Indifferentiable Authenticated Encryption Pooya Farshim Manuel - - PowerPoint PPT Presentation

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Indifferentiable Authenticated Encryption Pooya Farshim Manuel - - PowerPoint PPT Presentation

Sep 18, 2023 448 likes •1.26k views

Indifferentiable Authenticated Encryption Pooya Farshim Manuel Barbosa (Porto) (CNRS & ENS) Indifferentiable Authenticated Encryption Pooya Farshim Manuel Barbosa (Porto) (CNRS & ENS) Hash Functions long & short

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SLIDE 1

Indifferentiable
 Authenticated Encryption

Manuel Barbosa 


(Porto)

Pooya Farshim

(CNRS & ENS)

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SLIDE 2

Indifferentiable
 Authenticated Encryption

Manuel Barbosa 


(Porto)

Pooya Farshim

(CNRS & ENS)

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SLIDE 3

Hash Functions

long & arbitrary short &
 random-looking SHA

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SLIDE 4

Hash Functions

long & arbitrary short &
 random-looking SHA Provably security 
 not always possible.

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SLIDE 5

Random Oracles

long & arbitrary short &
 random-looking SHA

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SLIDE 6

Random Oracles

Random Function long & arbitrary short &
 random-looking

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SLIDE 7

Random Oracles

Random Oracle long & arbitrary short &
 random-looking

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SLIDE 8

Random Oracles are Practical

๏ Public-Key Enc. (OAEP, ECIES) ๏ Signatures (PSS, FDH) ๏ TLS 1.3 ๏ Symmetric schemes ๏ …. Provable Security for 
 Many Simple & Efficient Protocols Ideal Hash

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SLIDE 9

This Talk

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SLIDE 10

This Talk

Encryption

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SLIDE 11

This Talk

Encryption Ideal Hash

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SLIDE 12

This Talk

Encryption Inherit
 all strengths Ideal Hash

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SLIDE 13

This Talk

Encryption Inherit
 all strengths Ideal Ideal Hash

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SLIDE 14

This Talk

Random Function Encryption Inherit
 all strengths Ideal Ideal Hash

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SLIDE 15

This Talk

Random Function What Object? Encryption Inherit
 all strengths Ideal Ideal Hash

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SLIDE 16

Authenticated Encryption

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SLIDE 17
  • 1. K ↞ Gen(1λ)
  • 2. C ← Enc(K,N,A,M,!) |C|=|M| + !
  • 3. M/⟘ ← Dec(K,N,A,C,!)

Authenticated Encryption

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SLIDE 18

Security says: under an unknown random key K ๏ Nothing about messages leaks ๏ Cannot forge new valid ciphertexts

  • 1. K ↞ Gen(1λ)
  • 2. C ← Enc(K,N,A,M,!) |C|=|M| + !
  • 3. M/⟘ ← Dec(K,N,A,C,!)

Authenticated Encryption

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SLIDE 19

Simplifying

  • 1. K ↞ Gen(1λ)
  • 2. C ← Enc(K,M) |C|=|M| + !
  • 3. M/⟘ ← Dec(K,C)
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SLIDE 20

Simplifying

  • 1. K ↞ Gen(1λ)
  • 2. C ← Enc(K,M) |C|=|M| + !
  • 3. M/⟘ ← Dec(K,C)

A Keyed Injection

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SLIDE 21

Ideal Encryption

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SLIDE 22

Ideal Encryption

Hash

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SLIDE 23

Ideal Encryption

Function Hash

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SLIDE 24

Ideal Encryption

Ideal Hash Function Hash

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SLIDE 25

Ideal Encryption

Random Ideal Hash Function Hash

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SLIDE 26

Ideal Encryption

Cipher Random Ideal Hash Function Hash

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SLIDE 27

Ideal Encryption

Keyed Permutation Cipher Random Ideal Hash Function Hash

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SLIDE 28

Ideal Encryption

Ideal Cipher Keyed Permutation Cipher Random Ideal Hash Function Hash

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SLIDE 29

Ideal Encryption

Random Ideal Cipher Keyed Permutation Cipher Random Ideal Hash Function Hash

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SLIDE 30

Ideal Encryption

Encryption Random Ideal Cipher Keyed Permutation Cipher Random Ideal Hash Function Hash

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SLIDE 31

Ideal Encryption

Keyed Injection Encryption Random Ideal Cipher Keyed Permutation Cipher Random Ideal Hash Function Hash

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SLIDE 32

Ideal Encryption

Keyed Injection Encryption Random Ideal Cipher Keyed Permutation Cipher Ideal Encryption Random Ideal Hash Function Hash

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SLIDE 33

Random

Ideal Encryption

Keyed Injection Encryption Random Ideal Cipher Keyed Permutation Cipher Ideal Encryption Random Ideal Hash Function Hash

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SLIDE 34

Random

Ideal Encryption

Keyed Injection Encryption Random Ideal Cipher Keyed Permutation Cipher Ideal Encryption Random Ideal Hash Function Hash New 
 Ideal Model

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SLIDE 35

Encryption

Random Function Encryption Inherit
 all strengths Ideal Ideal Hash What Object?

