) The consortium decide to implement the final approach described in question 1, using Elgamal public key encryption with the following parameters: (p, g) = (103, 5). Aldebaran’s public key is pkA = 51, Borealis’ public key is pkB = 55 and Chandra’s public key is pkC = 38. Some time later, Chandra receives a different broadcast (38, cmsg, cdest) where cdest = (55, 10) and cmsg = (c1, c2) = ((101, 28),(90, 94)). i. (2 marks) Confirm whether or not Chandra’s public key corresponds to her secret key skC = 22. ii. (5 marks) Who is the final intended recipient of the message? (Hint: compute the Elgamal decryption Dec(skC, cdest) and compare with the known public keys.) iii. (6 marks) Hence, what does Chandra broadcast? (Hint: compute the Elgamal decryptions Dec(skC, c1) and Dec(skC, c2))
Question
) The consortium decide to implement the final approach described in question 1, using Elgamal public key encryption with the following parameters: (p, g) = (103, 5). Aldebaran’s public key is pkA = 51, Borealis’ public key is pkB = 55 and Chandra’s public key is pkC = 38. Some time later, Chandra receives a different broadcast (38, cmsg, cdest) where cdest = (55, 10) and cmsg = (c1, c2) = ((101, 28),(90, 94)). i. (2 marks) Confirm whether or not Chandra’s public key corresponds to her secret key skC = 22. ii. (5 marks) Who is the final intended recipient of the message? (Hint: compute the Elgamal decryption Dec(skC, cdest) and compare with the known public keys.) iii. (6 marks) Hence, what does Chandra broadcast? (Hint: compute the Elgamal decryptions Dec(skC, c1) and Dec(skC, c2))
Solution
i. To confirm whether Chandra's public key corresponds to her secret key, we need to check if the following equation holds true: pkC ≡ g^skC mod p. Substituting the given values, we get 38 ≡ 5^22 mod 103. If this equation holds true, then Chandra's public key corresponds to her secret key.
ii. To find out the final intended recipient of the message, we need to compute the Elgamal decryption Dec(skC, cdest). The Elgamal decryption function is defined as: Dec(skC, (c1, c2)) = c2 / (c1^skC) mod p. Substituting the given values, we get Dec(22, (55, 10)) = 10 / (55^22) mod 103. The result of this computation should be compared with the known public keys to identify the final recipient.
iii. To find out what Chandra broadcasts, we need to compute the Elgamal decryptions Dec(skC, c1) and Dec(skC, c2). Using the same decryption function as above, we get Dec(22, (101, 28)) = 28 / (101^22) mod 103 and Dec(22, (90, 94)) = 94 / (90^22) mod 103. The results of these computations will be the message that Chandra broadcasts.
Similar Questions
The consortium decide to implement the final approach described in question 1, using Elgamal public key encryption with the following parameters: (p, g) = (103, 5). Aldebaran’s public key is pkA = 51, Borealis’ public key is pkB = 55 and Chandra’s public key is pkC = 38. For each of the following questions, you may use an online tool or python to compute modular exponentiation and reduction, but show your working. (Hint: use the pow(x,y,z) function in python to compute x y (mod z), or using WolframAlpha, query “xˆy mod z ’’.) (a) Aldebaran wishes to send a message m = 33 to Borealis. i. (2 marks) Confirm whether or not Aldebaran’s public key corresponds to the secret key skA = 7. ii. (5 marks) In the first step, Aldebaran must compute the Elgamal encryption (c1, c2) = Enc(pkB, m). Suppose during encryption, Aldebaran randomly samples a = 33, as in where c1 = g a . What is (c1, c2)? Note: Aldebaran will perform the rest of the steps to convey this message by themselves.
Some time later, Chandra receives a different broadcast (38, cmsg, cdest) where cdest = (55, 10) and cmsg = (c1, c2) = ((101, 28),(90, 94)). i. (2 marks) Confirm whether or not Chandra’s public key corresponds to her secret key skC = 22. ii. (5 marks) Who is the final intended recipient of the message? (Hint: compute the Elgamal decryption Dec(skC, cdest) and compare with the known public keys.) iii. (6 marks) Hence, what does Chandra broadcast? (Hint: compute the Elgamal decryptions Dec(skC, c1) and Dec(skC, c2))
(a) Aldebaran wishes to send a message m = 33 to Borealis. i. (2 marks) Confirm whether or not Aldebaran’s public key corresponds to the secret key skA = 7. ii. (5 marks) In the first step, Aldebaran must compute the Elgamal encryption (c1, c2) = Enc(pkB, m). Suppose during encryption, Aldebaran randomly samples a = 33, as in where c1 = g a . What is (c1, c2)? Note: Aldebaran will perform the rest of the steps to convey this message by themselves.
Aldebaran computes cmsg = Enc(pkC , m), cdest = Enc(pkC , pkB ) and broadcasts (pkC , cmsg, cdest). Chandra observes the broadcast containing her public key. She then computes m = Dec(skC , cmsg) and pkdest = Dec(skC , cdest). Lastly, she re-encrypts c′ = Enc(pkdest, m) and broadcasts (pkdest, c′). Borealis identifies their public key in the broadcast and obtains the message m = Dec(skB , c′). state Secure or Insecure, and explain why that approach does or does not achieve the two desired notions of confidentiality described above.
. For each approach, state Secure or Insecure, and explain why that approach does or does not achieve the two desired notions of confidentiality described above.Aldebaran computes cmsg = Enc(pkC, m), cdest = Enc(pkC, pkB) and broadcasts(pkC, cmsg, cdest). Chandra observes the broadcast containing her public key. She then computes m = Dec(skC, cmsg) and pkdest = Dec(skC, cdest) and broadcasts (pkdest, m). Borealis identifies their public key in the broadcast and obtains the message m. 1 (d) Aldebaran computes cmsg = Enc(pkC, m), cdest = Enc(pkC, pkB) and broadcasts(pkC, cmsg, cdest). Chandra observes the broadcast containing her public key. She then computes m = Dec(skC, cmsg) and pkdest = Dec(skC, cdest). Lastly, she re-encrypts c ′ = Enc(pkdest, m) and broadcasts (pkdest, c′ ). Borealis identifies their public key in the broadcast and obtains the message m = Dec(skB, c′ ).
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