# Tagged Questions

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### ZK Proof for SIS

Let $A x = 0 \bmod q$ with $\Vert x \Vert < \beta$ be a lattice SIS problem. Does there exist an efficient zero knowledge proof of knowledge for such a solution? My idea is to use it for an ...
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### Gaussian distribution in lattices

In many lattice based cryptosystems, Gaussian distribution is used. Can you explain why only Gaussian distribution is preferred?
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### Decomposing an ideal in intersections

Let $R$ be an ring, and let $(a),(b)$ be the ideals generated by $a,b\in R^\times$ respectively. Let $c=a\cdot b$ and $(c)$ the ideal generated by $c$. I am supposing that, given $c$, it is ...
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### Distinguish two ciphers in Ring-LWE?

I am fairly new to this topic. so my question is: if I have $A=e_0a+e_1$ and $B=e_2a+e_3$ where $a$ is the agreed public parameter, $e_i \leftarrow \chi$ (drawn from the error distribution). if the ...
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### Quantum complexity of LWE

As per my understanding LWE is quantum secure because there is no known quantum algorithm to solve LWE in polynomial time. Due to the reductions given by Regev et al. If there is any algorithm that ...
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### Given a 'good' basis for a lattice, how can we solve the CVP?

I'm doing a little bit of reading about lattices. I read that if we can find a 'short' basis for our given lattice, we can solve CVP and SVP very efficiently. However, the paper didn't describe an ...
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### Would LWE problem be still secure if error were like this $e=2e_1$?

In the Learning with error problem, if the error term $e$ from equation $b=<a,s>/q+e$ were of this kind $e=2e_1$, where $e_1$ is chosen according to the probability distribution for the LWE ...
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### Why SIVP Is Worst Case Problem?

I just started to study lattice cryptography. I'm now studying worst-case to average-case reduction for SIS. In previous question, "worst means any and average means random". And I wonder why ...
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### In NTRU, if $N$ is not prime, prove that one can recover the private key by solving a lattice problem in dimension lower than $2N$

In the NTRU cryptosystem, it is suggested to take $N$ prime. I want to understand why. In Jeffrey Hoffstein, Jill Pipher and H. Silverman An Introduction to Mathematical Cryptography, they suggest (...
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### Construct new SIS solutions from given ones

Assume we have a lattice SIS problem $A x = 0$, with $\Vert x \Vert < \beta$ and we are given $k$ solutions $x_1, \dots, x_k$ by, say an oracle. Is it then hard or easy to construct from there a ...
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### Lattice attacks against Multilinear Maps [CLT13]

I am currently studying an article on a construction of Multilinear maps. There are some attacks on the scheme presented by the authors and I got stuck at the one in section 5.1. I will try to ...
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### Worst case to average case in Ring LWE

I am currently trying to understand this Ring LWE article and I have a question. I don't understand how to apply Lemma 5.11 in order to get the worst case to average case reduction in Lemma 5.12, as ...
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### The Inhomogeneous Short Integer Solution (ISIS) problem with a clue

The Inhomogeneous Short Integer Solution (ISIS) problem is as follows: given an integer $q$, a matrix $A \in \mathbb Z^{n\times m}_q$, a vector $b\in \mathbb Z^n_q$, and a real $\beta$, find an ...
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### ISIS as a one-way function

The usual formulation of the ISIS problem is the following: Given uniform $A$ and $u$, find a short $e$ such that $Ae = u \bmod q$. A different definition (call it ISIS-OWF) is to let \$f_A(e) = Ae \...
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### Choise enother scheme to basises of lattice cryptosystem

In the lattice cryptosystem to find a good or bad basis we apply "hadamard Ratio". But in high dimension computing of this ratio is hard. dose any other scheme exist to solve this problem?