Questions tagged [differential-analysis]

Differential cryptanalysis is a form of cryptanalysis which studies cryptographic algorithms by observing how differences in input affect differences in output.

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Whats the probability a random cipher has a high probability differential?

This is a bit vauge and long winded. Any partial answers or comments/ways to make this more precise would be greatly appreciated. Fix some general structure for a cipher, for example Sbox then ...
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Could a private key recovery via modulus fault attacks be optimised by being able to choose the faulty moduli?

The paper 'Why One Should Also Secure RSA Public Key Elements' describes an attack where an adversary can fully recover a private key by injecting faults into the modulus before exponentiation takes ...
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Markov ciphers - generalized group operation

I’m reading this paper of Lai and Massey where they give a very nice perspective on differential attacks in general http://www.isiweb.ee.ethz.ch/papers/arch/xlai-mass-inspec-1991-3.pdf They do their ...
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Linear approximattion of $(x+y) \bmod 2^n$ in FSM of SNOW 2.0 where $x,y$ in $F_{2}^n$

I would like to understand the linear approximation of $(x+y) \bmod 2^n$ by linear masking method in the paper refereed ""Improved Linear Distinguis'hers for SNOW 2.0" by Kaisa Nyberg and Johan Wall´...
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AES difference propagation

when does active S box count reduce in AES difference propagation? what is the relationship between active S-boxes and MixColumns? can you please explain it with an example?
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Definition Problem for toy SPN

I am reading Differential Attack from Stinson-Cryptography: Theory and Practice on a toy example of S-box(block Cipher) with Nr=n=m=4. I am mainly confused in the following definition Definition ...
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Related-key impossible differential search on SIMECK via MILP?

What should be the objective function , constraints and bounds for the model for Related-key impossible differential search on simeck cipher using mixed integer linear programming (MILP)?
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Unknown bit in the output of encryption of data using SIMECK32 cipher?

How is the unknown bits (annotated by red arrow in figure below) come in the OUTPUT after round 1 and round 2 ? Following is the pictorial representation of SIMECK round function operation. Ref: ...
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Differential cryptanalysis of FEAL-4 recovering last subkeys

I am familiar with the differential cryptanalysis of small SPN-based ciphers like here: Tutorial of Amazing King with SPN (or mentioned in the book "The Block Cipher Companion" or the Tutorial of ...
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what if the S-boxes in DES were “optimal”

if we assume that the s-boxes in DES were optimal. that is for each s-box, every cell in the DDT equals to 4. is there a differential characteristic in a good probability?
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Why isn't there a final permutation on SPN-based ciphers?

I am doing some research on differential cryptanalysis. Most people who are familiar with that cryptanalysis technique do know the tutorial from Heys (Heys Tutorial). I came currently to the question, ...
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AES - Non-linearity hinders differential cryptoanalysis

Can you explain me, in simple terms if possible (I'm not a mathematician :( ), why the non-linearity introduced by the AES s-boxes hinder the differential cryptoanalysis ?
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Enhancing Differential-Linear Cryptanalysis

I'm studying Differential-Linear Cryptanalysis, and I'm trying to understand the context from the article Enhancing Differential-Linear Cryptanalysis by Eli Biham et al. There are some difficult ...
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structure in modular arithmetic

I was playing around with modular arithmetic when I noticed something. \begin{align} g^k &= a \bmod n\\ g^{k+0.5(n-1)} &= b \bmod n \end{align} Then $a + b = n$, so you can also write $$g^{...
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How is it possible to define differential privacy on two databases that differ more than a single entry?

