$2.)$ Biometric $($Iris$)-$based Authentication $[16$ Points$]$

Suppose that a particular iris scan system generates $64-$bit iris codes. During the enrollment phase, the following iris codes $($in hex$)$ are determined.

$\backslash$table$[[$User$,$Iris code$],[$Alice$,$BE$439$AD$598$EF$5147],[$Bob$,9$C$8$B$7$A$1425369584],[$Charlie$,885522336699$CCBB$]]$

Note: some popular hex$-$codes are:

A: $1010$; B: $1011$; C:$1100$; D: $1101$; E: $1110$

During the recognition phase, the following iris codes are obtained.

$\backslash$table$[[$User$,$Iris code$],[$U$,$C$975$A$2132$E$89$CEAF$],[$V$,$DB$9$A$8675342$FEC$15],[$W$,$A$6039$AD$5$F$8$CFD$965],[$X$,1$DCA$7$A$54273497$CC$],[$Y$,$AF$8$B$6$C$7$D$5$E$3$F$0$F$9$A$]]$

Use the iris codes above to answer the following questions.

a$.[6$ Points$]$ Use the formula

$d(x,y)=\frac{\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{n}\text{o}\text{n}-\text{m}\text{a}\text{t}\text{c}\text{h}\text{b}\text{i}\text{t}\text{s}}{\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{b}\text{i}\text{t}\text{s}\text{c}\text{o}\text{m}\text{p}\text{a}\text{r}\text{e}\text{d}}$

to compute the following distances:

Alice, Bob$),$ d$($Alice$,$ Charlie$),$ d$($Bob$,$ Charlie$).$

Solution

The iris codes are in hexadecimal format,

Alice: BE$459$ADSYOETJT$4$T

b$.)$ b$.[10$ Points$]$ Based on the distance as defined above, which of the users, $U,V,W,x,Y,$ is most likely Alice? Bob? Charlie? None of the above?