All Questions
Tagged with cryptography linear-algebra
9 questions
6
votes
0
answers
130
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Bent vectors and $\pm 1$ eigenvectors with respect to non-Sylvester Hadamard matrices
A Hadamard matrix is an $n\times n$-matrix $H$ where each entry in $H$ is $\pm 1$ and where $H/\sqrt{n}$ is orthogonal. It is well-known that if $H$ is an $n\times n$-Hadamard matrix, then $n<3$ or ...
2
votes
0
answers
78
views
Partitions of bent vectors
Let $H=\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\ 1 & -1\end{bmatrix}.$ Let $A^{\otimes N}$ denote the tensor product of the matrix $A$ with itself taken $N$ times. We say that a vector $v$ of ...
3
votes
0
answers
67
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Efficiently finding solutions to the Rainbow cryptosystem using quotient spaces
Repost of a mathematics stackexchange question here as this concerns my research and it went unanswered on there.
In this paper, Ward Beullens gives another way to look at the Rainbow cryptosystem. In ...
- 173
10
votes
1
answer
1k
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Cryptographic Secret Santa
Is there a protocol for conducting a Secret Santa without a central authority? Precisely, we want to sample uniformly a permutation that has no one-cycles and reveal to each member his or her ...
- 101
1
vote
1
answer
92
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Dual lattices up to a q scaling factor
In this paper : https://eprint.iacr.org/2011/501.pdf
There is an equality page 10, in the second paragraph considered by the authors as "easy to check". If someone could explain to me why the set at ...
- 215
1
vote
1
answer
133
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Reduced echelon form of sparce matrices and constructing hash function
Let $G$ be a $d$-regular graph, and $A$ be the incidence matrix of $G$. Also suppose $B$ is a reduced echelon form of $A$ such that computations are in $\mathbb F_2$. Given matrix $B$, can we find ...
0
votes
0
answers
262
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Lattice basis reductions and finding minimal values
While reading several articles about lattice basis reduction I am left with a few questions.
For one, I came across this piece of text
Let $\alpha$ and $\beta \in \mathbb{R}$. Also let $X>0$ and $...
- 1
6
votes
1
answer
453
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Computing the correlation between two vectors without divulging them
Alice and Bob respectively know a vector of $N$ real numbers $u$ and $v$. They would both like to know $\rho = \langle u,v \rangle/N$ but Alice does not want Bob to gain anymore information about $u$ ...
- 1,902
1
vote
1
answer
737
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Matrix Conjugates over Finite Fields
Thinking about Diffe-Hillman for matrices brought me to the following question.
Given $\mathbb{F}_{p^k}$ the finite field with $p^k$ elements when can we find non-trivial solutions to
$\begin{...
- 4,842