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* SM503M-2526PSA01 - Mathematics for Cryptography (INGE-1-INT, INGE-1-BN, INGE-1)

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what is the value of : ?
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What is the (u,v) couple computed by the Extended Euclid algorithm such that :

978.u+726.v = pgcd(978,726) ?

The answer should be a (u,v) couple of integer numbers. For example, if you have found that u = 31 and v = -12, the expected answer is (31,-12)
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What is the (u,v) couple computed by the Extended Euclid algorithm such that :

3432.u+1740.v = pgcd(3432,1740) ?

The answer should be a (u,v) couple of integer numbers. For example, if you have found that u = 31 and v = -12, the expected answer is (31,-12)
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durée estimée : 15 Minutes

The alphabet contains characters, we use an affine Vigenere's transformation system based on 2x2 matrices .

Here are two ciphering keys :

1) Among those two keys, only one is correct. Which of the two keys is correct ?

2) Calculate the deciphering key corresponding to the correct key.

3) Decipher the following bigram : .

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durée estimée : 15 Minutes

The alphabet contains characters, we use an affine Vigenere's transformation system based on 2x2 matrices .

Here are two ciphering keys :

1) Among those two keys, only one is correct. Which of the two keys is correct ?

2) Calculate the deciphering key corresponding to the correct key.

3) Decipher the following bigram : .

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What is the (u,v) couple computed by the Extended Euclid algorithm such that :

3107.u+2145.v = pgcd(3107,2145) ?

The answer should be a (u,v) couple of integer numbers. For example, if you have found that u = 31 and v = -12, the expected answer is (31,-12)
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To communicate between them, Anaïs and Bastien use an alphabet of only ten letters: 

a = 0, b = 1, c = 2, d = 3, e = 4, f = 5, g = 6, h = 7, i = 8, j = 9.

To encipher their messages, they decide to use the generalised Vigenère cipher on bigrams.

Bastien receives from Anaïs the ciphertext CHFE

Decipher the message knowing that the enciphering key is

A : 

 4  1 

 5  2 

B : 

 4 

 4 

Your answer will be a four letters word written in capital letters with no spaces.

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The affine ciphering system is used with the previously defined alphabet.

So, the used set is

The ciphering key is :

You have received the ciphered message : " uhavni ".

Decipher this message, you should find an english word composed of 6 characters
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Again with the same data:

  • B wishes to send the message 12345 to A. What is the ciphertext?

  • Moreover, A receives the ciphertext 12345 from C. What is the corresponding plaintext?

Your answer will be a couple of integers (x,y).

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C receives the ciphered signature  2632215 but does not know who sent it (A, B or none).

To check if it comes from , needs to compute , then and finally compare with the expected result .

What are the values of ,,, and (in that order)?

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