Linked Questions
16 questions linked to/from Galois fields in cryptography
8
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1
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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 ...
- 195
9
votes
2
answers
2k
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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 + ...
- 1,211
5
votes
2
answers
3k
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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 ...
- 51
3
votes
2
answers
3k
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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 ...
- 31
1
vote
1
answer
6k
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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 ...
- 11
1
vote
1
answer
3k
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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.
...
1
vote
3
answers
7k
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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 ...
- 13
1
vote
2
answers
198
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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 ...
- 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 ...
- 81
1
vote
1
answer
1k
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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 ...
- 113
2
votes
1
answer
767
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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). ...
- 23
3
votes
1
answer
439
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 ...
- 3,527
2
votes
1
answer
367
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 ...
- 207
1
vote
0
answers
482
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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 ...
- 11
0
votes
1
answer
208
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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 ...
- 103