Public-Key Encryption in the Bounded-Retrieval Model PowerPoint Presentation, PPT - DocSlides

Public-Key Encryption in the Bounded-Retrieval Model PowerPoint Presentation, PPT - DocSlides

2016-05-21 96K 96 0 0

Description

Joël. Alwen, . Yevgeniy. . Dodis. , . Moni. . Naor. ,. Gil . Segev. , . Shabsi. . Walfish. , . Daniel . Wichs. . Earlier Today: . Yevgeniy. covered . ID schemes, Signatures, Interactive Encryption/Authentication/AKA. ID: 329478

Embed code:

Download this presentation



DownloadNote - The PPT/PDF document "Public-Key Encryption in the Bounded-Ret..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.

Presentations text content in Public-Key Encryption in the Bounded-Retrieval Model

Slide1

Public-Key Encryption in the Bounded-Retrieval Model

Joël Alwen, Yevgeniy Dodis, Moni Naor, Gil Segev, Shabsi Walfish, Daniel Wichs

Earlier Today:

Yevgeniy

covered

ID schemes, Signatures, Interactive Encryption/Authentication/AKA

Slide2

Leakage Resilience and the BRM

Leakage Resilience: Cryptographic schemes that remain secure even if adversary learns partial information about sk.Goal: High relative leakage.Bounded Retrieval Model: Absolute size of leakage can be arbitrarily large (bits, Mb, Gb…).Accommodate any leakage threshold by increasing key size flexibly.No other loss of efficiency!

sk

leak

f(sk)

90% of |sk|

[AGV09, NS09,…]

[Dzi06, CLW06,…]

Slide3

Why have schemes in the BRM?

Security against viruses:Virus downloads arbitrary information from local storage and sends it to a remote attacker.In practice, virus cannot download too much (< 10 GB).Bandwidth too low, Cost too high, System security may detect.Security against side-channel attacks:Adversary gets some “physical output” of computation.May be unreasonable to learn “too much” info, even after many physical readings.How much is “too much” depends on physical implementation (few Kb - few Mb).

Slide4

Prior Work

Leakage Resilience (

No BRM

):

Symmetric-Key Authenticated Encryption [DKL09]

Public-Key

Encryption

[AGV09, NS09, KV09]

Signatures [ADW09, Katz09]

Bounded Retrieval Model:

Secret Sharing [DP07]

Symmetric-Key Identification and Authenticated Key Agreement [Dzi06,CDD

+

07]

Public-Key

ID schemes

,

Signatures

,

Authenticated Key Agreement [ADW09]

Now:

Public-Key

Encryption in

the BRM.

Slide5

Public-Key Encryption in the BRM

Goal: PKE parameterized by security parameter

s

(e.g. 256 bits) and leakage bound

L

(e.g. 256 bits - 10GB).

Secret Key size is flexible: |

sk

| = (1 +

ε

)

L.

Public Keys and

Ciphertexts

are short, only depend on

s

.

Decryption is local. Number of bits accessed is proportional to

s

.

Naïve Attempt : “Take any leakage-resilient PKE tolerating

l

(|

sk

|) leakage. Increase security parameter

s

until

l

(|

sk

|) >

L

.”

Problem:

Public-key/

Ciphertext

size depends on L. May be huge.

Problem:

Decryption is not local.

Problem:

Computation over groups with 10 GB description length.

Positive:

Very Secure!

Slide6

PKE in the BRM via Composition of PKE

Attempt #1: “Compose n copies of Leakage-Resilient PKE”Generate n pairs (pk1,sk1),…, (pkn, skn). Set PK = (pk1,…, pkn), SK = (sk1,…, skn).To encrypt m: Compute shares (s1,…, sn) such that m = s1 + …+ sn. Set c1=Enc(pk1, s1),…, cn=Enc(pkn, sn). Ciphertext is C = (c1 ,…, cn).Hope: Composed scheme amplifies leakage from l to L = n l bits without unnecessary increase in security parameter.Intuition: To break the composed scheme, must leak l bits about each of (sk1,…, skn).Unfortunately ciphertext size, public key size and locality are still large.

