SIT281:Cryptography

Assign # 2

1. Find the square roots of

57

mod

107

.

2. (a).Consider

Z

5

[

x

]

modx

8

+

x

4

+

x

3

+

x

+ 1

. Show that

h

(

x

) = 3

x

5

+

2

x

3

+

x

2

+ 4

x

+ 4

is reducible.

Hint: consider

q

(

x

) = 4

x

3

+ 3

x

2

+ 4

and do a division.

(b). Find the multiplicative inverse of

1 + 2

x

in

Z

3

[

x

] mod

x

2

+ 1

3.(a) Let the input message be 100010110101 and the key be 111000111.

Perform two complete rounds of encryption using the simplied DES type

algorithm.

(b). Starting with the results from 3(a), decrypt the ciphertext

by using the algorithm in reverse.

4. The ciphertext is 182 and was obtained from the RSA algorithm using

n

= 437

and

e

= 283

. Find the plaintext. {Hint: you can use trial and

error (small integers) to determine

d

or use the Extended Euclidean

Algorithm}

5. Determine

L

3

(6)

mod

31

, using the Baby Step-Giant Stepmethod.