Questions tagged [sis]

For questions involving/related to the Short Integer Solutions(SIS) problem.

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Parameters for high density SIS

I am considering the SIS problem of finding $x\in \mathbb{Z}^m$ such that for random $A\in\mathbb{Z}_q^{n\times m}$, $Ax=0$ and $\lVert x\rVert < \beta$ for some $p$-norm and bound $\beta < q$. ...
3
votes
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61 views

Size of $q$ in reductions from lattice problems to R-SIS

The Short integer solution problem is parameterized by four values: $n$, the dimension of the vectors that must be added $m$, the number of samples (dimension of the solution) $\beta$, upper-bound ...
3
votes
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319 views

Short integer solution lattice problem with q=2

For large values of $q$, we know that there are worst-case lattice problems which reduce to the average-case short integer solution (SIS) problem. Does this means that for $q=2$, the SIS problem is ...
2
votes
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69 views

Estimating the Security of SIS-Based Signature, by verifiying a subset of coordinates?

As I understood, the GPV signature scheme works as follows: KeyGen($1^n$) : Generate a Lattice with public $A \in Z_q^{n.m}$ and a secret trapdoor $t$. Sign $m$: compute $\vec y = H(m) \in Z_q^n$ ...
2
votes
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157 views

Hardness of $SIS$ and its reduction to an NP-complete problem

Short Integer Solution ($ SIS_\gamma^{(q,n,m,\beta)}$): Given a matrix $A\in Z_{q}^{n×m}$, find $x \in Z^m $, such that $Ax=0\mod q$ and $||x|| \le \beta$ Is $SIS\in NP$ ? If $SIS \in NP$, then it ...
1
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22 views

polynomial time reduction from SIS to decisional-LWE?

Is the claim "If there is an efficient algorithm that solves SIS, then there is an efficient algorithm that solves decisional LWE" is sufficient? or, Is the claim above is equivalent to the ...
1
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68 views

How does the polynomial module impact the security of ring/lattices-based SIS problem?

Consider the following SIS problem: for a function $f_A(s)$=$As$, where $A$ is a fixed, randomly-chosen matrix in $(R_q)^{r \times n}$=$\left(\mathbb{Z}_q[X]/(X^N+1)\right)^{r \times n}$ and $q$ a ...