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This problem performs elliptic curve encryption/decryption using the scheme out-
lined in Section 10.4. The cryptosystem parameters are E11(1,6) and G = (2,7). B's
secret key is nb = 3. (Hint: Note the relationship of this system to the one discussed in
the previous question (10.14)]

a. Find B's public key PB.
b. A wishes to encrypt the message Pm = (10,9) and chooses the random value
k = 4. Determine the ciphertext Cm.

c. Show the calculation by which В recovers Pm from Cm.

(10.14----> for E11(1,6) consider the point G=(2,7). compute the multiple of G from 2G through 13G.)

Respuesta :

CPED

Answer:

Following is the solution fr the question step by step:

a. PB = (7,2)

b. Cm = {(8,3), (10,2)}

c. Pm= (10,9)

Explanation:

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Cricetus

(a) B's public key is "[tex]P_B = (7,2)[/tex]"

(b) The ciphertext is "[tex]C_m = {(8,3),(10,2)}[/tex]"

(c) Between the two points, addition as well as multiplication are proceeding.

(a)

The formula:

→ [tex]P_B = n_B\times G[/tex]

By substituting the values, we get

        [tex]= 7\times (2.7)[/tex]

        [tex]= (7,2)[/tex]

(b)

As we know,

The cipher text will be:

→ [tex]C_m = {\left\{ kG, P_m+kP_B \right \}}[/tex]

By putting the values,

        [tex]=\left \{ {3(2,7), (10,9)+3(7,2)} \right \}[/tex]

        [tex]= \left \{ (8,3),(10,2) \right \}[/tex]

(c)

B Recovers will be:

→ [tex]P_m = \left \{ kP-b-n_b(kG,P_m) \right \}[/tex]

        [tex]= (10,2)-7(8,3)[/tex]

        [tex]= (10,2)-(3,5)[/tex]

        [tex]= (10,2)+(3,6)[/tex]

        [tex]= (10,9)[/tex]

Thus the above responses is correct.                

Learn more about cipher text here:

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