The original definition of $\epsilon-$differential privacy is for two databases $D_1$, $D_2$ that differ at most one entry and an randomized algorithm $A$. We have a bound on the probability ratio $\...
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Differential cryptanalysis filtering process

This question is a little more implementation based. I am writing my masters thesis on differential cryptanalysis and I wrote a program to evaluate some things about differential cryptanalysis. I ...
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Constructing Differential Characteristics for Feistel Cipher

I have to construct for every i-round of Feistel cipher, for $i \in \{3,4,5,6,7,8\}$, a differential characteristic with there properties: $Pr[\Delta x = a \overset{f_i}{\rightarrow} \Delta y = b] = ...
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Guess the number of characteristics in differential cryptanalysis

I am doing some research on differential cryptanalysis for my master thesis. I analyzed some toy ciphers like the one in the popular tutorial about differential and linear cryptanalysis from heys Link....
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Why is DES secure against differential cryptanalysis

I was wondering, why DES is secure against Differential Attacks. Some of the S-Boxes have a very bad Differential Uniformity, only one has a DU of 4, 3 have a DU of 6 and the others are much worse. ...
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Symmetric property of DDT of inverse function

Given a bijective function $F: \mathbb{F}_2^n \rightarrow \mathbb{F}_2^n$. The entry of the Difference Distribution Table (DDT) at row $\alpha$ and column $\beta$ is defined as $$DDT_{F}(\alpha,\...
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Implementation of differential cryptanalysis

This question is a little bit more implementation based of differential cryptanalysis. I hope it is okay. I am working with the book "The Block Cipher Companion" on the topic differential ...
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Differential cryptanalysis in “The Block Cipher Companion”

I am practically implementing a differential cryptanalysis on a cipher which can be found in the book "The Block Cipher Companion". Following image shows the cipher: In Fig. 6.10 (page 126) there are ...
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Recover all keys on differential cryptanalysis

I am practically implementing differential cryptanalysis on a cipher from the book "the block cipher companion" . I am successful to get the last key $k_5$. Just to say some words about the ...
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Calculate number of required pairs for differential cryptanalysis

I am currently doing some study on differential cryptanalysis. However, I have two open questions in the field. The first question is: How can I calculate the number of messages necessary for a ...
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267 views

Searching for a differential characteristic (differential cryptanalysis)

Currently I am doing some research on differential cryptanalysis. In general I got a good idea about the attack and how it is done. I am currently talking about ciphers with multiple rounds. It ...
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What does it mean : “Canonical representative of Sbox is 0123468A5BCF79DE”? and How can we calculate this representative for Sbox?

In paper :Cryptographic Analysis of All 4 × 4-Bit S-Boxes Saarinen has classified $4 \times 4$ S-Boxes and defined Canonical representative for each class of S-Boxes. What does "Canonical ...
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Differential cryptanalysis tutorial of Howard M. Heys

I am currently working on some research about differential cryptanalysis. There is a lot of literature about that topic in the internet. One of the most known paper is the tutorial on linear and ...
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differential cryptanalysis on the second round of 4-variant DES

I am using differential cryptanalysis to attack the second key of a 4-variant DES and I am using Shamir and biham book as a reference . they say that we should choose two input Xor P3 and P4 that ...
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Can multiple Pearson permutation tables be reduced or merged?

There was a recent question answered where the accepted solution was a double Pearson hash. It consisted of the following pseudo code:- h = T1[h ^ x[i]] followed ...
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Attacking AES using Round 1 output

I was reading the paper Differential Scan Attack on AES with X-tolerant and X-masked Test Response Compactor and I have a question in the section Differential Scan Attack on AES. What I understand is ...
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Getting the s-box input from its output in differential cryptanalysis on DES

If we try to get K4 using differential cryptanalysis on 4-variant DES, how can we get the input of a certain S-box if we know it's output? This seems hard to do since the substitution operation is ...
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Differential and Linear trail propagation in Noekeon

In the Noekeon Cipher Specification they write the following : The propagation through Lambda is denoted by $(a \rightarrow A)$, also called a step. Because of the linearity of Lambda it is fully ...
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Additive differential probability

I am studying about additive differential probability. And I show a paper that is V.Velichkov et al., The Additive Differential Probability of ARX. I have a question in chapter 5.2. V.Velichkov et ...
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Additive Differential of XOR

