Questions tagged [sis]

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

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7
votes
1answer
586 views

Relation between decisional SIS and leftover hash lemma in lattices

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\...
4
votes
1answer
850 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}\}...
5
votes
1answer
431 views

Hardness of Short Interger Solution in Lattices

Short Integer Solution ($SIS_{n,m,q,\beta}$) is defined as: Given a matrix $A \in \mathbb{Z}_{q}^{n \times m}$, find a non-zero vector $x \in \mathbb{Z}^{m}$ such that $A \cdot x = 0\mod q$ and $||x|| ...