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SLIDE 36

Encryption

Random Function Random Keyed Injection Encryption Inherit
 all strengths Ideal Ideal Hash

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SLIDE 37

Encryption

Random Function Random Keyed Injection Encryption Inherit
 all strengths Ideal Ideal Hash

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SLIDE 38

Encryption

Random Function Indifferentiability Random Keyed Injection Encryption Inherit
 all strengths Ideal Ideal Hash

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SLIDE 39

Indifferentiability

CRO is “as good as” iEnc:

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SLIDE 40

Indifferentiability

≈ iEnc CRO CRO is “as good as” iEnc:

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SLIDE 41

Indifferentiability

≈ iEnc , RO CRO CRO is “as good as” iEnc:

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SLIDE 42

Indifferentiability

≈ iEnc , RO CRO , RO CRO is “as good as” iEnc:

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SLIDE 43

Indifferentiability

≈ , SiEnc iEnc , RO CRO CRO is “as good as” iEnc:

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SLIDE 44

Indifferentiability

C RO iEnc S D

≈ , SiEnc iEnc , RO CRO CRO is “as good as” iEnc:

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SLIDE 45

Indifferentiability

C RO iEnc S D

≈ , SiEnc iEnc , RO CRO Unified Attack Surface CRO is “as good as” iEnc:

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SLIDE 46

Indifferentiability

C RO iEnc S D

≈ , SiEnc iEnc , RO CRO Unified Attack Surface Keys can be under adversarial control CRO is “as good as” iEnc:

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SLIDE 47

Why Indifferentiability?

Theorem [MRH04]: If CRO is indifferentiable from iEnc, then it is secure in many adversarial environments in the RO model.

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SLIDE 48

Why Indifferentiability?

Theorem [MRH04]: If CRO is indifferentiable from iEnc, then it is secure in many adversarial environments in the RO model.

AE, MRAE, & RAE

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SLIDE 49

Why Indifferentiability?

Theorem [MRH04]: If CRO is indifferentiable from iEnc, then it is secure in many adversarial environments in the RO model.

RKA Security KDM Security Deduplication Committing Encryption Leakage Resilience AE, MRAE, & RAE

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SLIDE 50

Why Indifferentiability?

Theorem [MRH04]: If CRO is indifferentiable from iEnc, then it is secure in many adversarial environments in the RO model.

RKA Security KDM Security Deduplication Committing Encryption Leakage Resilience AE, MRAE, & RAE Unforeseen Models Combined Models

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SLIDE 51

Why Indifferentiability?

Theorem [MRH04]: If CRO is indifferentiable from iEnc, then it is secure in many adversarial environments in the RO model.

RKA Security KDM Security Deduplication Committing Encryption Leakage Resilience AE, MRAE, & RAE Unforeseen Models Combined Models Single stage

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SLIDE 52

So…

Are there any indifferentiable encryption schemes out there?

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SLIDE 53

Generic Composition [NRS14]

T N A M T N C

EK

T FL N A M T N FL IV IV IV IV T N IV T N IV N IV T N IV T

scheme

A1

scheme

A2

scheme

A3

scheme

A4

scheme

A7

scheme

A6

scheme

A5

scheme

A8

FL

EK EK EK EK EK EK EK

FL FL FL FL FL FL FL FL FL FL FL FL M M M M M C C C M A A A C C A A A C C

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SLIDE 54

Generic Composition [NRS14]

T N A M T N C

EK

T FL N A M T N FL IV IV IV IV T N IV T N IV N IV T N IV T

scheme

A1

scheme

A2

scheme

A3

scheme

A4

scheme

A7

scheme

A6

scheme

A5

scheme

A8

FL

EK EK EK EK EK EK EK

FL FL FL FL FL FL FL FL FL FL FL FL M M M M M C C C M A A A C C A A A C C

Enc-then-Mac

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SLIDE 55

Generic Composition [NRS14]

T N A M T N C

EK

T FL N A M T N FL IV IV IV IV T N IV T N IV N IV T N IV T

scheme

A1

scheme

A2

scheme

A3

scheme

A4

scheme

A7

scheme

A6

scheme

A5

scheme

A8

FL

EK EK EK EK EK EK EK

FL FL FL FL FL FL FL FL FL FL FL FL M M M M M C C C M A A A C C A A A C C

Enc-then-Mac Mac-then-Enc

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SLIDE 56

Generic Composition [NRS14]

T N A M T N C

EK

T FL N A M T N FL IV IV IV IV T N IV T N IV N IV T N IV T

scheme

A1

scheme

A2

scheme

A3

scheme

A4

scheme

A7

scheme

A6

scheme

A5

scheme

A8

FL

EK EK EK EK EK EK EK

FL FL FL FL FL FL FL FL FL FL FL FL M M M M M C C C M A A A C C A A A C C

Enc-then-Mac Mac-then-Enc SIV

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SLIDE 57

Attack on Enc-then-Mac

T N A M IV

scheme

A5

FL

EK

FL C

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SLIDE 58

Attack on Enc-then-Mac

T N A M IV

scheme

A5

FL

EK

FL C

Construction: Changing K does not affect T iEnc: Random Injection: changing K will change T

