# Questions tagged [sis]

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

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### 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 ...
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### 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 ...
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### 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}_{...
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### 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, ...
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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 $\beta < q$. ...
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### 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 ...
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### 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 ...
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### Is there any reduction from Short Integer Solution to $\textrm{SIVP}_\gamma$

Short Integer Solution (SIS) is proved to be hard by reducing $\textrm{SIVP}_\gamma$ to SIS, i.e., if we solve SIS, then we can solve $\textrm{SIVP}_\gamma$. Is there any way to reduce an instance of ...
The semantic security of Regev's cryptosystem [Reg05] is based on the LWE assumption and leftover hash lemma. This lemma implies that because $m \approx (n+1)\log q$ is large enough, so for uniform $A\... 1answer 795 views ### How to estimate the hardness of SIS instances? The Short Integer Solution (SIS) problem is to find, given a matrix$A \in \mathbb{F}_q^{n \times m}$with uniformly random coefficients, a vector$\mathbf{x} \in \mathbb{Z}^m \backslash \{\mathbf{0}\}...
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 ...