The signatures of A, B and C are , and . If wants to prove its identity to , what message should send?

Your message will be a number.

With the data of questions 1 or 2 (the correct one), 3 or 4 (the correct one) and 5: A wants to send to B the message 10000. What will be the ciphertext ?

Your answer will be a number.

With the same data of the previous question: B receives from C the ciphertext 10000. What is the corresponding plaintext?

There's a third agent with data and .

A and B wish to send to C the same message :102030

A ciphers the message and finds the number

A ciphers the message and finds the number

What is the value of  ?

Your answer will be a relative number.

B chooses and .

Compute Euler's function and, if the choice of is legitimate, find the public key .

Your answer will be either a couple of integers or the word "impossible" (without the inverted commas).

B chooses and .

Compute Euler's function and, if the choice of is legitimate, find the public key .

Your answer will be either a couple of integers or the word "impossible" (without the inverted commas).

A chooses and .

Compute Euler's function and, if the choice of is legitimate, find the private key .

Your answer will be either a couple of integers or the word "impossible" (without the inverted commas).

A chooses and .

Compute Euler's function and, if the choice of is legitimate, find the private key .

Your answer will be either a couple of integers or the word "impossible" (without the inverted commas).

You receive the following ciphertext: .

Decipher the message knowing that it has been enciphered using an affine transformation on digraphs, using the usual alphabet of 26 letters (a=, b=, etc) and with the following enciphering key:

.

Your answer will be a word (no capital letters).