(or substitution boxes), components in many block ciphers used to substitute parts of the data in a non-linear way. While often fixed by the algorithm (like in DES and AES), sometimes they are key-dependent (like in Blowfish).

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Finding Linear Redundancy by counting the number of distinct frequency distributions of absolute walsh transform

I am writing a program to find linear redundancy in 4x4 s boxes. Is the number of distinct frequency distributions of absolute walsh transform a direct measure of linear redundancy in s boxes? byte[] ...
3
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1answer
30 views

Is order of Correlation Immunity of AES S_box Zero?

I am working on AES S_box and trying to find out its properties like Correlation Immunity, Balancedness , Algebraic Degree , ANF form etc. These Papers 1, 2 give a nice definitions to above said ...
2
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1answer
475 views

DES S-Box properties

Two of the properties that lead to the design of DES S-Boxes are: For any non-zero 6-bit difference between inputs, no more than 8 of the 32 pairs of inputs exhibiting that difference may result in ...
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4answers
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Desirable S-box properties

What desirable properties should an S-box have? My current standard selection process is to just pick them at random and verify that they fit the following criteria: The probability that any random ...
5
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2answers
92 views

Is the difference distribution table of AES S-box uniform?

I am studying about various block ciphers and their weaknesses, so I have a doubt about AES S-boxes, Is the difference distribution table of AES uniform ?
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1answer
80 views

How does one practically calculate the non-linearity of a multi-output boolean function like the AES s-box?

I am working on multi-output boolean function i.e. a function that takes an $n$-bit input and gives an $m$-bit output for all possible inputs (i.e. $2^n$ inputs). To be more exact: I am trying to do ...
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Reason why “XOR” is a linear operation, but ordinary “addition” isn’t?

I'm new in cryptography and try to read some articles in this field. Many of these articles talk about non-linear S-boxes, and nothing more on what they mean by their non-linearity. I have a simple ...
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2answers
65 views

Why DES s-box non-linear? Why it makes the cracking of the cypher more difficult?

I know that if we have a cypher which makes only linear transformations (let's say a bunch of $XOR$'s), we break it simply writing a system of equations with $\oplus$ operation starting from the ...
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2answers
52 views

substitution Box(s-box) for AES

can anyone suggest me any fast searching method or algorithm to find best S-Box among a big number of S-boxes?for example ; if i have 100 different s-boxes. i want to pick any one which is secured ...
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2answers
75 views

What makes an open source encryption algorithm safe?

Take for example the popular AES algorithm where we have a combination of substitution, shift row, mix column, and add key steps involved in encrypting plain test. All of the mathematical operations ...
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1answer
31 views

Last Sbox of a block cipher for Linear Cryptanalysis

I figured I should try to learn about linear cryptanalysis with a super simple cipher with only one Sbox. The problem is that with that approach the last subkey bits seem to be involved in the linear ...
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1answer
73 views

Number of Sbox in a Cipher

Camellia has 4 SBOX and so does the TwoFish(key dependent 4 Sboxes). Where as AES uses only one. Would it have made AES more secure if AES had 4 or more SBOX too? Does using more Sbox with similar ...
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1answer
103 views

Is this a better involution S-Box for the Anubis cipher?

After swapping random indexes of trivial involution $S[x] = ¬x$, I found the following involution S-Box with a non-linearity of $98$ and a differential uniformity of $6$. Is there an upper limit to ...
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2answers
441 views

About the Rijndael/AES sbox polynomial (subBytes)

I've recently read a question about the irreducible polynomial behind the subBytes() operation in the Rijndael that has awakened and old curiosity I have: Why $\,m(x)$ was chosen as $\,x^8+x^4+x^3+x+...
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1answer
198 views

Rijndael S-boxes: Where do the $\mu$ and $\nu$ polynomial ring elements come from?

I've asked some other questions before about Rijndael's S-boxes, and step by step I'm coming to an understanding; but those steps often guide me to new questions. I did some lines of code to ...
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1answer
236 views

Do key-dependent S-boxes make efficient constant-time software implementations almost impossible?

