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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31 views

nonlinearity and autocorrelation of common s-boxes

I cannot find publications comparing the properties of popular cipher s-boxes. First of all, I am interested in nonlinearity and autocorrelation of s-boxes, which are used in seed, cast-128, camellia ...
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Conditional probability being Constant in Threshold Cryptography

I am working on Threshold implementation of algorithms to prevent side channel attacks. I am not that much proficient in Statistics and Probability theory. I want to know what is the significance of ...
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102 views

Division property table of SBox

In Table 12 (page 23) of the GIFT paper, the "Division property" table is given. I could not understand how it has been computed. My questions: May I have an algorithm on how to compute the ...
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44 views

Building a 4-bit S-box with a 4-uniform DDT

I am looking for a 4-bit S-box which has only 4s in its difference distribution table (except the top left corner) but I was not able to find one in the literature. Has such an S-box been already ...
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44 views

SHA3_512 as dynamic SBOX generator

I'm creating a substitution-permutation cipher (for learning purposes only of course) and I'd like to implement dynamic SBOXs. The cipher will have a block size of 128, and 32 rounds. These SBOXs will ...
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40 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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57 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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101 views

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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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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21 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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78 views

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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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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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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59 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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272 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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59 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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58 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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128 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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58 views

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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132 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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57 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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68 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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35 views

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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99 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
82 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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42 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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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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103 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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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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91 views

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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79 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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124 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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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
252 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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442 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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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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117 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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401 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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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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Are there any publicly available Serpent s-boxes of a non-linear order 3, optimized for x86_64?

The original serpent paper claims that the s-boxes provided are of non-linear order 3, the maximum. However, this has turned out to be false, as some of them are of order 2. Are there any s-boxes ...
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91 views

Generate $4\times 4$ Sboxes with a given branch number

Say, I want to generate a lot of $4\times4$ Sboxes with linear (or differential) branch numbre of $3$. One idea is to take all the $302$ affine classes, expand each of those classes and check if any ...
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624 views

Choosing the size of an S-box

The most common S-boxes that I've seen are 4-bit and 8-bit (I've seen a 3-bit S-box in PRINTcipher, but I'm pretty sure they only did so due to significant hardware constraints). I understand that ...
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How to find multiplicative inverse of a hexadecimal number in the finite field GF(2^8)? [duplicate]

I am new to cryptography. As I was reading a note regarding S-box construction, I found a step mentioning multiplicative inverse of a number in the finite field GF(2^8). I couldn't understand it!! Can ...
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72 views

Extract one unique SBox from Canonical Representative

In paper https://eprint.iacr.org/2011/218.pdf, the author has examined 16! different 4 bit SBoxes and at the end of investigation, introduced an optimal class which named "Golden SBoxes". How can I ...
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128 views

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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593 views

What is the inverse function of the finite field GF($2^3$) and GF($2^4$)?

I am currently reading a paper Cryptanalysis of a Theorem Decomposing the Only Known Solution to the Big APN Problem. In this paper, they mention that they used $I$ which is the inverse of the finite ...
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215 views

If the S-Box is given. How to calculate the affine transformation matrix?

Example using SAGE sage: sr = mq.SR(1, 1, 1, 8, gf2=True) sage: S = sr.sbox(); S (99, 124, 119, 123, 242, 107, 111, 197, 48, 1, 103, 43, 254, 215, 171, 118, 202, 130, 201, 125, 250, 89, 71, 240, 173, ...
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73 views

What does $x^{1/e}$ mean in cryptography in this open butterfly structure?

I am currently reading a research paper that introduces this thing called a butterfly structure. I am confused about the structure of the open butterfly in this paper which has the equation $H^{\...
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163 views

Find substitution of a decimal number from s-box

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