We look at a hash function that computes an $8-$bit hash value by applying the following equation:

$C_i=b_{i1}o+b_{i2}o+b_{i3}o+b_{i4}o+b_{i5}o+b_{i6}o+b_{i7}o+b_{i8}$

where

$C_i=i$ th bit of the hash code, $1i8$

$m=$ number of $8-$bit blocks in the input

$b_{ij}=i$ th bit in the $j$ th block.

Every block of $8$ bits is the binary string corresponding to the letter$/$ASCII code appearing in the message.

a$.$ Encode the string CRYPTO to its binary representation.

b$.$ Calculate the hash value of the character string using the above defined equation.

c$.$ "Break" the hash function by pointing out how it is possible to find $($meaningful$)$ character strings which result in the same hash value. Provide an appropriate example.

d$.$ Which crucial property of hash functions is missing in this case?

$($The next page contains the correspondence between letters and ASCII codes$)$

$\backslash$table$[[$A$,065,01000001],[$B$,066,01000010],[c,067,01000011],[D,068,01000100],[E,069,01000101],[F,070,01000110],[G,071,01000111],[H,072,01001000],[$I$,073,01001001],[J,074,01001010],[,075,01001011],[L,076,01001100],[M,077,01001101],[N,078,01001110],[0,079,01001111],[P,080,01010000],[Q,081,01010001],[R,082,01010010],[s,083,01010011],[T,084,01010100],[u,085,01010101],[v,086,01010110],[w,087,01010111],[x,088,01011000],[r,089,01011001],[z,090,0101101]]$