All Questions
Tagged with cryptography polynomials
8 questions with no upvoted or accepted answers
7
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0
answers
199
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Polynomial representation of modular arithmetic in finite fields
Let $n \in \mathbb{N}$ be a predefined integer. Consider the following bijection (between the ring of integers modulo $2^n$ and finite field with $2^n$ elements:
$$ \phi: \mathbb{Z}_{2^n} \to \mathbb{...
- 81
4
votes
0
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264
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Polynomial dynamical systems
The question is somewhat related to the theory of permutation polynomials. Let $\mathbb{F}_p$ be a finite field of $p$ elements ($p$ is prime) and $\mathcal{V} = \mathbb{F}_p^2 = \{ (t_1,t_2)\::\: t_1,...
- 411
3
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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
3
votes
0
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151
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determine degree of boolean polynomial given as black box
I searched a lot but couldn't find a good resource that addresses this question. Given a boolean polynomial with $n$ boolean variables as a black box, what is the most efficient way to compute its ...
- 103
2
votes
0
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38
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Criterion for unicity and existence of pre-image in multivariate cryptography
Repost from math.stackexchange since no one could help me there and it concerns my research.
I am reading Ding's Multivariate Public Key Cryptosystems and in the book the author explains the so-called ...
- 173
2
votes
0
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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
2
votes
0
answers
121
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How to choose a prime p s.t. n-th cyclotomic polynomial splits into as much as possible irreducible polynomials while p is almost constant size?
The reason I ask this question is that cyclotomic polynomial is critical to the construction of lattice-based cryptography. In most of the existing lattice-based cryptographic schemes, $n$ is usually ...
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1
vote
0
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276
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Method of Coppersmith optimal for multivariate?
It is shown that Coppersmith method yields optimal integer root extraction for univariate polynomials in https://arxiv.org/abs/1605.08065 and a follow up work attempts this for bivariate polynomials ...
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