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)(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′ ).
Question
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)(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′ ).
Solution
(e) This approach is Secure. It achieves the two desired notions of confidentiality. The first notion of confidentiality is that an adversary should not be able to learn anything about the message. In this approach, the message is encrypted twice, first with Borealis's public key and then with Chandra's public key. This double encryption ensures that an adversary cannot learn anything about the message without having both Borealis's and Chandra's private keys. The second notion of confidentiality is that an adversary should not be able to learn who the intended recipient of the message is. In this approach, the intended recipient's public key is also encrypted with Chandra's public key, which prevents an adversary from learning who the intended recipient is without Chandra's private key.
(d) This approach is Insecure. It does not achieve the two desired notions of confidentiality. The first notion of confidentiality is that an adversary should not be able to learn anything about the message. In this approach, the message is only encrypted once with Chandra's public key. This means that an adversary who has Chandra's private key can learn the message. The second notion of confidentiality is that an adversary should not be able to learn who the intended recipient of the message is. In this approach, the intended recipient's public key is encrypted with Chandra's public key. However, since Chandra re-encrypts the message with the intended recipient's public key and broadcasts it, an adversary can learn who the intended recipient is by observing the broadcast.
Similar Questions
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.(a) Aldebaran computes c = Enc(pkB , m) and broadcasts (pkB , c). Borealis observes the broadcast containing their public key and obtains the message as m = Dec(skB , c). (b) 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 des-tination address as pkdest = Dec(skC , cdest) and broadcasts (pkdest, cmsg). Borealis then obtains the message as m = Dec(skB , cmsg).
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.
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))
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))
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.