Modify the above protocol so that we can detect any foul play from the malicious database holder. $($Hint: Along

with the shares of a standard basis vector the client sends the shares of a standard$-$basis vector scaled with a random

$\backslash$alpha $.).$ Prove the correctness.The answer to the question is:$-1.$Key Idea :$-$The key idea here is that :$-$Along with the shares of a

standard basis vector the client sends the shares of a standard$-$basis

vector scaled with a random variable say $\backslash$alpha $.$

$2.$Setup :$-$Again the server generates two random strings r$0$ and r$1$

such that r$0$ r$1=$ e

$$

i

$[$standard basis vector$]$ and $\backslash$alpha $.($r$0$ r$1)=\backslash$alpha $.$

$($e

$$

i

$)$

$3.$Client$-$Sever Interation : $-$The client send $$r$0,\backslash$alpha $.($r$0)$ to S$0$ and

$$r$1,\backslash$alpha $.($r$1)$ to S$1.$

$4.$ Server$-$Client Interaction : $-$ The server responds with $($r$0,$

$$b$$

and $\backslash$alpha $$ r$0,$

$$b$)$ to S$0,$ and $($r$1,$

$$b$$ and $\backslash$alpha $$ r$1,$

$$b$)$ to server S$1.$

$5.$ Client Verification :$-$ The server checks if

$\backslash$alpha $.($r$0,$

$$b$$r$1,$

$$b$)=$r$0,$

$$b$$r$1,$

$$b$$ then returns true and holds the

queried index of database as $$r$0,$

$$b$$r$1,$

$$b$$

Otherwise returns false means that one of the Servers is malicious.Can you do prove of correctness