Simulatable Channels: Extended Security that is Universally - - PowerPoint PPT Presentation

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Simulatable Channels: Extended Security that is Universally - - PowerPoint PPT Presentation

Simulatable Channels: Extended Security that is Universally Composable and Easier to Prove. ASIACRYPT 2018 J. P. Degabriele M. Fischlin 1 What this talk is about We propose and explore new security definitions for symmetric encryption


slide-1
SLIDE 1

Simulatable Channels:

Extended Security that is Universally Composable and Easier to Prove.

ASIACRYPT 2018

  • M. Fischlin
  • J. P. Degabriele

1

slide-2
SLIDE 2

What this talk is about…

  • We propose and explore new security definitions for symmetric

encryption based on simulation.

  • Our primary focus is on secure channels rather than nonce-based

encryption but it could be adapted to the latter.

  • Conceptually

interesting, non-trivial to formalise, allow simpler proofs, and imply universal composability.

2

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SLIDE 3

Outline of this talk

  • Background and Motivation
  • The New Definitions and Relations
  • SSH-CTR and Universal Composability

3

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SLIDE 4

Background and Motivation

4

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SLIDE 5

Extensions of Symmetric Encryption

  • Stateful Security: protects against replay and reordering of

ciphertexts [BKN02, KPB03, BHMS16].

  • Leakage From Invalid Ciphertexts: protects against multiple

errors, release of unverified plaintext, and other forms of leakage [BDPS13, ABLMMY14, HKR14, BPS15].

  • Encryption Supporting Fragmentation: encryption operating
  • ver channels which may deliver ciphertexts in a fragmented

fashion [PW10, BDPS12, FGMP15, ADHP16].

5

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SLIDE 6

The Price We Pay…

6

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SLIDE 7

Compare to Nonce-based Encryption

  • For nonce-based encryption, IND$-CPA and nAE are the security

notions of choice.

  • Conceptually simpler, easier to prove, and stronger security.
  • Inapplicable to channels due to specially formatted ciphertexts,

multiple errors, and don’t support fragmentation.

  • Can IND$-CPA and nAE be generalized to more complex settings?

7

IND$-CPA nAE

A

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EK(·)

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$(·)

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DK(·)

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⊥(·)

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A

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EK(·)

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$(·)

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slide-8
SLIDE 8

New Definitions and Relations

8

slide-9
SLIDE 9

Syntax

  • We consider two types of encryption schemes:
  • Atomic:

! ← ℰ$(&) ; ((, &) ← *$(!)

  • where ( ∈ {⊤, ⊥} and & corresponds respectively to a message or a

leakage string.

  • Supporting Ciphertext Fragmentation:

! ← ℰ$(&) ; (0, &0 … ((2, &2) ← *$(3)

  • where 4 ∈ {0,1,2, … }.

9

slide-10
SLIDE 10

Encryption Simulatability (ES)

  • IND$ can be viewed as requiring encryption to be simulatable, where

in this case the simulator is of a specific type.

  • Then a natural generalization is to require the existence of an efficient

simulator ! such that "[$ℰ& ⋅ ⇒ 1] − "[$, ⋅ ⇒ 1] ≤ . .

  • However this does not quite work, encryption could leak the message

and still be simulatable!

  • Replacing ,(⋅) with ,(| ⋅ |) solves the issue.

10

slide-11
SLIDE 11

Encryption Simulatability (ES)

IND$-CPA ⟹ ES ⟺ IND-CPA

  • For any IND-CPA scheme, we can let # ℓ = ℰ'

((*ℓ) for a key '

, sampled independently (simulator is stateful).

  • However the equivalence does not extend to chosen-ciphertext security:

ES-CCA ⟸ IND-CCA

  • If we further require the simulator to be stateless we get key-privacy.

ES ∧ Stateless(#) ⟹ KP-CPA

11

slide-12
SLIDE 12

Decryption Simulatability (DS)

  • Similarly, we can consider a notion where we require decryption to

be simulatable.

  • Then DS requires the existence of an efficient simulator ! such that

"[$ℰ& ⋅ ,)& ⋅ ⇒ 1] − "[$ℰ& ⋅ ,. ⋅ ⇒ 1] ≤ 0 .

  • To be satisfiable, we need, as usual, to suppress/prohibit queries from

ℰ1 ⋅ to . ⋅ .