Can intuition be formalized? Stay tuned…

pk

1

pk

2

pk

n

PK

SK

sk

1

sk2

skn

Slide7

PKE in the BRM via Composition of IBE

Attempt #2: Use Leakage-Resilient IBE to Reduce Public-Key Size.Generate a master-key pair (MPK, MSK) for an IBE. Use MSK to generate keys sk1,…, skn for identities 1,…,n. Set PK = MPK, SK = (sk1,…, skn). Delete MSK.To encrypt m: Compute shares (s1,…, st) such that m = s1 + …+ st. Choose t random identities IDi ∊ [n].Set c1=Enc(ID1, s1),…, cn=Enc(IDt, st).Ciphertext is C = (ID1 ,…, IDt , c1 ,…, ct).Good news: Ciphertext, Public-Key, Locality is proportional to security parameter.Need leakage resilient IBE. (Of Independent Interest)Is the composition secure?

MPK

SK

sk

1

sk

2

sk

n

ID=1

ID=2

ID=n

Random Subset of [n]

Slide8

Does Composition Amplify Leakage Resilience?

Composition of Leakage-Resilient PKE (Attempt 1):

Intuition

does not

formalize into a reduction.

Problem:

cannot simulate

L

bits leakage on SK = (sk

1

,…,

sk

n

) by leaking only

l

< L

bits of sk

i

.

Do not know of an counterexample (even artificial).

but black-box reductions won’t work…

Composition using Leakage-Resilient IBE (Attempt 2):

Have an (artificial)

counterexample

.

Idea: secret keys of identities 1,…,n contain secret-sharing of master secret key.

Good news

: composition amplifies leakage resilience for PKE/IBE of

special form.

Based on hash-proof-systems [CS02, NS09].

Slide9

Leakage Resilience from Hash-Proof Systems

Earlier today: construction of Leakage-Resilient PKE from Hash-Proof Systems [NS09].

R= {(

pk,sk

) pairs}.

Many valid

sk

for each

pk

.

Three algorithms

(

Encap

,

BadEncap

,

Decap

)

Good encapsulation:

(e, k) =

Encap

(

pk

).

Bad encapsulation:

e =

BadEncap

(

pk

).

Decapsulation

:

k =

Decap

(e,

sk

).

Can’t distinguish if

e

is good or

bad

(even given

sk

).

For fixed

pk

, bad

e

:

Decap

(

e

,sk

)

is statistically uniform.

Encryption/Decryption: use

k

as a one-time-pad.

Encrypt(m,

pk

) = (e,

k+m

)

where

(

e,k

) =

Encap

(

pk

).

Slide10

Composition of Hash Proof Systems

Let PK = (pk

1

,…, pk

n

), SK = (sk

1

,…, sk

n

).

Encrypt(m,pk) = (E, K+m) where

E = (e

1

,…, e

n

, r) for (e

i

, k

i

) = Encap(pk

i

)

K = Extract(k

1

,…, k

n

; r)

Slide11

Theorem: Composition of Hash-Proof Systems Amplifies Leakage

Show that: E = [e1,…, en, r], Leak(SK), K = Extract(k1,…, kn; r) Where (ei ,ki ) = Encap(pki) E = [e1,…, en, r], Leak(SK), K = Extract(k1,…, kn; r) Where ei = Encap(pki), ki = Decap(ei , ski) E = [e1,…, en, r], Leak(SK), K = Extract(k1,…, kn; r) Where ei = BadEncap(pki), ki = Decap(ei , ski) E = [(e1,…, en), r], Leak(SK), Uniform

|Uniform| = n|ki | - |Leak(SK)| - O(S)

INDISTINGUISHABLE

Slide12

How to get PKE in BRM?

Recap: “Attempt 1” scheme can be fixed using Hash-Proof Systems.Long ciphertexts, public-keys, and no locality.How to fix “Attempt 2” scheme based on IBE?Need “Identity Based Hash-Proof System” (IB-HPS).Formalized this new notion.Result 1: IB-HPS gives us Leakage-Resilient IBE.Result 2: IB-HPS gives us efficient PKE in BRM.Resulting IBE is used to instantiate “Attempt 2” scheme.Constructions?

Slide13

Constructing IB-HPS

Construction based on the [Gentry06] IBE .

Based on “q-ABDHA” (pairing stuff....)

Allows leakage of (½ -

ε

) of secret key.

Construction based on [GPV08] IBE.

Based on “LWE” (lattice stuff + RO)

Proven as leakage-resilient IBE by [AGV09].

Allows leakage of (1 -

ε

) of secret key.

Slide14

Slide15

Slide16


About DocSlides
DocSlides allows users to easily upload and share presentations, PDF documents, and images.Share your documents with the world , watch,share and upload any time you want. How can you benefit from using DocSlides? DocSlides consists documents from individuals and organizations on topics ranging from technology and business to travel, health, and education. Find and search for what interests you, and learn from people and more. You can also download DocSlides to read or reference later.