I'm studying about Additive differential of XOR I saw two papers that are "H.Lipmaa et al., On the Additive Differential Probability of Exclusive-or" and "V.Velichkov et al., The Additive ...
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Differential probability of modular subtraction $xdp^-$

The modular addition has been a main component in block cipher. The use of modular subtraction in block cipher is not common but there are some cipher such as Bel-T cipher which uses both modular ...
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Selection of rotation constants in ARX design

My question is about choosing the rotation values in ARX design such as SIMON-like or SPECK-like ciphers to provide optimal differential and linear immunity. According to this, the selection of $a$ ...
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208 views

Minimum number of active s box to be resistance to differential cryptanalysis

I am calculating the minimum number of active s_boxes for block cipher using mixed integer programming, when can we say that block cipher is resistance to differential cryptanalysis after which round? ...
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How does linear vs. non-linear operations relate to cryptographic security and differential cryptanalysis?

I understand what a linear operation is and what a non-linear operation is, but I would like an explanation of specifically how a non-linear operation on input data mitigates differential crytanalysis ...
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Cryptanalysis of MD4 (Wang et al) — how did the authors come up with the collision differential?

Edit: ok, after I re-read the paper a couple of times it is clear that Table 6 is easily derived from Table 5, which describes the collision differential. So the real question is: how did the ...
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The Collision Differential for MD4 - a question on notation (Wang, et al)

In the paper "Cryptanalysis of the Hash Functions MD4 and RIPEMD" the authors introduce the following notation (paragraph 4.1): $\Delta$$H_0$ = 0 $\xrightarrow{(M_,M')}$ $\Delta$$H$ = 0 What exactly ...
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Adding bit constants to the key schedule to reduce rounds?

Bit constants are often added to the key schedule to reduce slide attacks. I have reviewed David Wagner's work, where he showed that the increased rounds in a Feistel network do not help if you have ...
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Compression function cryptanalysis

A compression function converts a fixed-sized input into a smaller fixed size output. Suppose that one has a large collection of input-output pairs for an unknown compression function. We can assume ...
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Calculating the number of rounds required for block cipher with known differential [closed]

Suppose we have a 128-bit block cipher for which the best two-round differential holds with probability $p = 2^7$. Suppose as well that this differential is iterative and that the best differential ...
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it is possible to use quantum algorithm search (Grover's algorithm) for new searching strategies for differential and linear attacks

I am trying to use Grover's algorithm to find Differential characteristic of Feistel and SPN structures block ciphers. basically, which is Finding a good differential characteristic with high ...
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Understanding the wide trail design strategy

I am trying to understand the wide trail design strategy. I have read the paper (paywall-free preprint) which describes it from the point of view of AES. From what I understand, it is a technique to ...
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Security of the AES with a Secret S-box

In this paper they change the $AES$ S-box to a uniformly random one and answer the questions: How does the security of AES change when the S-box is changed by a secret S-box? Would it be safe to ...
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Does CPA-secure means security against differential cryptanalysis?

I've read on differential cryptanalysis where it traces the differences on the changes of ciphertexts of the same plaintext, except for some bits. However, I wonder is the differential cryptanalysis ...
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Are SHA-2's $\mathit{Maj}$ and $\mathit{Ch}$ functions non-linear?

SHA-2 has two functions: $\mathit{Maj}(x, y, z) = (x \land y) \oplus (y \land z) \oplus (x \land z)$ $\mathit{Ch}(x, y, z) = (x \land y) \lor (\neg x \land z)$ Are these two functions non-linear? ...
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Security of an S-box based on modular multplicative inverse

The construction of Rijndael's S-box starts with the multiplicative inverses of each number over a finite field. It seems like this is the main source of its non-linearity. I figured that modular ...
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Why is variable rotation uncommon in cryptographic primitives?

Most cryptographic primitives I've seen rotate by a constant. RC5 did something different though: For a word size $w=2^n$, you can take the last $n$ bits of a value as a rotation amount. There's more ...