  • Alternatively, in this case, we can give the simulator access to a

transcript of the encryption queries.

12

slide-13
SLIDE 13

Decryption Simulatability (DS)

  • Intuitively, the information in the transcript is already known to the

adversary and should not degrade security.

  • However, if ! is given unrestricted access to the transcript then

IND-CPA ⋀ DS ⟹ IND-CCA.

13

S(·)

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W

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EK(·)

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A

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T

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  • Problem: The simulator can use the

transcript to answer queries not in the transcript!

  • Solution: Control the simulator’s

access to the transcript via a fixed wrapper algorithm $.

slide-14
SLIDE 14

Relations Between ES and DS

  • As desired, DS reduces chosen-ciphertext security to chosen-

plaintext security: IND-CPA ∧ DS ⟹ IND-CCA where an ES version also holds.

  • On the other hand:

IND-CCA ⟹ DS but ES-CCA ⟹ DS thereby establishing a relation between encryption simulatability and decryption simulatability.

14

slide-15
SLIDE 15

DS and Ciphertext Integrity

  • We can formulate ciphertext integrity as a special case of decryption

simulatability by imposing an extra requirement on the simulator.

  • Informally, a scheme is DS-I secure if it is DS secure, and the

simulator ! always returns outputs "# $%& #"'( (⊥, ,).

  • Thus if a scheme is shown to be DS, ciphertext integrity follows

simply from the design of the simulator.

  • As expected, it can be shown that:

DS-I ⟹ INT-CTXT

15

slide-16
SLIDE 16

Combining ES and DS-I

  • We can now combine encryption simulatability and decryption

simulatability into a single notion (ES ∧ DS-I).

  • ∃#$, #&∀( it holds )[(ℰ, ⋅ ,., ⋅ ⇒ 1]−)[(#3 |⋅| ,5[#6] ⋅ ⇒ 1] ≤ 8 .
  • Intuitively it says that oracle access to the channel provides no

additional computational abilities to the adversary.

  • It’s an IND-CCA/AE type of definition with no prohibited queries!

16

slide-17
SLIDE 17

The Case of SSH

17

Encrypt PRF-MAC

Payload Ciphertext MAC tag Sequence Number

4

Packet Length

4

Pad Len 1 Padding

≥4

  • Encode-then-Encrypt&MAC construction.
  • Decryption: (a) decrypt the Packet Length field,

(b) wait until that many bytes are received, (c) resume decrypting the rest of the ciphertext.

slide-18
SLIDE 18

SSH Cannot Satisfy ES ∧ DS-I

  • Problem: In the fragmentation setting "# needs to identify ciphertext

boundaries in order to determine when to return an output.

  • At the same time, for "$ to be a good simulator the contents of the

length field should remain hidden (if the encryption is good).

  • Solution: Let "$ and "# share randomness or memory.
  • We go a step further and replace them with a single simulator

(with an encryption interface and a decryption interface).

18

slide-19
SLIDE 19

Channel Simulatability

  • This leads us to the following definition:

∃"∀$ such that +[$ℰ. ⋅ ,1. ⋅ ⇒ 1]−+[$" 6,|⋅| ,8["] 9,⋅ ⇒ 1] ≤ ; .

  • Satisfiable by a larger class of schemes while retaining all the

nice properties of ES ∧ DS-I. CS-I ⟹ IND-CCA, INT-CTXT

  • New proof goal: transform the scheme, through a sequence of game

hops, into an algorithm devoid of the secret key and the message.

19

slide-20
SLIDE 20

SSH-CTR and Universal Composability

20

slide-21
SLIDE 21

21

  • alg. SSH-CTR-EK(m)
1 :

parse K as (Ke, Km, IV )

2 :

if e-seqnr = 0

3 :

e-ctr Ω IV / / initialise on first call

4 :

mlen Ω |m|B

5 :

/ / calculate padding length

6 :

padlen Ω blocksize ≠ (5 + mlen)%blocksize

7 :

if padlen < 4

8 :

padlen Ω padlen + blocksize

9 :

/ / encode the message

10 :

pad ⌘ {0, 1}padlen·8

11 :

len Ω 1 + mlen + padlen

12 :

ptxt Ω ÈlenÍ32 Î ÈpadlenÍ8 Î m Î pad

13 :

