Question

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.)

Answer 1

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:

I hope it will help you!

Answer 2

(a) B's public key is "$P_B = (7,2)$"

(b) The ciphertext is "$C_m = {(8,3),(10,2)}$"

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

(a)

The formula:

→ $P_B = n_B\times G$

By substituting the values, we get

        $= 7\times (2.7)$

        $= (7,2)$

(b)

As we know,

The cipher text will be:

→ $C_m = {\left\{ kG, P_m+kP_B \right \}}$

By putting the values,

        $=\left \{ {3(2,7), (10,9)+3(7,2)} \right \}$

        $= \left \{ (8,3),(10,2) \right \}$

(c)

B Recovers will be:

→ $P_m = \left \{ kP-b-n_b(kG,P_m) \right \}$

        $= (10,2)-7(8,3)$

        $= (10,2)-(3,5)$

        $= (10,2)+(3,6)$

        $= (10,9)$

Thus the above responses is correct.                

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