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6 changes: 2 additions & 4 deletions lattices/cryptographic-lattice-problems/short-integer-solutions-sis.md
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Expand Up @@ -29,9 +29,9 @@ Solution existence is based on parameters set. One should think about them as fo
* $$m$$ is set depending from application to application. Usually $$m \gg n$$
* $$q = \text{poly}(n)$$, think of it as $$q = \mathcal{O}(n^2)$$
* $$\beta = $$the bound is set depending on application and $$\beta \ll q$$
* $$\delta_1(L)$$ is the length of the shortest nonzero lattice vector. It is called the _minimum distance of the lattice $$L$$_.

### SIS as a SVP problem

// TODO

## Ajtai's hashing function
Expand All @@ -51,9 +51,7 @@ We know $$x \in \{0, 1\}^m \Rightarrow |\mathcal{X}| = 2^n$$ and $$Ax \in \mathc

**Collision resistance:**

{% hint style="danger" %}
halp here
{% endhint %}
We can prove collision resistance by contradiction. Assume an attacker can find a collision such that $$x\neq x' \in \{0,1\}^m:f_A(x)=f_A(x'),$$ $$z:=x-x'$$ is a solution for the corresponding SIS problem.

**Sage example**:

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