All Questions
14
questions
0
votes
0
answers
16
views
AES S-box as simple algebraic transformation
The next matrix represents the Rijndael S-box according to wikipedia and other sources
$$\begin{bmatrix}s_0\\s_1\\s_2\\s_3\\s_4\\s_5\\s_6\\s_7\end{bmatrix} =
\begin{bmatrix}
1 & 0 & 0 &...
- 463
1
vote
1
answer
30
views
Distinct derivations of polynomial over finite field
I am a student studying algebra and cryptography.
I wonder below question is possible.
Can I make some polynomials $f(x)$ over finite field that all derivations $f^{(k)}(x)$ are distinct when x is ...
- 13
0
votes
0
answers
145
views
Evaluation of a polynomial over the finite field $\mathrm{GF}\left(2^{8}\right).$
I am trying to make a program that, among other things, considers a polynomial $p$ whose coefficients are elements of $\mathrm{GF}\left(2^{8}\right)$ and shows the user the graph of that polynomial. ...
- 152
0
votes
1
answer
74
views
Exponentiation and Other Operators with Ring Arithmetic
I'm interested in ring/finite field arithmetic. The typical setup for this is a space of integers modulo a large prime number such that there are operators for addition, multiplication and their ...
- 1,679
1
vote
2
answers
804
views
Calculate a Primitive Polynomial LFSR
I tried to search on the internet, to read my course multiple times, but the only thing I see are definitions of the primitive polynomials for an LFSR.
I have an exercise:
Find the primitive ...
2
votes
2
answers
1k
views
Find the elements of the extension field using primitive polynomial over $GF(4)$
Let $p(z) = z^2 + z + 2$ be a primitive polynomial. I want to construct the elements of the extensional field $GF(4^2)= GF(16).$
Since $p(z)$ is primitive polynomial , it should generate the ...
- 427
6
votes
1
answer
525
views
Verifying if a given polynomial is primitive polynomial
Given a polynomial: $f(x) = x^2 + 2x + 2$ over $GF(3)$. I want to know if i can use it to construct $GF(3^2)$.
My approach:
This equation satisfies first condition: A primitive polynomial is ...
- 427
0
votes
1
answer
658
views
Why does the cube root of a polynomial in a finite field produce a different polynomial when re-cubed?
I'm using SageMath to try and determine whether the cube root of a polynomial exists in a finite field GF(2^8). Whilst raising the polynomial to the minus 3 does produce a root (that is in the finite ...
3
votes
2
answers
5k
views
Calculating AES Round Constants
I am attempting to calculate the round constants used in AES. Using the formula found on Wikipedia's Rijndael Key Schedule page results in answers that the same page says are correct, but the primary ...
- 131
1
vote
0
answers
710
views
Find GCD of polynomials over GF(101)
Hello all I'm teaching myself cryptography, and I'm struggling with polynomial arithmetic over finite fields. I've some what been able to teach myself how to do the arithmetic over $GF(2)$, but when ...
6
votes
1
answer
4k
views
Primitive polynomials in LFSRs
I need help proving the following theorem. I found it many books but on every single one it says that they omit the proof because it is in every good textbook.
THM
Let $c(x)$ be a connection (...
- 83
1
vote
1
answer
164
views
Discrete Logarithm Problem in $GF(p^m)$
I have question regarding DLP in $GF(p^m)$
I know the algorithms for solving the DLP in $GF(p)$ like Baby Step-Giant Step, Pohlig-Hellman etc...
But what if we move into the $GF(p^m)$ and are ...
- 131
6
votes
2
answers
1k
views
Understanding Intel's white paper algorithm for multiplication in $\text{GF}(2^n)$?
I'm reading this Intel white paper on carry-less multiplication. For now, suppose I want to do multiplication in $\text{GF}(2^4)$. We are using the "usual" bitstring representation of polynomials here....
- 261
2
votes
1
answer
13k
views
multiplication in GF(256) (AES algorithm)
I'm trying to understand the AES algorithm in order to implement this (on my own) in Java code.
In the algorithm all byte values will be presented as the concatenation of its individual bit values (0 ...
- 141