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

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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.

View this question
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 receives the ciphered message : from Bill

What is the original message?

The answer is an integer number.
View this question
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
View this question

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).

View this question

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).

View this question

Anna and Benoît exchange messages using the following coding table for characters.

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.

View this question
Andrew wants to use the Elgamal cryptosystem

The data he chooses is the following :

public domain :

public key :

private key :

Is this data correct regarding Elgamal cryptosystem requirements ?

Answer with yes or no (no capital letters)
View this question
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 receives the ciphered message : from Bill

What is the original message?

The answer is an integer number.
View this question
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
View this question

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 wants to send the message to Bernard and chooses . Which couple of values should Albert send ?

Your answer will be a couple of numbers.  For example, if you think the values are 15 and 9, your answer will be (15,9).

View this question

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