scholarly journals Accurate Estimate of the Advantage of Impossible Differential Attacks

2017 ◽  
pp. 169-191 ◽  
Author(s):  
Céline Blondeau
Keyword(s):  
Time Complexity ◽  
Block Cipher ◽  
Poisson Approximation ◽  
Accurate Estimate ◽  
Random Permutations ◽  
Differential Attack ◽  
Impossible Differential ◽  
Impossible Differential Attack ◽  
Differential Attacks ◽  
Multivariate Hypergeometric Distribution

Impossible differential attacks, which are taking advantage of differentials that cannot occur, are powerful attacks for block cipher primitives. The power of such attacks is often measured in terms of the advantage — number of key-bits found during the key sieving phase — which determines the time complexity of the exhaustive key search phase. The statistical model used to compute this advantage has been introduced in the seminal work about the resistance of the DEAL cipher to impossible differential attacks. This model, which has not been modified since the end of the 1990s, is implicitly based on the Poisson approximation of the binomial distribution. In this paper, we investigate this commonly used model and experimentally illustrate that random permutations do not follow it. Based on this observation, we propose more accurate estimates of the advantage of an impossible differential attack. The experiments illustrate the accuracy of the estimate derived from the multivariate hypergeometric distribution. The maximal advantage –using the full codebook– of an impossible differential attack is also derived.

scholarly journals On the Complexity of Impossible Differential Cryptanalysis

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Qianqian Yang ◽  
Lei Hu ◽  
Danping Shi ◽  
Yosuke Todo ◽  
Siwei Sun
Keyword(s):  
Time Complexity ◽  
Differential Analysis ◽  
Differential Attack ◽  
Symmetric Key ◽  
Impossible Differential ◽  
Complexity Estimation ◽  
Impossible Differential Attack ◽  
Differential Attacks ◽  
Impossible Differentials ◽  
Impossible Differential Cryptanalysis

While impossible differential attack is one of the most well-known and familiar techniques for symmetric-key cryptanalysts, its subtlety and complicacy make the construction and verification of such attacks difficult and error-prone. We introduce a new set of notations for impossible differential analysis. These notations lead to unified formulas for estimation of data complexities of ordinary impossible differential attacks and attacks employing multiple impossible differentials. We also identify an interesting point from the new formulas: in most cases, the data complexity is only related to the form of the underlying distinguisher and has nothing to do with how the differences at the beginning and the end of the distinguisher propagate in the outer rounds. We check the formulas with some examples, and the results are all matching. Since the estimation of the time complexity is flawed in some situations, in this work, we show under which condition the formula is valid and give a simple time complexity estimation for impossible differential attack which is always achievable.

scholarly journals Different Types of Attacks on Block Ciphers

2020 ◽  
Vol 9 (3) ◽  
pp. 28-31
Keyword(s):  
Block Cipher ◽  
Classical Method ◽  
System Of Nonlinear Equations ◽  
Algebraic Attack ◽  
Differential Attack ◽  
Different Types ◽  
Important Challenge ◽  
Impossible Differential ◽  
Linear Differential ◽  
Truncated Differential

Cryptanalysis is a very important challenge that faces cryptographers. It has several types that should be well studied by cryptographers to be able to design cryptosystem more secure and able to resist any type of attacks. This paper introduces six types of attacks: Linear, Differential , Linear-Differential, Truncated differential Impossible differential attack and Algebraic attacks. In this paper, algebraic attack is used to formulate the substitution box(S-box) of a block cipher to system of nonlinear equations and solve this system by using a classical method called Grobner  Bases . By Solving these equations, we made algebraic attack on S-box.

scholarly journals Provable Security Against a Differential Attack

1994 ◽  
Vol 23 (473) ◽  
Author(s):  
Kaisa Nyberg ◽  
Lars Ramkilde Knudsen
Keyword(s):  
Upper Bound ◽  
Provable Security ◽  
Block Cipher ◽  
Differential Cryptanalysis ◽  
Font Size ◽  
Differential Attack ◽  
Round Function ◽  
Differential Attacks

The purpose of this paper is to show that there exist DES-like iterated ciphers, which are provably resistant against differential attacks. The main result on the security of a DES-like cipher with independent round keys is Theorem 1, which gives an upper bound to the probability of <em>s</em>-round differentials, as defined in <em>Markov Ciphers and Differential Cryptanalysis </em> by X. Lai et al. and this upper bound depends only on the round function of the iterated cipher. Moreover, it is shown that there exist functions such that the probabilities of differentials are less than or equal to 2<sup><span style="font-size: x-small;">3-n</span></sup>, where <em>n</em> is the length of the plaintext block. We also show a prototype of an iterated block cipher, which is compatible with DES and has proven security against differential attacks.

Impossible Differential Attack on 30-Round SHACAL-2

2003 ◽  
pp. 97-106 ◽  
Author(s):  
Seokhie Hong ◽  
Jongsung Kim ◽  
Guil Kim ◽  
Jaechul Sung ◽  
Changhoon Lee ◽  
...  
Keyword(s):  
Differential Attack ◽  
Impossible Differential ◽  
Impossible Differential Attack

scholarly journals Partial and Higher Order Differentials and Applications to the DES

1995 ◽  
Vol 2 (9) ◽  
Author(s):  
Lars Ramkilde Knudsen
Keyword(s):  
Block Cipher ◽  
Higher Order ◽  
Differential Attack ◽  
Running Time ◽  
Differential Attacks ◽  
Derivatives Of ◽  
Discrete Functions

In 1994 Lai considered higher order derivatives of discrete functions and<br />introduced the concept of higher order differentials. We introduce the concept<br />of partial differentials and present attacks on ciphers presumably secure<br />against differential attacks, but vulnerable to attacks using higher order and<br />partial differentials. Also we examine the DES for partial and higher order<br />differentials and give a differential attack using partial differentials on DES<br />reduced to 6 rounds using only 46 chosen plaintexts with an expected running time of about the time of 3,500 encryptions. Finally it is shown how to find a minimum nonlinear order of a block cipher using higher order differentials.

Related-Key Impossible Differential Attack on Reduced-Round LBlock

2014 ◽  
Vol 29 (1) ◽  
pp. 165-176 ◽  
Author(s):  
Long Wen ◽  
Mei-Qin Wang ◽  
Jing-Yuan Zhao
Keyword(s):  
Differential Attack ◽  
Impossible Differential ◽  
Impossible Differential Attack
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