Questions tagged [s-boxes]

(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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0answers
38 views

What does “the input difference of each Sbox should be zero” mean?

While going through the article, The MALICIOUS Framework: Embedding Backdoors into Tweakable Block Ciphers. I came across this statement in order to have a deterministic differential characteristic ...
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1answer
53 views

AES with other SBoxes

I'm not a cryptologist, just an interested engineer (& now retired). I used to design hardware with AES en/decryption blocks & generate test vectors using my own Tcl script using the embedded ...
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2answers
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Differential and Linear Cryptanalysis on Random Sbox

Assume that we use the key to perform a uniform permutation to generate a sbox. The literature is rich supporting the statement that a random Sbox can make any cryptographic scheme weaker. I have ...
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1answer
857 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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2answers
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Why is the nonlinearity of this Boolean function evaluating to $\frac12$?

I am using the method presented in this paper to find the nonlinearity of the function $$ f: \mathbb{F}^1_2 \to \mathbb{F}^1_2 \\ f(x) = x$$ The truth table is $f = [0 \space \space 1]$. Now, I read ...
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22 views

Calculating equivalent substitutions to AES operations(MixColumn/ ARK)

When the AES algorithm is implemented in a table lookup(SubByte, MixColumn) fashion, how many substitutions required in full round encryption? When AES is encrypted without using the table lookup(only ...
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17 views

How do I invert the final round S Boxes during linear cryptanalysis

I'm using Howard Hey's tutorial on linear cryptanalysis, however I don't understand the final stages. I understand using exhaustive partial subkeys to turn the ciphertext into the final round output, ...
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3answers
9k views

Why do block ciphers need a non-linear component (like an S-box)?

Why is there a requirement of "Non-Linear functions" as a component of many popular block ciphers (e.g. the S-box in DES or 3DES)? How does it make the cipher more secure? The only intuition I have ...
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1answer
569 views

S-Box and it's linearity

I am trying to figure out why it is necessary S-box's to be nonlinear. I have been searching for some materials but was not able to find out clear proof why it means that if we use S-box in DES, it ...
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36 views

Avalanche effect SBOX

It is possible to achieve the avalanche effect in an SPN or in a Feistel network that use a single round of an SPN in his function (like DES) using SBOX that receive 2 bit in input and output 2 bit?
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1answer
386 views

DES - Weakness in Sbox

In the book "Introduction to Cryptography with Coding Theory ", in the chapter about the Differential Cryptanalysis for Four Rounds for DES algorithm, the authors say: There is a weakness in the ...
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1answer
380 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
54 views

Is it possible to use an S-box similar to the one used in DES in AES? How would this work?

I'm reviewing some questions given to me by a professor and am stumped on this one. My initial guess is that yes, this is possible, but I do not know how to explain it, specifically for a function $\{...
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1answer
255 views

AES-CTR security if S-boxes substituion is omitted?

I understand why s-boxes are needed in general especially when ECB mode is used(because of using the same key for encryption of other blocks)but I wonder if it's ...
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4answers
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Generate ANF from SBox

Given an SBox, how can I generate its component equations (in ANF)? For example, let's say I have this SBox: 6, 4, 7, 8, 0, 5, 2, 10, 14, 3, 13, 1, 12, 15, 9, 11 Then, the equations are: $y_0 = x_1 ...
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1answer
40 views

Problems on ANF equation?

I tried to solve SBox as given in this link I am trying to understand this paper SBox. In this on page no.4 the correct equation of given SBox is mentioned. I am not getting how to design ANF equation ...
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1answer
57 views

Generate ANF equation? [duplicate]

Given an SBox, how can I generate its component equations (in ANF)? given in this link: https://en.wikipedia.org/wiki/Algebraic_normal_form For example, let's say I have this SBox: $$\{1, a, 4, c ,6 ,...
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1answer
4k views

How can I calculate the Rijndael SBox?

I would like to implement the Rijndael subBytes() operation using calculation instead of tables, because I like to play with this on different wordsizes, as an ...
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1answer
121 views

What Is The Number of Active S-boxes over 5 Rounds of Fides AE cipher?

It is mention in the paper " Fides: Lightweight Authenticated Cipher with Side-Channel Resistance for Constrained Hardware" , the number of active S-boxes of Fides cipher is 22 over 5 rounds but my ...
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1answer
552 views

Active S-boxes for AES with 8x8 MDS matrix

One way to enhance the security of AES is by increasing the number of active S-boxes. Larger MDS matrices are used to increase the number of active S-boxes. Using a $4\times4$ MDS matrix results in 25 ...
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1answer
54 views

LAT of an SBox, values are even

This is probably a silly question, but I could not find any reference. For the DDT of an SBox, it is easy to see why all the values are even. Is there any related result for LAT (i.e., all its values ...
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How to implement arbitrary s-box in a side-channel-free way in C?

This could be a question for CodeReview.SE, but I thought it might require non-trivial cryptographic knowledge to merit it on-topic here. The C language is chosen as it's a common language for ...
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1answer
113 views

Is AES S-Box resistant to side-channel attacks?

