(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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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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74 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 ...
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81 views

Generating S boxes that satisfy Coppersmith's criteria?

I'd like to generate all possible 6-bit to 4-bit S-Boxes that satisfy the criteria for S-Box design given by Coppersmith, but I have a few doubts: How many such S-Boxes are possible? Is there any ...
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78 views

DES S-Box properties

Two of the properties that lead to the design of DES S-Boxes are: 1)For any non-zero 6-bit difference between inputs, no more than 8 of the 32 pairs of inputs exhibiting that difference may result ...
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164 views

Polynomial representation of the affine part of the AES S-box

I have been reading up on the polynomial representation of the AES Sbox (PDF: “Essential Algebraic Structure Within the AES” by Murphy and Robshaw) and I can't get it to produce the correct output. ...
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1answer
197 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
122 views

Math to replace s-boxes - Good or bad idea?

The following was going through my brain for the past week. If my thoughts are generally known to the cryptographic community would someone provide a link or two. Even if I’m making a classic newbie ...
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175 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 ...
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80 views

How can I find the multiplicative inverse in the first transformation of the SubBytes() transformation in AES?

In FIPS-197 §5.1.1 , it says the first transformation in the SubBytes() transformation is: Take the multiplicative inverse in the finite field $\text{GF}(2^8)$ described in Sec. 4.2; the ...
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1answer
218 views

How to calculate inverse affine transform in AES from forward affine transform?

In AES the forward affine tranformation matrix is defined as: $$ \begin{bmatrix} 1& 0& 0& 0& 1& 1& 1& 1 \\ 1& 1& 0& 0& 0& 1& 1& 1 \\ 1& ...
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205 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 ...
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1answer
190 views

Are the MD5 constants an S-Box?

I noticed that several hash algorithms, in this case MD5, defines some constants. MD5 defines 64 constant values (the shift count per round) which also gets expand (via sine) to a summand for a ...
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784 views

Why xor is a linear operation but ordinary adding is not

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
238 views

Two-dimensional S-Box

Consider the following simple cipher: $$c_1 = S(m_1 \oplus k_1) \oplus k_2$$ Where $S$ is S-box, $m_1$ - 16-bit plain text, $k_1$ and $k_2$ is two parts of 16-bit key. If S-box is standard then this ...
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117 views

How would using only one s-box affect security of Blowfish?

Schneier says: Fewer and smaller S-boxes. It may be possible to reduce the number of S-boxes from four to one. Additionally, it may be possible to overlap entries in a single S-box: entry 0 ...
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3answers
264 views

AES column mixing and S-Box confusion

I am trying to understand the AES encryption algorithm. I know that we process 128 bits at a time for a 128 bit key in a 4x4 octet form, but am confused by the following: How does the substitution ...
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1answer
340 views

Serpent cipher : Osvik S-Boxes confusion and test vectors

I'm having hard time with the implementation of the S-Boxes by Osvik found in this paper: Speeding up Serpent. At the end of the paper, all the s-boxes are given and then, I just implement them. ...
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359 views

Serpent block cipher : S0 to S7 functions unclear

I am presently implementing the serpent block cipher in C++ following the specifications. It's important to mention that I'm implementing the cipher in bitslice mode. You'll need the The full ...
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1answer
4k views

How are the AES S-Boxes calculated?

I'm trying to understand how the AES S-Boxes are calculated. I understand how the multiplicative inverse is calculated over GF(2^8), but I'm confused by the description of the affine transformation. I ...
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1answer
388 views

Where is the S-Box generated in Rijandel/AES?

It's rather kind of lame questions, and I can't find good and clear explanation: In which step of Rijandel is S-box generated? Is the S-box reused in every round of cipher or is generated in every ...
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1answer
5k views

How does DES decryption work? Is it the same as encryption or the reverse? [duplicate]

If DES decryption is the same as encryption done in reverse order, then how can the reversed S-Box convert 4 bits into 6 bits?
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286 views

How do I choose the best 3*3 s-boxes?

I've read about 20 papers about the criteria for choosing best $n \times n$ s-boxes. Now, I've got two problems: How to generate $2^{24}$ s-boxes, and how to test them considering the criteria. ...
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713 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
213 views

S-box with differential uniformity = 2

I read that we do not know if there exists an 8x8 sbox with differential uniformity = 2. I suppose we cannot compute every possible sbox because there are $64!$ possible s-boxes. Am I right?
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S-box design criteria and random sboxes

What are the disadvantages of using random s-boxes? In AES, the s-boxes had to obey certain mathematical rules, which? And why? What security does using hidden s-boxes (GOST) or generating them from ...
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2k 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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265 views

S-box Cryptanalytic Resistance

In DES, different S-boxes were tested for cryptanalytic resistance and the most secure one was chosen for the algorithm itself. How do different S-boxes offer different levels of security against ...
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1k 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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3answers
1k views

Security of simple xor and s-box cipher?

What weaknesses (or strengths) do block ciphers based on only key xor and s-box have when operating in CBC mode? A cipher's internal primitive might be a simple as this: $C = S[M \oplus k]$, where ...
9
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1answer
786 views

Replacing the Rijndael S-Box?

The Rijndael S-Box design generates a permutation cycle of type $2+27+59+81+87$. What effect would replacing that permutation with a cycle of type $256$ have on the security of AES?
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3k 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?