Slide $76\mathrm{.}1$

n$\text{'}$ bits n$\text{'}>=$n

fixed value n bits

X$2$

$$

h$\backslash$deg

Z$1$

$..$

hs

ZB$-1,$

$$H$\backslash$deg $($X$)$

n bits

FIGURE $6\mathrm{.}1$: The Merkle Damg$$rd transform.

fix$/<=$ n$\text{'}$

$1$x$|=$L$<=2\text{'}$

$.....$ last byte of x $1000.\mathrm{.}00|$x$|$

I bits

Question $1.$ n context of the Merkle$-$Damgard Transform $($module $6\mathrm{.}1,$ slide $7)$ let n$=512$ bits, l$=64$ bits and n$=1024$ bits.

What is the size $($in bits$)$ of the largest file that can be hashed using this scheme? Explain.

Question $2.$ With the same parameters as in question $1,$ what is the size of the hash for a file whose size is $232$ bits? Explain.

Question $3.$ How many applications of hs will be required to compute the hash for a file of size $2176$ bits? Explain.

Question $4$ Consider the password hashing schemes of module $6\mathrm{.}3,$ slides $5$ and $6.$ Slide $5$ is without a salt, slide $6$ is with a salt. Suppose there is a standard hash function h used at multiple sites. Consider a user who uses the same email id $($say alice@exa.edu$)$ as their id at $2$ different sites, as well as reuses the same password at both sites. Discuss what will happen in the stored hashed password for that user at these two sites $($say A and B$).$

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