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Simplifying algebraic attacks with univariate analysis

Tor Helleseth, Sondre Ronjom
2011 2011 Information Theory and Applications Workshop  
Such a view 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  ... 
doi:10.1109/ita.2011.5743578 dblp:conf/ita/HellesethR11 fatcat:37elv3fpdzg4tgdbn5hm2tmv7e

Using SAT Solving to Improve Differential Fault Analysis of Trivium [chapter]

Mohamed Saied Emam Mohamed, Stanislav Bulygin, Johannes Buchmann
2011 Communications in Computer and Information Science  
In particular, 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.  ... 
doi:10.1007/978-3-642-23141-4_7 fatcat:tqkwtijj5zcm5n65snm2mre4de

Mutant Differential Fault Analysis of Trivium MDFA [chapter]

Mohamed Saied Emam Mohamed, Johannes Buchmann
2015 Lecture Notes in Computer Science  
We study the efficiency of our improved 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.  ... 
doi:10.1007/978-3-319-15943-0_26 fatcat:bqj4wiqe7bf5dorkes6j5zfcmm

Using LLL-Reduction for Solving RSA and Factorization Problems [chapter]

Alexander May
2009 The LLL Algorithm  
mod q − 1 A Coppersmith-type 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  ... 
doi:10.1007/978-3-642-02295-1_10 dblp:series/isc/May10 fatcat:4osx6ny2w5gqfdjls3uon6dsh4

Some Algebraic Aspects of the Advanced Encryption Standard [chapter]

Carlos Cid
2005 Lecture Notes in Computer Science  
Rijndael is a cipher 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.  ... 
doi:10.1007/11506447_6 fatcat:fflppp4cabblbgwcfhpxatmp6u

Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization [chapter]

Aviad Kipnis, Adi Shamir
1999 Lecture Notes in Computer Science  
The new type of 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  ... 
doi:10.1007/3-540-48405-1_2 fatcat:5rzw5u5nm5et7ohvl3zja644pu

Algorithm 959

José Antonio Álvarez-Cubero, Pedro J. Zufiria
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 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  ... 
doi:10.1145/2794077 fatcat:4tgey4sslzbxjfly4t3sra6hc4

Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants [chapter]

Luk Bettale, Jean-Charles Faugère, Ludovic Perret
2011 Lecture Notes in Computer Science  
First, we propose an improved version of the basic Kipnis-Shamir key recovery 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.  ... 
doi:10.1007/978-3-642-19379-8_27 fatcat:gn3tb3322bdqbhnl3wpzbn5mie

Dynamic Anomaly Detection with High-fidelity Simulators: A Convex Optimization Approach [article]

Kaikai Pan, Peter Palensky, Peyman Mohajerin Esfahani
2020 arXiv   pre-print
The proposed diagnosis filter aims to achieve two desired features: (i) performance robustness 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  ... 
arXiv:2004.13927v3 fatcat:enoenvt5xje3lezk3op2wajoq4

Cryptanalysis of a Theorem: Decomposing the Only Known Solution to the Big APN Problem [chapter]

Léo Perrin, Aleksei Udovenko, Alex Biryukov
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 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.  ... 
doi:10.1007/978-3-662-53008-5_4 fatcat:cl6lv3qnqzbhdnsr42tuv4ylca

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.  ... 

Building Secure Public Key Encryption Scheme from Hidden Field Equations

Yuan Ping, Baocang Wang, Yuehua Yang, Shengli Tian
2017 Security and Communication Networks  
It is shown that the proposed public key encryption scheme is secure against known 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.  ... 
doi:10.1155/2017/9289410 fatcat:x2vjeoyxo5ds7ipklq4i2ayzaa

Non-Linear Collision Analysis [chapter]

Xin Ye, Cong Chen, Thomas Eisenbarth
2014 Lecture Notes in Computer Science  
Such data dependency has usually been described 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.  ... 
doi:10.1007/978-3-319-13066-8_13 fatcat:oqrgntkw5ngj5eny47rkx3kkou

A New Second-Order Side Channel Attack Based on Linear Regression

Guillaume Dabosville, Julien Doget, Emmanuel Prouff
2013 IEEE transactions on computers  
In this paper, we propose a new 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).  ... 
doi:10.1109/tc.2012.112 fatcat:irvp45dhw5fjtc6dc6bljoa7ra

Quantum resistant random linear code based public key encryption scheme RLCE

Yongge Wang
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
This paper proposes linear code based encryption scheme RLCE which shares many characteristics 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.  ... 
doi:10.1109/isit.2016.7541753 dblp:conf/isit/Wang16a fatcat:4bvyuaciw5bylglb6trpcrtxlu
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