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9 questions
2
votes
0
answers
184
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Will Coppersmith's method work for this bivariate modular polynomial shape?
I have a bivariate modular polynomial of shape
$$f(x,y)=x^2y-g(x)\equiv 0\bmod q$$
where
$q=(2p-1)(2p+1)$ is a product of two primes $2p-1$ and $2p+1$,
$g(x)\in\mathbb Z[x]$ is of degree four and
$f(...
- 13.9k
2
votes
0
answers
87
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Complexity of finding solutions of trapdoored polynomial?
Related to this question Cryptography signature scheme based on hardness of finding points on varieties.
Working over $K=\mathbb{Q}[x_1,...,x_n,y_1,...y_m]$.
By abuse of notation, for polynomial $f$, ...
- 25.4k
1
vote
0
answers
98
views
Hardness of solving $0=\sum_{i=1}^k \operatorname{linear}_i(x_1,\ldots,x_n)^D$ over the rationals
This is related to cryptography and this question
and another question.
In short, we are asking about decomposing multivariate polynomial
as sum of perfect powers of linear polynomials.
Working over $\...
2
votes
0
answers
96
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Cryptography signature scheme based on hardness of finding points on varieties?
Related to this question Complexity of finding solutions of trapdoored polynomial.
I am trying to build signature scheme based on hardness
of finding points on varieties.
Let $K$ be field and $M=K[x_1,...
- 25.4k
6
votes
1
answer
566
views
Public key cryptography based on non-invertible matrices?
Added Wed 13 Apr 2022
I have written a short note with experimental data,
which shows not all pseudo keys are good keys.
Public key cryptography based on non-invertible matrices
We got public key ...
- 25.4k
-1
votes
1
answer
186
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Public key cryptography based on non-invertible matrices, part II
Closely related to this question
and extending comment
of R. van Dobben de Bruyn.
Working over $\mathbb{F}_p$ and all matrices of square $n \times n$.
Alice chooses invertible $X_A$ and non-...
- 12.9k
3
votes
1
answer
164
views
Mestre-type algorithm for higher-genus curves?
Is there an analogous algorithm for genus $g>2$ curves that, given a complete set of invariants, outputs a curve with those invariants?
(I'm interested in particular in $g=3$.)
Any references ...
CommunityBot
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2
votes
1
answer
162
views
DL-problem on abelian variety
Let $A$ be an abelian variety over $\mathbb{F_q}$ with dimension $n$. Let $q$ be a constant.
Is there polynomial algorithm of finding discrete logarithm in $A$?
UPD: really I don't undestend: can we ...
- 30.5k
0
votes
1
answer
748
views
Pairing on elliptic curve
Let $E(\mathbb{F_q})$ - elliptic curve.
$G_1 = E(\mathbb{F_q})[r]$. $|G_1| = r$.
$k$ is minimal such $r | q^k - 1$.
$\pi_q$ - $q$-power Frobenius endomorphism.
$G_2 = E(\mathbb{F_{q^k}})[r] \cap ...
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