Question#$1$: $[1$ Mark$]$

Suppose that we have a computer that can test $240$ or $(2^40)?$Question# $1$: $[1$ Mark$]$

Suppose that we have a computer that can test $240$ keys each second.

a$.$ What is the expected time $($in years$)$ to find a key by exhaustive search

if the key size is $64$ bits?

b$.$ What is the expected time $($in years$)$ to find a key by exhaustive search

if the key size is $128$ bits?

Question# $2$: $[2$ Marks$]$

Decrypt the ciphertext

"TDEUNOTFTHAKITNFGAHDEOMCPTUEREIMAAPORUDSNINGEREINGUIVNES

RITYDPAERMTENT"

This message was encrypted with a double transposition $($of the type discussed

in the text$)$ using a matrix of $7$ rows and $10$ columns. $($Hint: The first $2$ words

are "I am$")$

Question#$3$: $[2$ Marks$]$

Suppose that Alice's RSA public key is $(N,e)=(33,7)$

a$.$ Find her private key, $d.$

b$.$ If Bob encrypts the message $M=17$ using Alice's public key, what is the

ciphertext C$?$ Show that Alice can decrypt C to obtain M$.$

c$.$ Let $S_{?}$ be the result when Alice digitally signs the message $M=19.$ What

is $S?$ If Bob receives $M$ and $S,$ explain the process Bob will use to verify

the signature and show that in this particular case, the signature

verification succeeds.

Question#$4$: $[1$ Mark$]$

On a particular system, all passwords are $8$ characters, there are $128$ choices

for each character, and there is a password file containing the hashes of $212$

passwords. Trudy has a dictionary of $224$ passwords, and the probability that

a randomly selected password is in her dictionary is $\frac{1}{4}.$ Work is measured in

terms of the number of hashes computed.

a$.$ Suppose that Trudy wants to recover Alice's password. Using her

dictionary, what is the expected work for Trudy to c keys each second.

a$.$ What is the expected time $($in years$)$ to find a key by exhaustive search if the key size is $64$ bits?

b$.$ What is the expected time $($in years$)$ to find a key by exhaustive search if the key size is $128$ bits?

Question#$2$: $[2$ Marks$]$

Decrypt the ciphertext

$$TDEUNOTFTHAKITNFGAHDEOMCPTUEREIMAAPORUDSNINGEREINGUIVNESRITYDPAERMTENT$$

This message was encrypted with a double transposition $($of the type discussed in the text$)$ using a matrix of $7$ rows and $10$ columns. $($Hint: The first $2$ words are $$I am$)$

Question#$3$: $[2$ Marks$]$

Suppose that Alice$$s RSA public key is $($N$,$ e$)=(33,7)$

a$.$ Find her private key, d$.$

b$.$ If Bob encrypts the message M $=17$ using Alice$$s public key, what is the ciphertext C$?$ Show that Alice can decrypt C to obtain M$.$

c$.$ Let S be the result when Alice digitally signs the message M $=19.$ What is S$?$ If Bob receives M and S$,$ explain the process Bob will use to verify the signature and show that in this particular case, the signature verification succeeds.

Question#$4$: $[1$ Mark$]$

On a particular system, all passwords are $8$ characters, there are $128$ choices for each character, and there is a password file containing the hashes of $212$ passwords. Trudy has a dictionary of $224$ passwords, and the probability that a randomly selected password is in her dictionary is $1/4.$ Work is measured in terms of the number of hashes computed.

a$.$ Suppose that Trudy wants to recover Alice$$s password. Using her dictionary, what is the expected work for Trudy to crack Alice$$s password, assuming the passwords are not salted?

b$.$ Repeat part a$,$ assuming the passwords are salted.

c$.$ What is the probability that at least one of the passwords in the password file appears in Trudy$$s dictionary?

Question#$5$: $[2$ Marks$]$

Suppose all passwords on a given system are $8$ characters and that each character can be any one of $128$ different values. The passwords are hashed $($with a salt$)$ and stored in a password file. Now suppose Trudy has a password cracking program that can test $128$ passwords per second. Trudy also has a dictionary of $224$ common passwords and the probability that any given password is in her dictionary is $1/4.$ The password file on this system contains $512$ password hashes.

a$.$ How many different passwords are possible?

b$.$ How long, on average, will it take Trudy to crack the administrator$$s password?

c$.$ What is the probability that at least one of the $512$ passwords in the password file is in the dictionary?

d$.$ What is the expected work for Trudy to recover any one of the passwords in the password file?

Question#$6$: $[2$ Marks$]$

Suppose that when a fingerprint is compared with one other $($nonmatching$)$ fingerprint, the chance of a false match is $1$ in $1010,$ which is approximately the error rate when $16$ points are required to determine a match as in the British legal standard. Suppose that the FBI fingerprint database contains $108$ fingerprints.

a$.$ How many false matches will occur when $1,000,000$ suspect fingerprints are each compared with the entire database?

b$.$ For any individual suspect, what is the chance of a false match?