(Sign-then-Encrypt 1) Aldebaran computes σ = Sign(sk′ A, m), and cσ = Enc(pkC, σ). Aldebaran sends this ciphertext along with their usual broadcast(pkC, cdest, cmsg). Chandra performs her usual steps, as well as decrypting to obtain σ = Dec(skC, cσ). She sends it along with her usual broadcast (pkB, c′ msg) for Borealis. Lastly, Borealis, decrypts to obtain the message m. Borealis believes the message should have come from Aldebaran. He runs Verify(pk′ A, m, σ) and is satisfied only if the signature accepts.
Question
(Sign-then-Encrypt 1) Aldebaran computes σ = Sign(sk′ A, m), and cσ = Enc(pkC, σ). Aldebaran sends this ciphertext along with their usual broadcast(pkC, cdest, cmsg). Chandra performs her usual steps, as well as decrypting to obtain σ = Dec(skC, cσ). She sends it along with her usual broadcast (pkB, c′ msg) for Borealis. Lastly, Borealis, decrypts to obtain the message m. Borealis believes the message should have come from Aldebaran. He runs Verify(pk′ A, m, σ) and is satisfied only if the signature accepts.
Solution
This passage describes a cryptographic communication process involving three parties: Aldebaran, Chandra, and Borealis. Here's a step-by-step breakdown:
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Aldebaran starts the process by creating a signature, σ, using their private key (sk'A) and the message (m). This is done through the Sign function: σ = Sign(sk'A, m).
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Aldebaran then encrypts this signature using Chandra's public key (pkC). This is done through the Enc function: cσ = Enc(pkC, σ).
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Aldebaran sends this encrypted signature (cσ) along with their usual broadcast, which includes Chandra's public key (pkC), the encrypted destination (cdest), and the encrypted message (cmsg).
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Upon receiving this, Chandra performs her usual steps and also decrypts the encrypted signature using her private key (skC) to obtain the original signature: σ = Dec(skC, cσ).
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Chandra then sends this signature along with her usual broadcast, which includes Borealis's public key (pkB) and the encrypted message (c'msg).
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Borealis, upon receiving this, decrypts to obtain the original message (m).
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Borealis then verifies the message using Aldebaran's public key (pk'A), the message (m), and the signature (σ) through the Verify function. Borealis is satisfied only if the signature is accepted: Verify(pk'A, m, σ).
This process ensures that the message is securely transmitted from Aldebaran to Borealis, with Chandra acting as an intermediary. The use of encryption and decryption ensures that only the intended recipient can read the message, and the use of signatures ensures that the message is indeed from the claimed sender and has not been tampered with during transmission.
Similar Questions
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?
. 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′ ).
(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))
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