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
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
This question seems to be related to cryptography, specifically the Elgamal encryption system. Here's how you can solve it:
i. To confirm whether Chandra’s public key corresponds to her secret key skC = 22, you need to know the public key and the parameters of the Elgamal system (p, g). The public key in Elgamal system is calculated as (p, g, g^sk mod p). If you have these values, you can check if the public key corresponds to the secret key.
ii. To find out the final intended recipient of the message, you need to compute the Elgamal decryption Dec(skC, cdest). The Elgamal decryption is computed as follows: m = c2 * (c1^x)^-1 mod p, where x is the secret key, c1 and c2 are parts of the cipher text, and p is a prime number from the public key. After decryption, you will get a pair of numbers which should correspond to someone's public key.
iii. To find out what Chandra broadcasts, you need to compute the Elgamal decryptions Dec(skC, c1) and Dec(skC, c2). These are computed in the same way as in the previous step. The decrypted messages are what Chandra broadcasts.
Please note that without the specific values of the public keys and the parameters of the Elgamal system, I can't provide a more specific answer.
Similar Questions
(e) Aldebaran computes cmsg = Enc(pkC, Enc(pkB, m)), cdest = Enc(pkC, pkB) and then broadcasts (pkC, cmsg, cdest). Chandra observes the broadcast containing her public key. She then computes c ′ msg = Dec(skC, cmsg), pkdest = Dec(skC, cdest), and broadcasts (pkdest, c′ msg). Lastly, Borealis observes a broadcast containing their public key, and obtains the message as m = Dec(skB, c′ msg).
. 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.(e) Aldebaran computes cmsg = Enc(pkC, Enc(pkB, m)), cdest = Enc(pkC, pkB) and then broadcasts (pkC, cmsg, cdest). Chandra observes the broadcast containing her public key. She then computes c ′ msg = Dec(skC, cmsg), pkdest = Dec(skC, cdest), and broadcasts (pkdest, c′ msg). Lastly, Borealis observes a broadcast containing their public key, and obtains the message as m = Dec(skB, c′ msg).
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 decrypts the destination address as pkdest = Dec(skC, cdest) and broadcasts (pkdest, cmsg). Borealis then obtains the message as m = Dec(skB, cmsg).Is it secure?
) 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))
(Sign-then-Double-Encrypt) Aldebaran computes σ = Sign(sk′ A, m), and cσ = Enc(pkC, Enc(pkB, σ)). Aldebaran sends cσ along with their usual broadcast, (pkC, cdest, cmsg). Chandra performs her usual steps, as well as decrypting to obtain c ′ σ = Dec(skC, cσ). She sends it along with her usual broadcast, (pkB, c′ msg) for Borealis. Lastly, Borealis, who will receives the message m, now also obtains σ = Dec(skB, c′ σ ). Borealis believes the message should have come from Aldebaran. He runs Verify(pk′ A, m, σ) and is satisfied only if the signature accepts
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