1. (Multimedia University) Ji-Jian Chin Swee-Huay Heng Bok-Min Goi
An Efficient and Provable Secure Identity-Based Identification Scheme in the Standard Model
(Multimedia University)
Ji-Jian Chin
Swee-Huay Heng
Bok-Min Goi

2. Contents 1 Introduction 3 2 Preliminaries 9 Formal Definition of IBI11 4
Construction 16 5
Security Analysis 21 6
Conclusion 25 7
Open Problems 26

3. 1. Introduction
An identification scheme enables one party to identify itself securely to another party authentically and without repudiation.
ID-based cryptography – user generates own public key using an identity string.
ID-based cryptography does away with certificates binding the public key to the private key, as opposed to traditional public key infrastructure systems.

4. 1. Introduction
Why Passwords Aren’t Enough?
If I can guess/know your password, I can impersonate you.
(Easy to guess: keyloggers, peek into your password database, sticky notes with passwords in your office, steal from your hand phone etc)
Why IBI and SI can overcome this?
Challenge-response identification.
Zero-knowledge of secret key involved.

5. 1. Introduction
History of IBI
IBI fundamental paper proposed by Fiat and Shamir in 1984.
Rigorous definition and security proofs only formalized in 2004
- Kurosawa and Heng
- Bellare, Namprempre and Neven
Schemes’ mostly have provable security based on the random oracle model
Schemes’ with provable security in the standard model are not very efficient and few in number

6. 1. Introduction first introduced by Bellare and Rogaway in 1993.
The Random Oracle
first introduced by Bellare and Rogaway in 1993.
The Random Oracle
I answer anybody’s queries with totally
random and uniformly distributed
answers
I’ve seen this New
query before query
Give new random answer, and save query for next time
query
Existing answer

7. 1. Introduction The Random Oracle Disadvantages of RO:
- heuristic in nature
- Canetti et al. showed certain schemes secure in the random oracle model is insecure once implemented
- idealistic: doesn’t exist in real world
Conclusion
- scheme secure in ROM better than no proof at all
- best to prove in standard model

8. 1. Introduction Recent Developments
Kurosawa and Heng proposed the first 2 IBI schemes in the standard model in 2005.
Kurosawa and Heng used a trapdoor commitment scheme and a digital signature scheme to construct another IBI scheme in the standard model in 2006.
Yang et al. proposed a general framework to construct IBI schemes in the random oracle model in 2007.

9. 2. Preliminaries a) Bilinearity. e(ga,gb)=e(g,g)ab
Bilinear Pairings
a) Bilinearity. e(ga,gb)=e(g,g)ab
b) Non-degeneracy. e(g,g) ≠1
c) Efficiently computable.

10. 2. Preliminaries Security Assumptions
a) Security against Passive Attacks:
Computational Diffie-Hellman problem (CDHP)
- Find gab given g and ga ,gb
b) Security against Active/Concurrent Attacks:
One-More Computational Diffie-Hellman Problem (OMCDHP)
- Adversary is given a challenge oracle and a CDH oracle.
Adversary queries random challenge point from challenge oracle and obtains solution by querying the CDH oracle.
Adversary wins the game if at the end the number of queries to the solution oracle is strictly less than the queries to the challenge oracle.

11. 3. Formal Definitions For IBI
Definition of IBI
IBI=(S,E,P,V) - 4 probabilistic, polynomial-time algorithms
The Canonical Three Move Protocol
input param
mpk, usk, ID
mpk, ID
Setup(S)
Prover(P)
(Prove
that
I know
usk)
Verifier(V)
Accept only
if you
Know usk
mpk, msk
CMT ID
Extract(E)
CHA
RSP
usk

12. 3. Formal Definition of IBI
Security Model for IBI
Goal of adversary towards IBI - impersonation.
Considered successful if:
- Interact with verifier as prover with public ID
- Accepted by verifier with non-negligible probability
Stronger assumptions of IBI vs SI:
1. The adversary can choose a target identity ID to impersonate as opposed to a random public key.
2. IBI has access to extract oracle -> the adversary can possess private keys of some users which she has chosen.

13. 3. Formal Definition for IBI
Security Model for IBI
Passive attacks (imp-pa)
Eavesdrop
Active attacks (imp-aa)
Interacts with provers as a cheating verifier
Concurrent attacks (imp-ca)
Interacts with provers as a cheating verifier concurrently.

14. 3. Formal Definition for IBI
Security Model for IBI
The impersonation attack between the impersonator I, and challenger C is described in a two phase game.
Phase 1:
I either extracts transcript queries for imp-pa or acts as a cheating verifier in imp-aa and imp-ca.
Phase 2:
I plays the cheating prover it picks to convince the verifier.

15. 3. Formal Definition for IBI
Security Model for IBI
An IBI scheme is (t,qI,ε)- secure against imp-pa/imp-aa/imp-ca if for any I who runs in
time t, Pr(I can impersonate)<ε, where I can make at most qI queries.

16. 4. Construction
Construction of IBI scheme based on the Waters Signature Scheme
Let and be finite cyclic groups or order and let be a generator of . Let be an efficiently computed bilinear map. Use a collision-resistant hash function to hash identities to an arbitrary length to a bit string of length .

17. 4. Construction
Setup
Select an n-length vector 17

18. 4. Construction ID:hashed user identity string of length n
Extract
ID:hashed user identity string of length n
Let :ith-bit of ID
Let
be the set of all i where di=1 18

19. 4. Construction
Prove and Verify
Prove
Verify
Accept if 19

20. 4. Construction
Correctness 20

21. 5. Security Analysis Theorem 1:
Security against Passive Attacks
Theorem 1:
The proposed IBI scheme is (t,qI,ε)-secure
against impersonation under passive attacks in
the standard model if the CDHP is (t’,ε’)-hard
where
: time for multiplication in
: time for exponentiation in
: extract queries made
: transcript queries made and 21

22. 5. Security Analysis Theorem 2:
Security against Active/Concurrent Attacks
Theorem 2:
The proposed IBI scheme is (t,qI,ε)-secure
against impersonation under active/concurrent
attacks in the standard model if the OMCDHP is
(t”,qCDH,ε”)-hard where
: time for multiplication in
: time for exponentiation in
: extract queries made
: transcript queries made and 22

23. 5. Security Analysis Table 1: Complexity Cost Efficiency
Multiplication
Exponentiation
Pairing
Setup 2
Extract
Max:n+2, Avg:(n/2)+2
Prove
Max:n+1, Avg:(n/2)+1 3
Verify
Max:n+3, Avg:(n/2)+3
Table 1: Complexity Cost 23

24. 5. Security Analysis Table 2: Comparisons with other IBI Efficiency
Efficiency of P and V
Imp-pa assumption
Imp-aa/ca assumption
HKIBI05a
6G,6E,4P
q-SDH
Unknown
HKIBI05b
12G,12E,6P
HKIBI06
9G,11E,3P,1 SOTSS
Proposed IBI
(n+4)G,5E,3P
CDH
OMCDHP
Table 2: Comparisons with other IBI 24

25. 6. Conclusion Merits of Proposed IBI Direct proof
Provable security against both imp-pa and imp-aa/ca in the standard model.
More efficient than other IBI schemes in standard model. 25

26. 7. Open Problems
More IBI schemes that are efficient and provably secure in the standard model.
More IBI Schemes with direct proof to a hard-mathematical problem as opposed to reductions from transformations.
An IBI scheme with provable security against imp-aa/ca using a weaker assumption like DLOG or CDH. 26

27. Thank You Q&A