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April 27th, 2016, 06:29 AM   #1
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Cryptography- some easy exe.

1/ Prove the correctness of the following statements, where a ∈ Z and m ∈ N:

1. If gcd(a, m) = 1 then a · i 6 /≡ a · j mod m for 0 ≤ i < j < m.
2. If gcd(a, m) = 1 then there is an x ∈ Zm with a · x ≡ 1 mod m.
3. If gcd(a, m) > 1 then there is no x ∈ Zm with a · x ≡ 1 mod m.

2/ For positive integers x and y, how can x y be calculated with as few multiplications as possible? How many multiplications does your algorithm use in the worst case?

3/ Choose a valid key k for a 2 × 2-Hill cipher over Z8, where k is not the identity matrix. Encrypt the word w = 012346 block by block using k and decrypt the resulting ciphertext to obtain w again.

4/ We consider a 3 × 3-Hill cipher over Z6. Let's assume that an attacker knows the encryption matrix k except for entries x and y:

matrix :
| 4 2 y |
| 3 x 2 |
| 1 1 3 |

What are possible values for x and y?

Last edited by skipjack; April 27th, 2016 at 08:06 AM.
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April 27th, 2016, 06:31 AM   #2
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It will be nice if we juxtapose our answers I will publish at Sunday so you can see it too.

Last edited by skipjack; April 27th, 2016 at 08:07 AM.
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April 29th, 2016, 12:08 PM   #3
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Help me I have problems
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