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|| \le \beta $.
In the paper Trapdoors for hard lattices and new Cryptographic Constructions, SIS is proved to be hard by reducing standard worst-case lattice problem approx. SIVP to SIS i.e., if we solve a random instance of SIS, then any instance of approx. SIVP is solved.
In the paper On the complexity of computing short Linearly Independent Vectors and Short Bases in a lattice, approx. SIVP is proved to be NP-COMPLETE.
By this, can we say Short Integer Solution (SIS) problem in lattices is NP-Complete?