It seems to me that algorithms like Blowfish and Twofish with key-dependent S-boxes are almost impossible to implement without table lookups, and thus are almost impossible to implement in software ...
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1answer
227 views

How are calculated numbers in AES S-box?

I have a problem calculating the 0x02 value of the AES S-Box. I followed the steps descibed in “How are the AES S-Boxes calculated?”, but my answer is not correct. ...
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1answer
80 views

What is the security gain of applying Two S-boxes in Different Ways?

In a 128-bits Feistel Cipher: I need suggestions about two variations of the Round Function Variation-1 $64$ bit input is divided into $8$ bytes Byte $0,1,2,3$ are substituted with Sbox1 Byte $4,5,...
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2answers
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Converting a 5-bit s-box to its bit-sliced format

I'm currently trying to convert a 5-bit sbox (the one from this cipher: http://primates.ae/wp-content/uploads/primatesv1.02.pdf) to its bit-sliced format (i.e. to a boolean network). Most papers ...
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2answers
117 views

AES S-Box Affine Mapping - how to do it?

For the byte substitution layer in AES how do we determine B(i)? I follow how to use the multiplicative inverse table and using that to get B`(i), but how do I actually calculate the affine mapping? ...
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0answers
34 views

Can we use more than one irreducible polynomial in AES?

I understand that the irr. poly is used to form the s-box (and inv. s-box), the key schedule and the mix columns. But could we use a different irr. poly for the mix columns and another for the key ...
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1answer
147 views

How does non-linearity (S-box) add security to AES?

I'm trying to understand how AES guarentees security. One of the named points on the web is that AES uses a non-linear step (the SubBytes step). But how exactly does the Rijndael key schedule add ...
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0answers
40 views

AES - Size of T-Boxes and obtaining T-Box values

In article "A high performance ST-Box based unified AES encryption/decryption architecture on FPGA" (http://www.sciencedirect.com/science/article/pii/S0141933115001945) two 32Kb dual-port BRAMs are ...
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1answer
101 views

DES: Computing the output of S-Box 1?

If the 48-bit input to the S-box is 0xAAAAAAAAAAAA, what are the first four bits emitted by S-box 1? Answer: 0110 I know that an S-Box takes n inputs and give m outputs and that n != m, but I really ...
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2answers
4k views

How were the DES S-box values determined?

It seems like the S-boxes in DES have essentially random values. How were these chosen?
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52 views

I am trying to understand how AES works

I am trying to understand how AES encryption operates. I am trying to run through the steps on paper to understand. So far, I am creating a simple example. I have the plain text "MESSAGE TESTTEXT" ...
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0answers
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Differential bound of the S-Box in GOST R34.11-2012

In Russian GOST R34.11-2012 LPS-transformation is used. LPS gets all of its non-linearity from the 8-bit S-box S, which apparently has been designed to offer resistance against classical methods of ...
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1answer
111 views

Why is not there any ideal S-Box?

i read about linear cryptanalysis and about S-Box that there is not any ideal S-Box (ideal S-Box is a random S-Box in another words S-Box that bias of input and output bits is zero) then i read about ...
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0answers
57 views

Active s-box of 8x8 MDS for AES

one way to enhance the security of AES by increasing the number of active s-boxes .larger MDS matrices are used to increase the number of active s-boxes. using 4x4 MDS matrix generate 25 active s-box ...
2
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2answers
88 views

BOOLEAN FUNCTIONS: generate a function $f: \{0, 1\}^n \rightarrow \{0, 1\}$ from a $n \times n$ S-Box

I want to calculate the hamming weight of a S-Box using this formula: $\text{hw}(f) = \sum_{x=0}^{2^n-1} f(x)$. Where $f: \{0, 1\}^n \rightarrow \{0, 1\}$ My problem is that I don't know how to get ...
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350 views

Evaluating Algebraic Complexity of a S-box

While studying the design and the desirable properties of an AES S-box , I came to know that Algebraic Complexity is also an important property of an S-box which is usually considered while evaluating ...
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42 views

Finding differentials and space complexity

Most of article about differential cryptanalysis present the generic method, the way to find sub keys. But I can't find a clear explanation about how to find the differentials used in examples. In ...
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50 views

What are the negative consequences for choosing 8 S-boxes for DES vs 1 S-box for AES?

