtc6dc6bljoa7ra
*attack*technique which shares many similarities*with*stochastic*attacks*but does not require any profiling stage. ... We conduct an in-depth*analysis*of this new*attack*to highlight its core foundations. ...*Attack*Distinguisher. 1) Correlation Power*Analysis*(CPA). ...##
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Quantum resistant random linear code based public key encryption scheme RLCE

2016
*
2016 IEEE International Symposium on Information Theory (ISIT)
*

This paper proposes linear code based encryption scheme RLCE which shares many characteristics

doi:10.1109/isit.2016.7541753
dblp:conf/isit/Wang16a
fatcat:4bvyuaciw5bylglb6trpcrtxlu
*with*random linear codes. Our*analysis*shows that the scheme RLCE is secure against existing*attacks*. ... In recent years, several important techniques such as Sidelnikov-Shestakov*attack*, filtration*attacks*, and*algebraic**attacks*have been developed to crypt-analyze linear code based encryption schemes. ... , and*algebraic**attacks*. ...
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