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

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Presentation transcript:

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

Dan Boneh 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.

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

Dan Boneh The One Time Pad (Vernam 1917) msg: key: CT: msg: key: CT: ⊕

Dan Boneh 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.

Dan Boneh 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?

Dan Boneh 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

Dan Boneh Information Theoretic Security (Shannon 1949)

Dan Boneh Information Theoretic Security R

Dan Boneh Lemma: OTP has perfect secrecy. Proof:

Dan Boneh None 1 2

Dan Boneh Lemma: OTP has perfect secrecy. Proof:

Dan Boneh The bad news …

Dan Boneh End of Segment