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Advanced information, computation, communication II

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Question 4b

are valid exponents.

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Question 4a

are valid exponents.

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Question 3c

Show that and find and expression for in terms of . What is the coefficient of in the expression of ?

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Question 3b

Is the source stationary?

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Question 3a

Calculate the marginal distribution of . What is the value of ?

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Question 2

Passing on secrets:

Alice has posted her RSA credentials as , with the modulus and the encoding exponent. As required by RSA, she keeps her decoding exponent $d$ preciously secret.

Bob has a message , RSA-encrypts it using and passes the resulting cryptogram on to Carlos.

Carlos has a message , RSA-encrypts it using to obtain the cryptogram . Then, Carlos multiplies the two cryptograms, and passes this to Alice.

Alice applies her regular RSA decryption to Under what condition is the result of this decryption exactly equal to the product ?

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Question 1

Consider the group . Find how many elements are in the group.

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Question 5

Find all solutions of in the range . How many different solutions are there?
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Question 4

Find such that .

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Question 3.2

Eve can tell for sure if Alice and/or Bob received full points.

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