My Math Forum Cryptography- some easy exe.

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 April 27th, 2016, 06:29 AM #1 Newbie   Joined: Apr 2016 From: Bulgaria Posts: 13 Thanks: 0 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.
 April 27th, 2016, 06:31 AM #2 Newbie   Joined: Apr 2016 From: Bulgaria Posts: 13 Thanks: 0 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.
 April 29th, 2016, 12:08 PM #3 Newbie   Joined: Apr 2016 From: Bulgaria Posts: 13 Thanks: 0 Help me I have problems

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