I know that implemntations with T-tables such as Golang's are prone to side-channel attacks, but is AES's S-Box wihtout any additional table also insecure ?
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1answer
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Is ShiftRows(SubtBytes(x)) = SubtBytes(ShiftRows(x)) the same for the same entry : in AES

Is ShiftRows(SubtBytes(x)) = SubtBytes(ShiftRows(x)) the same for the same entry : in AES It seems like these two are equal, can someone explain in theoretically?
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1answer
130 views

Cryptanalysis of a feedback shift reigister with an S-box

I’m just getting started on learning cryptography and here is a problem from exercises about which I'm totally confused: This is a 32-bit feedback shift register to encrypt some message. The register ...
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56 views

S-box for byte substitution where the s-box values are multiplicative inverses of 257

The title basically says it. We have a 16 by 16 s-box, $256$ entries total. And the first value is the multiplicative inverse of $257$, so $1 \times k \bmod 257, \space k = 1$. $2 \times k \bmod ...
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1answer
65 views

What are the standard properties of an S-Box [duplicate]

Apart form the following, what are the other properties of a good cryptographic Substitution box or the S-Box: Changing one input bit should change about half of the output bits. Each output bit ...
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AES S_BOX Generator additive constants

I try to generate other S_BOX for AES but I don't realize how to choose additive constants for S_BOX from decryption if for encryption it is 0x63 why is ...
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1answer
96 views

Inversion in $GF(2^{10})$ Using Composite Fields

I'm designing a circuit that uses many $GF(2^{10})$ inverters. Normally for this sort of thing I use lookup tables. (Itoh-Tsujii is not efficient for these smaller fields.) This application is for ...
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1answer
77 views

How to generate a 16 X 8 perfectly nonlinear S-box

I want to generate a 16,8 perfectly nonlinear S-box for an encryption algorithm I am working on. I don't have a background in math, and I'm an undergrad, so a lot of the math involved is very ...
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1answer
761 views

How constant value 0x63 in affine transformation is chosen or generated while AES Substitution Box is formed?

Me and one of my friends are working on AES algorithm. We have understood how multiplicative inverse table is generated. Rijndael AES algorithm shows us how S-Box is generated through the affine ...
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Design of SIMD-implemented cipher

Design of efficient of block ciphers needs consideration of many factors such as register size. i found that some ciphers can be SIMD implemented such as TWINE , SM4 , chacha20 ,SPIX ,and others. ...
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5answers
7k views

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 ...
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41 views

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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1answer
97 views

Would using perfect S-boxes in F function of an unbalanced Feistel network produce a simple and secure cipher?

When I read some articles about cryptography on wikipedia, I took note of the following statements (please, correct me, if any of these are wrong): Perfect S-box (based on bent functions) provides ...
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1answer
76 views

A bit-sliced implementation (or the algebraic normal form) of the two FIDES S-Boxes

I want to see a bit-sliced implementation of 5-bit and 6-bit S-Boxes of FIDES or, at least, a representation of these two functions in algebraic normal form. Where can I find it?
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910 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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0answers
71 views

Side-channel vulnerability of AEGIS naive AES implementation

AEGIS, one of the finalists of CAESAR competition, uses a naive implementation of AES encryption round as its reference implementation. By naive I mean it uses secret dependent table lookups, so it is ...
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Do the keys in AES determine the S and P boxes? [closed]

I once read somewhere that the keys determine the S and P boxes. If so, how does that work?
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1answer
681 views

Explain the fast Walsh–Hadamard transform in simple steps or pseudocode

I've read that the fast Walsh–Hadamard transform is a way to efficiently calculate the linearity/non-linearity of an S-box. Can I get a description of it in simple steps or pseudocode that is ...
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1answer
117 views

Can I change the S-box and P-box in DES?

I am a newbie to crypto and just one quick question on the s-box and p-box of DES. I understood that the s-box is where the security comes from and NSA has somehow decided how it should be filled in. ...
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2answers
400 views

Reverse Fixed Points in Kalyna S-Boxes and Reverse Engineering the S-Boxes

I was examining the S-Boxes of the Kalyna Cipher and found that 3 of the 4 S-boxes have reverse fixed points i.e S[x] = (255 - x). Is this an exploitable weakness? I was not able to find any open ...
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71 views

How TAU function of SM4ni cipher is implemented?

I am trying to understand the SIMD implementation of TAU function of SM4 which is as follows: ...
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2answers
221 views

Is the following s-box more linear or more non-linear?

I am trying to figure out whether the following simple s-box configuration I created is more linear than non-linear or vice versa more non-linear than linear? The parameters for this 16*4 table of ...
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2answers
378 views

how can I test quality of sbox?

I have 11 sboxes, I want to test them and find the best one. How can I do that, I found several criterions for that but I could not understand.
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1answer
632 views

how to compute the correlation between two binary vectors?

We find different equations to compute the correlation or correlation coefficient: $\begin{align*} corr &= \frac{a+d}{a+b+c+d}\\ &= \frac{(a+d) - (b+d)}{a+b+c+d}\\ &= \frac{(a+...
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71 views

how to compute Bit Independence criterion of SBOX?

I want to compute BIC's of my Sboxes, I found out some theses for that but I could not understand how to do it. Can someone help me?
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2answers
109 views

$\alpha^{2^{m} + 1}$ is a generator of $\operatorname{GF}(2^m)$?

This is from a paper (Partitions in the S-Box of Streebog and Kuznyechik) about S-Boxes: Let $\operatorname{GF}(2^{2m}) = \mathbb{F}_2[X]/p(X)$ be a finite field of even degree defined by a primitive ...
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1answer
84 views

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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1answer
181 views

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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