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Stream ciphers - PowerPoint Presentation

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Stream ciphers - PPT Presentation

Stream ciphers are semantically secure Online Cryptography Course Dan Boneh Goal secure PRG semantically secure stream cipher Stream ciphers are semantically secure ID: 398575

secure adv adversary stream adv secure stream adversary sem prg proof advprg event sec claim advss semantically ciphers chal

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Slide1

Stream ciphers

Stream ciphers are semantically secure

Online Cryptography Course Dan Boneh

Goal: secure PRG ⇒ semantically secure stream cipherSlide2

Stream ciphers are semantically secure

Thm

: G:K ⟶{0,1}n is a secure PRG ⇒ stream cipher E derived from G is sem. sec. ∀ sem. sec. adversary A , ∃a PRG adversary B s.t.

Adv

SS[A,E] ≤ 2 ∙ AdvPRG[B,G] Slide3

Proof: Let A be a sem. sec. adversary.For b=0,1:

Wb := [ event that b’=1 ].

AdvSS[A,E] = | Pr[ W0 ] − Pr[ W1 ] |

Chal.

b

Adv. A

k

K

m

0

, m

1

 M : |m

0

| = |m

1

|

c

m

b ⊕ G(k)

b’

 {0,1}

r

{0,1}

nSlide4

Proof: Let A be a sem. sec. adversary.For b=0,1:

Wb := [ event that b’=1 ].

AdvSS[A,E] = | Pr[ W0 ] − Pr[ W1 ] |

For b=0,1: Rb := [ event that b’=1 ]

Chal.

b

Adv. A

k

K

m

0

, m

1

 M : |m

0

| = |m

1

|

c

mb ⊕ r

b’

 {0,1}

r

{0,1}

nSlide5

Proof: Let A be a sem. sec. adversary.Claim 1: |Pr[R0] – Pr

[R1]| =

Claim 2: ∃B: |Pr[Wb] – Pr[Rb]| =

AdvSS[A,E] =

|Pr[W0] – Pr[W1

]

|

≤ 2 ∙

Adv

PRG

[B,G]

0

1

Pr

[W

0

]

Pr

[W

1

]Pr[Rb]Slide6

Proof of claim 2: ∃B: |Pr[W0] – Pr[R

0]| = AdvPRG

[B,G] Algorithm B:AdvPRG[B,G

] =

PRG adv. B (us)

Adv. A(given)

c

m

0

y

y ∈ {0,1}

n

m

0

, m

1

b

∈ {0,1}Slide7

End of Segment