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Key management1
07_lect06_key_management.pdf
Public-key cryptography3
08_lect07_intro_public_key_crypto.pdf
09_lect08_rsa_elgamal.pdf
10_lect09_pki.pdf
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ust.hk · COMP 5631 reading list

Hybrid encryption

7.3 · Combining public-key and symmetric schemes
  • Public-key encryption is slow and limited to short messages; symmetric encryption is fast but needs a shared key.
  • Hybrid: pick a fresh session key k, encrypt the message with AES-256-GCM under k, then encrypt k itself with RSA-OAEP under Bob’s public key.
  • Send the pair (c₁, c₂): c₁ = RSA-OAEP(pkB, k), c₂ = AES-GCM(k, N, M) with tag T.
  • Bob recovers k from c₁ with skB, then decrypts c₂ and verifies T.
AAlice
k ← randomc₁ ‖ N ‖ c₂ ‖ T
BBob
Fig. 7.4 — only Bob’s private key can unwrap k
Key pointThe session key k never crosses the channel in the clear.
COMP 5631 · Cryptography and SecurityLecture 07 · Public-key cryptography12 / 28
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Hybrid encryption

7.3 · Combining public-key and symmetric schemes
  • Public-key encryption is slow and limited to short messages; symmetric encryption is fast but needs a shared key.
  • Hybrid: pick a fresh session key k, encrypt the message with AES-256-GCM under k, then encrypt k itself with RSA-OAEP under Bob’s public key.
  • Send the pair (c₁, c₂): c₁ = RSA-OAEP(pkB, k), c₂ = AES-GCM(k, N, M) with tag T.
  • Bob recovers k from c₁ with skB, then decrypts c₂ and verifies T.
AAlice
k ← randomc₁ ‖ N ‖ c₂ ‖ T
BBob
Fig. 7.4 — only Bob’s private key can unwrap k
Key pointThe session key k never crosses the channel in the clear.
COMP 5631 · Cryptography and SecurityLecture 07 · Public-key cryptography12 / 28
Lecture 07 · Hybrid Encryption.pptxPage 12
Why can’t Alice just send the key k to Bob directly?
Thinking complete, referenced 9 sources
Anyone on the channel could read it and decrypt c₂. That is why this slide wraps k with RSA-OAEP under Bob’s public key — only Bob can recover it.1
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Hybrid encryption

7.3 · Combining public-key and symmetric schemes
  • Public-key encryption is slow and limited to short messages; symmetric encryption is fast but needs a shared key.
  • Hybrid: pick a fresh session key k, encrypt the message with AES-256-GCM under k, then encrypt k itself with RSA-OAEP under Bob’s public key.
  • Send the pair (c₁, c₂): c₁ = RSA-OAEP(pkB, k), c₂ = AES-GCM(k, N, M) with tag T.
  • Bob recovers k from c₁ with skB, then decrypts c₂ and verifies T.
AAlice
k ← randomc₁ ‖ N ‖ c₂ ‖ T
BBob
Fig. 7.4 — only Bob’s private key can unwrap k
Key pointThe session key k never crosses the channel in the clear.
COMP 5631 · Cryptography and SecurityLecture 07 · Public-key cryptography12 / 28
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Why does key management collapse for one-key ciphers?
Every pair needs its own shared key, so 10,000 people need 4,995,000 of them — and each person keeps 9,999. That is the problem public-key ciphers set out to solve.1
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Lecture 07 knowledge checkQuestion 2 of 5

In hybrid encryption, what does RSA-OAEP protect?

  • AThe session key k
  • BThe file contents
  • CThe nonce N
  • DThe authentication tag T
CorrectWhy A is the correct answer

OAEP wraps k under Bob’s public key; the file itself is protected by AES-256-GCM.

Hybrid encryption flash cards3 / 12
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Why does the session key k never cross the channel in the clear?

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QuizLecture 07 · Knowledge check

Why is the session key k never sent across the channel in the clear?

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Lecture 07 · Page 12
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