/ / encrypt and mac

14 :

τ Ω MAC(Km, Èe-seqnrÍ32 Î ptxt)

15 :

z Ω ε

16 :

while |z| < |ptxt|

17 :

z Ω z Î BC(Ke, e-ctr)

18 :

e-ctr Ω e-ctr + 1

19 :

c Ω (ptxt ü z) Î τ

20 :

e-seqnr Ω e-seqnr + 1

21 :

return c

  • alg. SSH-CTR-DK(f)
1 :

parse K as (Ke, Km, IV )

2 :

if d-seqnr = 0 · α = ε

3 :

d-ctr Ω IV / / initialise on first call

4 :

if closed

5 :
  • ut Ω (‹, CONN_CLOSED); break
6 :

α Ω α Î f; out Ω ε / / update buffer and reset output

7 :

while (true) / / process buffer (α)

8 :

if |α|B < blocksize

9 :

break / / first ciphertext block is incomplete

10 :

/ / decrypt first ciphertext block

11 :

ptxtÕ Ω α[1, blocksize] ü BC(Ke, d-ctr)

12 :

d-ctr Ω d-ctr + 1

13 :

clen Ω ÈptxtÕ[1, 32]Í≠1 + 4 + macsize

14 :

inRange Ω (16 + macsize Æ clen Æ 35000)

15 :

isMult Ω ((clen ≠ macsize)%blocksize ”= 0)

16 :

if ¬ inRange ‚ isMult / / validate length

17 :
  • ut Ω out Î (‹, INVALID_LENGTH)
18 :

closed Ω true; break

19 :

if |α|B < clen

20 :

break / / wait to complete ciphertext

21 :

z Ω ε / / decrypt and verify mac

22 :

while |z| < (clen ≠ blocksize ≠ macsize)

23 :

z Ω z Î BC(Ke, e-ctr)

24 :

d-ctr Ω d-ctr + 1

25 :

ptxtÕ Ω ptxtÕ Î z ü α[blocksize + 1, clen ≠ macsize]B

26 :

τ Õ Ω α[clen ≠ macsize + 1, clen]B

27 :

α Ω α[clen + 1, ú]B / / remove decrypted ciphertext

28 :

if τ Õ ”= MAC(Km, Èd-seqnrÍ32 Î ptxtÕ)

29 :
  • ut Ω out Î (‹, INVALID_MAC)
30 :

closed Ω true; break

31 :

padlen Ω ÈptxtÕ[5, 5]BÍ≠1 / / validate padding length

32 :

mlenÕ Ω clen ≠ padlen ≠ 4 ≠ 1 ≠ macsize

33 :

if (mlenÕ > 32789) ‚ (mlenÕ < 1)

34 :
  • ut Ω out Î (‹, INVALID_PAD_LENGTH)
35 :

closed Ω true; break

36 :

mÕ Ω ptxtÕ[6, clen ≠ macsize ≠ padlen]B

37 :
  • ut Ω out Î (€, mÕ)
38 :

d-seqnr Ω d-seqnr + 1

39 :

return out

36

  • SSH-CTR in OpenSSH was

analysed in [PW10] using a different security model supporting fragmentation.

  • We provide a considerably

simpler proof showing that SSH-CTR is CS-I secure.

  • Corollary: SSH-CTR is

universally composable.

slide-22
SLIDE 22

UC Secure Channel [CK02]

22

[Channel] P1 P2 m m |m| deliver Sim Env ℱSC [CE] ℱSC (EstCh,sid,P1,P2) Ideal World (without corruptions)

slide-23
SLIDE 23

Compare to Channel Simulatability

23

A

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T

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CS-I Simulated World

  • The

simulated world in CS-I corresponds quite closely to the ideal world in the UC setting.

  • ⋅ + # + T ⟶ ℱ&' [Channel]

( ⟶ Env + P1 + P2 )(+/-,⋅) ⟶ Sim

S(e, | · |)

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S(d, ·)

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W

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slide-24
SLIDE 24

Summary and Concluding Remarks

  • The aim was to generalize IND$ and reached a notion that is

very close to a UC secure channel (Channel Simulatability).

  • Arguably, CS is easier to use and understand than UC.
  • It is closer in spirit to AE/CCA but more versatile, devoid of

prohibited queries. 24