All Questions
Tagged with cryptography linear-algebra
71
questions
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374
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Finding key for Hill Cipher
Suppose a Hill cipher with block size 2 is given, with known plaintext and corresponding encryption
$E_K( ‘guns’ ) = ‘YGJC’$
What are the possibilities for the key $K$?
My initial thought was to setup:...
4
votes
1
answer
109
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Solve System of Equations to find LFSR coefficients
Let the sequence $(s_n)_n$ be generated by an LFSR (linear feedback shift register) of order $k$. We know $s_0,\dots,s_{2k-1}$ and want to determine $a_0,\dots,a_{k-1}$. If the solution is not unique, ...
- 447
2
votes
1
answer
153
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Quick exponentiation of bit matrices
Is there a method for quickly rising to a power a matrix with only 0s and 1s? I am aware of the diagonalization method. However, it is general and requires a lot of work. Due to the constraint I ...
- 1,037
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1
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53
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how find a basis of free module (n-torsion points on ECs )
I am studying elliptic curves. From the very underlying group to groups of n-torsion points, free modules are all around.
For example you read Elliptic Curves: Number Theory and Cryptography (By ...
2
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45
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How to create a generating matrix and a set of code words?
The binary uniform linear code C is given by the generating matrix G:
0 0 1
1 0 0
0 1 0
0 0 1
1 1 1
a) Define the code parameters.
b) Highlight the information and verification categories.
c) Encode ...
- 21
2
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1
answer
147
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How can $S=\{g_1^{e_1}\cdots g_t^{e_t}\}$ induce an hypercube?
According to https://eprint.iacr.org/2022/1363.pdf at section 2.4, an hypercube can be induced by the equation 6:
Can someone explain to me how an hypercube can be induced? What are $g_1,\cdots, g_t$?...
- 103
1
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0
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32
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Invertible submatrices in matrices of a special form
Suppose you are given an ordered sequence consisting of $n$ pairs of length-$N$ bit vectors (i.e., each entry in each vector is $0$ or $1$), say
$$(b_{0,0},b_{0,1}),(b_{1,0},b_{1,1}),\ldots,(b_{n-1,0},...
- 11
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74
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$n=s^2-t^2$ how many values can $s$ take?
Let's say we have $n=pq$ with $p,q$ prime. We can write $n=s^2-t^2$ for some whole numbers $s,t$.
Now prove that if $q<p\leq (1+\epsilon)\sqrt{n}$ then $s$ has at most $\frac{\epsilon^2}{2}\sqrt{n}$...
- 1,604
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64
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Confusing operators in algebra for newbies
I am reading an article about group signatures - a concept in application cryptography.
There are 3 operators I'm not very clear on what they mean. Please explain to me or where can I search?
I'm ...
1
vote
1
answer
696
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Distributivity of XOR over boolean matrices multiplication-Decrypt AES
I'm currently reading Introduction to Cryptography with Coding Theory by Wade Trappe. On Page 159, it talked about how to decrypt AES. Although the book is about Cryptography, this question is ...
- 1,732
1
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0
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34
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Is the whole plain text of a message translated into a unique code?
Suppose that we have a cryptosystem, say $(P,C,K,E,D)$ where $P$ denotes the plain text, $C$ is the cipher text, $K$ is the key space, $E:K\times P\to C$ is the encryption function and $D:K\times C\to ...
- 429
1
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0
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66
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Coefficent alteration of the elliptic curve equation in Elliptic Curve Cryptography
Something caught my attention while reading about the mathematics behind Elliptic Curve Cryptography.
When setting up the elliptic curve equation for communicating between parties, why are only the $a$...
- 11
1
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0
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106
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If we re-define this function could it be bijective?
According to this paper in page $4$ where it describes the encryption scheme where a cipher function is defined as it follows
$$\rho:T\times Y \to X$$
such that $|Y|\geq |T|$, where $y\in Y$ is the ...
- 253
0
votes
2
answers
162
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What is the formula for determining how many errors a generator matrix can correct?
I am wondering whether or not there is a generic formula for determining how many errors a generator matrix is able to correct if also provided the field the code is in. For example, given the ...
- 313
1
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0
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137
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Using random invertible matrices over finite fields to define the hash of a list
This is a follow-up to a prior question Does matrix multiplication of hash digests admit manipulation of the result?; this formulation failed because it admitted singular matrices and therefore ...
- 111