DES has 8 different S-boxes, and AES has only 1. What are the negative consequences of such choices?
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1answer
143 views

DES and using the S-Box 1

Can someone please check my work and correct me if I am wrong, I am just starting to learn about DES. I am trying to solve the following problem: Show that ...
6
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1answer
2k views

How can an S-Box be reversed?

So, as an exercise to greater understand some things about cryptography, I decided to try and implement GOST 28147-89, which uses eight 4x4 S-Boxes. I can grasp the concept of putting 4 bits through ...
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1answer
324 views

How to build a difference distribution table?

i am studying about differential cryptanalysis, and found one metric to measure the resistance of a sbox to it, but to use it, it is necessary to build a difference distribution table, like the one in ...
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0answers
87 views

How do we generate AES S-BOX?

I am new to AES and I am too much confused about the generation of S-box in AES. I don't have any idea of $GF(2)^8$ field and how the things are happening around. Please answer this question with a ...
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0answers
116 views

How can I design a cryptographically secure, key-dependent s-box?

I would like to design a cryptographically secure, key-dependent s-box, but I am not sure how. Mainly, because I am unsure about the difference in design compared to a random s-box. What is the ...
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0answers
169 views

How to calculate the non-linearity of an s-box? [duplicate]

I am struggling to understand how to calculate non-linearty of an s-box, could someone show me a detailed example? I found “How to calculate non linearity of AES S-box?” which helped a little, but I ...
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1answer
66 views

Are more S boxes more secure in a SP-Network?

The classic DES uses 8 different fixed S boxes. If computer memory was not an issue, would say 800 different S boxes be more secure? I'm thinking of a SP-network that would only run on a server like ...
2
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1answer
117 views

How to generate the APA SBox?

I am trying to generate the S-Box provided in the Affine Power Affine paper (PDF) but I'm not sure I understand it fully. The essence of the paper is this: ...
0
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1answer
88 views

AES inversion operation in sub byes

I was wondering why in the AES sub-bytes operation one can represent the inversion as computing $x^{254}$. What is the reason for this? Moreoever, I was wondering what the text on page 212 of https://...
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1answer
126 views

What makes this mixer function resistant to differential cryptanalysis?

I recently learned how differential cryptanalysis works, and decided to have a play around with testing various designs for resistance against attack. My testing algorithm is essentially to loop ...
13
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1answer
617 views

Choice of multiplication polynomial in Rijndael s-box affine mapping

The Rijndael specification details the design choices for the s-box in section 7.2. They describe the choice of affine mapping as follows: We have chosen an affine mapping that has a very simple ...
2
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1answer
166 views

Performing differential cryptanalysis for randomly generated S-boxes

As far as I know, performing differential or linear cryptanalysis always requires a knowledge of the S-boxes' content and order. Yet in Bruce Schneier's Applied Cryptography, it is stated that random ...
2
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1answer
975 views

How are the AES inverse S-Boxes calculated?

I would like to know, how to calculate the inverse S-box. I followed this link (with affine transformation first, then multiplicative inverse), but the result is wrong. For example, if I use the value ...
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2answers
212 views

Is the DES F-function injective for a given subkey?

Is it possible for two different half-block inputs to the DES F-function, with the same round subkey, to produce the same output? That is, if we feed two different half-block inputs $b_1$ and $b_2$ ...
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CAST-256 (CAST6) versions or S-Boxes

Are there different versions of CAST-256 - also known as CAST6 - available? Are there different S-Boxes available for CAST-256? If there are different versions or S-Boxes what identifier should I use ...
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266 views

About the Algebraic Normal Form (ANF) of S-Box in DES

I've thought up a way to represent the transformation of S-Box in DES by ANF. Let $x_i\;(1\le i\le 6)$ be the input of an S-Box, $y_i\;(1\le i\le 4)$ be the output, for example, then $$y_1= 1\oplus ...
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1answer
609 views

What benefits do substitution boxes and permutation boxes offer in DES?

I understand that with more encryption rounds the more complex the ciphertext becomes due to multiple substitutions and permutations. What I don't understand is the purpose of these features. I am ...