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

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

964.u+668.v = pgcd(964,668) ?

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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How many divisors does the number 121500 have?

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In calculate the inverse of .

The answer is an integer number between 0 et 32

If has no inverse, the expected answer is : "no inverse"
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In , solve the equation .

the answer is an integer numberbetween 0 et 29
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In , solve the equation .

This equation has either no or several solutions.

If this equation has no solution, the answser is 'no solution'.

If this equation has several solutions, the answer is a list of integer numbers, separated with commas and no spaces. For example, the solution set for in is 4,11,18
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What is the (u,v) couple computed by the Extended Euclid algorithm such that :

252.u+172.v = pgcd(252,172) ?

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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Consider the set equipped with the commutative and associative binary operation described in the table below:

If is a not group, your answer will be "no".

If is a group, find the order of the element (in this case your answer will be a number).

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Anna and Benoît exchange messages using the following coding table.

Moreover, they use as message unit the tetratagrams (blocks of four letters) that they encode as a number in the following

way:

For example, the word "TEST" becomes the number .

They use the Elgamal cryptosystem with public domain .

Anna's public and private keys are .

Benoît's public and private keys are .

Anna receives the message from Benoît. To which four-letter word this message correponds to ?

Your answer will be a four-letter word in capital letters.

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EXERCISE - estimated duration : 10 minutes

Andrew and Bill use the Elgamal cryptosystem, with the following data :

public domain :

Andrew :

    public key :

    private key :

Bill :

    public key :

    private key : ??

Andrew wants to send the message to Bill

He chooses

What is the couple of values Andrew should send to Bill ?

Your answer will be a couple of numbers, with parenthesis, and separated by a comma. For example, if you think that those values are and , your answser will be . Don't add extra spaces after the comma or around the parenthesis
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EXERCISE - 3 points - estimated duration : 10 minutes

Andrew and Bill use the Elgamal cryptosystem, with the following data :

public domain :

Andrew :

    public key :

    private key :

Bill :

    public key :

    private key : ??

Andrew receives the ciphered message : from Bill

What is the original message?

The answer is an integer number.
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