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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 :

732.u+512.v = pgcd(732,512) ?

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 :

1536.u+1352.v = pgcd(1536,1352) ?

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 :

1272.u+1020.v = pgcd(1272,1020) ?

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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Albert and Bernard  choose the Elgamal cryptosystem to communicate. They have the following information:

Public domain:

Albert:

    public key:

    private key:

Bernard:

    public key:

    private key: ??

Albert receives from Bernard the message: (20,23)

What is the plaintext ?

Your answer will be an integer.

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Let , calculate its order in the group.

The answer is an integer number.
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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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Give the list of all elements that have an inverse in

the answer is a list of values separates with commas, with no spaces

example : the list of invertible elements in is 1,3,7,9
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In calculate the inverse of .

The answer is an integer number between 0 et 28

If has no inverse, the expected answer is : "no inverse"
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what is the value of : ?
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