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SLIDE 59

Attack on Enc-then-Mac

T N A M IV

scheme

A5

FL

EK

FL C

Construction: Changing K does not affect T iEnc: Random Injection: changing K will change T Interpretation: Related-Key Attacks

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SLIDE 60

General Attacks

  • Algo. AE(K, N, A, M, τ)

(est0, est1) ← Ie(K, N, A, M, τ) (K0, N 0, M 0, τ 0) ← E H

0 (est0)

C0 ← E(K0, N 0, ε, M 0, τ 0) C ← E H

1 (C0, est1)

return C

  • Algo. AD(K, N, A, C, τ)

(dst0, dst1) ← Id(K, N, A, C, τ) (K0, N 0, C0, τ 0) ← DH

0 (dst0)

M 0 ← D(K0, N 0, ε, C0, τ 0) M ← DH

1 (M 0, dst1)

return M

A template for generic composition. Two types of attacks based on how information flows.

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SLIDE 61

Attacks: Specifics Schemes

M C M1 M1 C1 C1 X1 S M M C C
  • 1, 1
Mm Mm Cm Cm Xm Y1 S S ’ ’ ’ ’ Zl-1 Z1 Zl Z1 L R L R X S
  • 1, 5
0, 5 0, 5 0, 0 0, 0 2, 1 2, m 0, 0 0, 0 0, 1 1, 1 1, m 1, m 1, 1 0, 2 i+2, 1 i+2, l −1 Y ∆i
  • 1, 2
∆ ∆ ∆ ⊕ 1 0, 6 0, 6 0, 6 0, 6 0, 6 0, 6 0, 6 0, 6 ∆ ⊕ 0 ∆ ⊕ 3 ∆ ⊕ 2 ∆ ⊕ 6 ∆ ⊕ 5 ∆ ⊕ 7 X Y Ym * * ∆ ⊕ 4

...

10*

... ...

C
  • 1, 4
0, 4 0, 4 S X Y M ∆i Zl Zl -1 i+2, 1 i+2, l −1 i+2, l i+2, 0

AEZ [HKR17] OCB [Rog et al.] Deoxys [JNP15]

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SLIDE 62

Indifferntius

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SLIDE 63

So…

Any indifferentiable encryption schemes?

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SLIDE 64

Feistel

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SLIDE 65

Feistel

R L

RO1 RO2 RO3

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SLIDE 66

Feistel

R L

RO1 RO2 RO3

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Permutation

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SLIDE 67

Feistel

R L

RO1 RO2 RO3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Permutation

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SLIDE 68

Feistel

R L

RO1 RO2 RO3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Permutation

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SLIDE 69

Feistel

R L

RO1 RO2 RO3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Permutation

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SLIDE 70

Feistel

RO1 RO2 RO3

M

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Permutation

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SLIDE 71

Feistel

Theorem: 3 rounds of Feistel are necessary and sufficient to build a random injection.

RO1 RO2 RO3

M

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Permutation

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SLIDE 72

Feistel

Theorem: 3 rounds of Feistel are necessary and sufficient to build a random injection.

RO1 RO2 RO3

M

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Permutation Injection

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SLIDE 73

Online Encryption

Some applications need to process messages “on the fly”:

M1 C1 M2

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M3

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M`

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C`

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C2

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C3

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EK

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EK

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EK

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EK

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Leads to: A definition of online random keyed injections.

slide-74
SLIDE 74

Turning It On

Theorem: Chaining an AEAD up indifferentiability turns it on.

slide-75
SLIDE 75

Turning It On

K N E M1 M3 C3 C1 A1 A3 S H0 H1 `1 `3 `1 + ⌧1 `3 + ⌧3 E S S H1

K1

M2 C2 A2 `2 `2 + ⌧2 H2 H2 H3

K1 K1 K2 K2

E τ1 τ2 τ3

Theorem: Chaining an AEAD up indifferentiability turns it on.

slide-76
SLIDE 76

Efficiency Lower Bound

Theorem: Any indifferentiable construction of a wn-bit random injection from an n-bit permutation must place at least 2w-2 queries.

slide-77
SLIDE 77

Efficiency Lower Bound

Theorem: Any indifferentiable construction of a wn-bit random injection from an n-bit permutation must place at least 2w-2 queries. Lower/upper bounds remain open for:

ρ := # blocks # queries ∈ [2,3) .

slide-78
SLIDE 78

Summary

RO1 RO2 RO3

M

C RO iEnc S D

New view of AE as a random keyed injection;
 Implies security in many adversarial environments.

slide-79
SLIDE 79

Summary

RO1 RO2 RO3

M

C RO iEnc S D

Thank you. New view of AE as a random keyed injection;
 Implies security in many adversarial environments.