Recall Merkle Hash Tree discussed in the class. Let us consider a followingFind:

Transfer function $H_S(\frac{?}{\text{b}\text{a}\text{r}}())$ between $P(t)$ and the spring force $ku(t)$

Transfer function $H_D(\frac{?}{\text{b}\text{a}\text{r}}())$ between $P(t)$ and the damping force $c{u}^{}(t)$

Transfer function $H_M(\frac{?}{\text{b}\text{a}\text{r}}())$ between $P(t)$ and the spring force ${}^{}(t)$

Plot these functions over the range: $04$

These functions may give complex results, in such a case, plot the magnitude. $($SRSS of the

real and imaginary parts$)$ identity management system. A user has a set of data about herself, such as $($Tx$1)$ first name, $($Tx$2)$ last name, $($Tx$3)$ NRIC number, $($Tx$4)$ driver licence number, $($Tx$5)$ date of birth, $($Tx$6)$ mailing address, $($Tx$7)$ phone numbers, and $($Tx$8)$ primary bank account, which are stored as the leaf nodes of Merkle Hash Tree. Also assume that the root hash value is signed by a publicly$-$trusted entity, such as a government agency.

Assuming the signature is kept by the user, describe how the user can disclose ONLY selected personal information for preserving privacy while the receiver $($e$.$g$.,$ a service provider$)$ can be convinced with the authenticity of the disclosed data. Also provide example that only Tx$1,$ Tx$2,$ and Tx$8$ are disclosed to the service provider $($e$.$g$.,$ online payment$).$