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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

Online Cryptography Course Dan Boneh

Stream ciphers

The One Time Pad


Symmetric ciphers definition
Symmetric Ciphers: definition Dan Boneh

Def: a cipher defined over

is a pair of “efficient” algs (E, D) where

  • E is often randomized. D is always deterministic.


The one time pad vernam 1917
The One Time Pad Dan Boneh(Vernam 1917)

First example of a “secure” cipher

key = (random bit string as long the message)


The one time pad vernam 19171
The One Time Pad Dan Boneh(Vernam 1917)

msg: 0 1 1 0 1 1 1

key: 1 0 1 1 0 1 0

CT:


The one time pad

Y Dan Bonehou 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.


The one time pad vernam 19172
The One Time Pad Dan Boneh(Vernam 1917)

Very fast enc/dec !!

… but long keys (as long as plaintext)

Is the OTP secure? What is a secure cipher?


What is a secure cipher
What is a secure cipher? Dan Boneh

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


Information theoretic security shannon 1949
Information Theoretic Security Dan Boneh(Shannon 1949)

Def: A cipher (E, D) over () has perfect secrecyif


Information theoretic security
Information Theoretic Security Dan Boneh

Def: A cipher (E, D) over () has perfect secrecyif

(|) and Pr[E(k, m0) = c]= Pr[E(k, m1) = c]where

R


The one time pad

Lemma Dan Boneh: OTP has perfect secrecy.

Proof:


The one time pad

Let Dan Bonehand .

How many OTP keys map to ?

None

1

2

Depends on


The one time pad

Lemma Dan Boneh: OTP has perfect secrecy.

Proof:


The bad news
The bad news … Dan Boneh

Thm: perfect secrecy ⇒


End of segment

End of Segment Dan Boneh