Linked Questions

8 votes
1 answer
32k views

Multiplication/Division in Galois Field (2^8)

I'm attempting to implement multiplication and division in $GF(2^8)$ using log and exponential tables. I'm using the exponent of 3 as my generator, using instructions from here. However I'm having ...
Jacob Wang's user avatar
9 votes
2 answers
2k views

On what Galois field AES really works?

I'm trying to understand the GF theory, but every time I come across information about AES it all makes no sense. In my opinion $GF(2^8)$ defines any polynomial of the form: $a_{7} x^7 + a_{6} x^6 + ...
Tom's user avatar
  • 1,221
5 votes
2 answers
3k views

Shamir's Secret Sharing Scheme - prime security?

Does the prime (which needs to be larger than the message) have to be chosen randomly for security, or can it just be a huge constant? Also, the Wikipedia article for SSSS states The size of each ...
David's user avatar
  • 51
3 votes
2 answers
3k views

How are these AES MixColumn multiplication tables calculated?

I'm using the mul2, mul3, mul9, mul11, mul13 and mul14 tables for the MixColumn and InvMixColumn steps in AES-128. However, I got these off some Github repository, and now I'm looking for an actual ...
Satoutan's user avatar
1 vote
1 answer
6k views

Multiplicative Inverse in AES [duplicate]

I want to calculate the S-box for AES. But I have a problem with the multiplicative inverse step. For example, the inverse of 95 is ...
user39534's user avatar
1 vote
1 answer
3k views

How to generate a random polynomial of degree $m$?

I am trying to do a homework in which implement a variation of this paper and I don't know how to generate a polynomial of degree $m-1$. This polynomial is used to generate the $y_0$ and $y_1$ values. ...
TheRookierLearner's user avatar
1 vote
3 answers
7k views

How to do Hexadecimal multiplication in GF(2^8)

I'm trying to do a hexadecimal multiplication in GF(2^8). Now, I know the technique of shifting left the binary numbers in some cases, for example: 02 * 9E 0000 0010 * 1001 1110 you shift one time ...
Erik Torres's user avatar
1 vote
2 answers
200 views

Does GHASH use XOR or addition?

I've been looking into GHASH and some sites describe it as a polynomial: A1*(H* *M-1)+A2*(H* *M-2)...C1*H(H* *M-N)+C2*H(H* *(M-N-1))...+len(A||C)*H+E(0)=t while ...
Itai's user avatar
  • 19
1 vote
1 answer
2k 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 ...
Hannah's user avatar
  • 81
1 vote
1 answer
2k views

Prime fields vs non-prime fields

I was watching this class about AES in this LINK and I was trying to grasp the concept of prime fields, which is a finite field with prime order $p$. The non-prime field part (order is $p^n$) is ...
Filipe Rodrigues's user avatar
2 votes
1 answer
775 views

How are Rijndael's S-Boxes generated?

Wikipedia: Rijndael's Forward S-box I'm writing C Code to generate S-boxes but I'm stuck. Would you mind explaining one entry of the S-box? (say for x = 0x2). ...
Mithil's user avatar
  • 23
3 votes
1 answer
444 views

Galois field step in XEX mode

I'm reading through the XEX mode spec, and I want to make sure I've understood the $\alpha^j$ step correctly: $X = E_K(I) \oplus \alpha^j$ $C = E_K(M \oplus X) \oplus X$ where: $M$ is the ...
Polynomial's user avatar
  • 3,527
2 votes
1 answer
371 views

XEX mode - how to perturb the tweak

The first part of the classical description of XEX is $X = E_{k}(I) \otimes \alpha^j$ What I see a lot in sample code on the Internet is that you start with $T_ = E_{k}(I)$ and use that for the ...
nsayer's user avatar
  • 207
1 vote
0 answers
484 views

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 ...
Salini's user avatar
  • 11
0 votes
1 answer
216 views

AES and quantum computing

I am trying to understand the AES-256 encryption algorithm as it would be implemented on a gated quantum computer (actually, a simulator), and I am having some trouble understanding the theory behind ...
Robert Singleton's user avatar

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