# 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 $\beta < q$. ...
1 vote
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### non-prime modulus for Ring-SIS

Consider the Ring-SIS problem for $R_q=\mathbb{Z}_q[x]/(x^n+1)$ when $n$ is power of $2$ and $q=1 \mod 2n$. Does the modulus $q$ need to be prime? if yes, it seems that it is mainly because of the way ...
1 vote
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### 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 vote
96 views

### Frobenius inner product polynomial rings

I'm trying to implement the zero-knowledge proof presented in this paper. The proof has a rejection step (page 14), which can be computed as follows: Where B and Z are in $R^{m \times n}$ for some ...
201 views

### SIS vs LWE Problem

The Ajtai one way function is defined by $$f_A(x)= Ax \; mod\; q$$ where the x $\in \{0,1\}^m$ and A $\in \mathbb{Z_q}^{n \times m}$. $f_A(x)$ is one way function ( Ajtai 96) While the Regev One way ...
150 views

### SIS without the modulus

Consider the following modification to the Short Integer Solution (SIS) problem: Let $n$ be an integer and $\alpha=\alpha(n),\beta=\beta(n),m=m(n)>\Omega(n\log \alpha)$ be functions of $n$. Sample ...
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### Reduction of decison SIS

In Lyu12, Lemma 3.6 is as follows. Lemma 3.6 For any non-negative integer $\alpha$ such that $gcd(2\alpha+1, q)=1$, there is a polynomial time reduction from the $SIS_{q, n, m, d}$ decsion ...
82 views

### average-case SIS and average-case BDD

In lattice based cryptography, we say the average-case SIS (short integer solution) problem because it is such kind problem " $A \stackrel{\$}{\leftarrow} \mathbb{Z}^{n\times m}_{...
216 views

### Is LPN not as important as LWE and SVP?

I've been learning about lattice cryptography and have noticed that most resources such as this survey by Chris Peikart, the Winter School on Lattice Cryptography etc don't include material on LPN, ...
318 views

### ZK Proof for SIS

Let $A x = 0 \bmod q$ with $\Vert x \Vert < \beta$ as part of 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 ...
### 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 ...