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The One Time Pad

Online Cryptography Course Dan Boneh. Stream ciphers. The One Time Pad. Symmetric Ciphers: definition. Def : a cipher defined over is a pair of “efficient” algs ( E , D ) where E is often randomized. D is always deterministic.

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The One Time Pad

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  1. Online Cryptography Course Dan Boneh Stream ciphers The One Time Pad

  2. Symmetric Ciphers: definition Def: a cipher defined over is a pair of “efficient” algs (E, D) where • E is often randomized. D is always deterministic.

  3. The One Time Pad (Vernam 1917) First example of a “secure” cipher key = (random bit string as long the message)

  4. The One Time Pad (Vernam 1917) msg: 0 1 1 0 1 1 1 key: 1 0 1 1 0 1 0 CT: ⊕

  5. You are given a message (m) and its OTP encryption (c). Can you compute the OTP key from m and c ? No, I cannot compute the key. Yes, the key is k = m⊕c. I can only compute half the bits of the key. Yes, the key is k = m ⊕m.

  6. The One Time Pad (Vernam 1917) Very fast enc/dec !! … but long keys (as long as plaintext) Is the OTP secure? What is a secure cipher?

  7. What is a secure cipher? Attacker’s abilities: CT only attack(for now) Possible security requirements: attempt #1: attacker cannot recover secret key attempt #2: attacker cannot recover all of plaintext Shannon’s idea: CT should reveal no “info” about PT

  8. Information Theoretic Security (Shannon 1949) Def: A cipher (E, D) over () has perfect secrecyif

  9. Information Theoretic Security Def: A cipher (E, D) over () has perfect secrecyif (|) and Pr[E(k, m0) = c]= Pr[E(k, m1) = c]where R

  10. Lemma: OTP has perfect secrecy. Proof:

  11. Let and . How many OTP keys map to ? None 1 2 Depends on

  12. Lemma: OTP has perfect secrecy. Proof:

  13. The bad news … Thm: perfect secrecy ⇒

  14. End of Segment

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