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A 3 Let Pk: Z10 -> Z10 be an illustration with the rule Pk (n) = (k n) mod 10,

k N. The figure yr is an encryption of Z10 if yr is injective.

(a) Alice would like to send her friend Bob her phone number 0152-347896.

For security reasons, she would like to encrypt the number and add a

Find encryption of the form pr. First, she tries to do this with the- educations

y2 and p3. What is your phone number in each case, after you click on every

digit that has applied figures y2 and p3 respectively?

(b) Show that v3 is an encryption. For which k € Z10 N N is

the decoding (i.e. reverse graphing) of y3?

(c) Why is 22 not an encryption?

(d) For which k € N is yr an encryption and for which k € N is yk

no encryption? Justify your answer.

4k

(1+2+1 +2 Points)

For the summer semester beginners: A figure f: X-> Y is called injective if there are no two

x values that are mapped to the same y value: for all x1 # x2 € x, f(x1) # f(x2) apply.

An equivalent formulation is: if f(x1) = f(x2) for two values x1, x2 € X, then x1 must be = x2

apply.

Fig: 1