(Solved): (20 points) Consider the following hash function. Messages are in the form of a sequence of decimal ...

(20 points) Consider the following hash function. Messages are in the form of a sequence of decimal numbers, $M=\left(a_1,a_2,\dots ,a_t\right)$. The hash value $h$ is calculated as $h=\left({?}_{i=1}^t{\left(a_i\right)}^2\right)\mathrm{mod}n,$ for some predefined value $n$. a. Does this hash function satisfy any of the requirements for a hash function listed in Section 3.2 of the textbook (or on Slide 11 of Lect03a)? Explain your answer. H can be applied to a block of data of any size. H produces a fixed-length output. - $\mathrm{H}(\mathrm{x})$ is relatively easy to compute for any given $\mathrm{x}$, making both hardware and software implementations practical. - For any given code $\mathrm{h}$, it is computationally infeasible to find $\mathrm{x}$ such that $\mathrm{H}(\mathrm{x})=\mathrm{h}$. A hash function with this property is referred to as one-way or preimage resistant. - For any given block $\mathrm{x}$, it is computationally infeasible to find $\mathrm{y}x$ with $\mathrm{H}(\mathrm{y})=\mathrm{H}(\mathrm{x})$. A hash function with this property is referred to as second preimage resistant. This is sometimes referred to as weak collision resistant. - It is computationally infeasible to find any pair $(\mathrm{x},\mathrm{y})$ such that $\mathrm{H}(\mathrm{x})=$ $\mathrm{H}(\mathrm{y})$. - A hash function with this property is referred to as collision resistant. This is sometimes referred to as strong collision resistant.