Improvement of Hwang-Lo-Lin scheme based on an ID-based

cryptosystem

No author given

(Korea information security Agency)

Presented by J.Liu

Outline • Introduction

• Review of the Hwang-Lo-Lin scheme

• Cryptanalysis

• The modified ID-based identification scheme

• Security analysis

• Performance analysis

• Conclusions

Introduction

• ID-based public key cryptosystem.

• Maurer-Yacobi(1996)Tseng-Jan(1998) Hwang-Lo-Lin(2004)Horng-Liu-Liu(2005)

This Letter(2005)

• Hwang et al. developed the improved scheme was suitable for the wireless environment.

Review of the Hwang-Lo-Lin scheme

• TA setup the system parameters as following:1. N = p1p2 p3p4, where pi are primes and their

decimal digits are between 60-70, (pi-1)/2 are odd and pair wise relatively prime.

2. DLP is feasible but factoring N is infeasible.

3. g is a primitive root in each GF(pi).

4. h(.) is an one way hash function.

5. ed = 1 mod (N) and tv = 1 mod (N).

Cont

6. IDb, IDm: identity of base station(BS) and mobile device(M), respectively.

7. sb = et logg(IDb2) mod (N) is secret key for

BS.

8. sm = et logg(IDm2) mod (N) is secret key for

M.

9. T: timestamp

{N, g, e, h(.)}are public parameters and keep {p1, p

2 , p3, p4 , t, v, d } secret.

Login and authentication

1. Choose kR ZN*, computes Y = (IDm2)k mo

d N , Z = (IDb2)ksmT mod N

2. Sends {IDm, Y, Z, T } to BS.

3. BS computes Z’ = (Y)sbT, checks Z = Z’

If yes then… else….

?

Key points

)(mod')(

)()()(.2

}mod){(

mod)(

)(mod)(log

)(mod)(log.1

2

2

2

2

2

2

NZYID

ggIDZ

NgID

NgID

NIDdvs

NIDets

TsTksm

TksdvsTksdvsTksb

dvsm

dvsb

bgb

bgb

bb

bmmbm

m

b

Cryptanalysis

• Attacker forge {IDm, Y1, Z1, T’ } from a valid login message {IDm, Y, Z, T } by Y1 = YrT mod N and Z1 = ZrT’ mod N.

'1

'

''1

)(

)(TsTsrT

rTTsrT

bb

b

YY

YZZ

The modified ID-based identification scheme

• The parameters are the same of Hwang’s scheme, but the 4 primes have bit size more than 1024 bits. (DLP OK? about 300 decimal digits)

1. M sends {IDm, Z, T} to BS, where Z = H((IDb

2)smT mod N)

2. BS verifies by Z = H((IDm2)sbT mod N)

bm sm

ss IDID )()( 22

Security analysis

1. Passive replay attack: Changes timestamp T. H((IDm

2)sbT mod N) H((IDm2)sbT’ mod N)

2. Active replay attack: The attacker can not change Z and T without sm and sb.

3. ID-stolen attack: The same with 2.

Performance analysis

• Without random number generator(hash function).

• Shorter message length (1/2).

• Fewer exponential operation (21).

• More suitable in wireless environment.

Conclusion

• Secure

• More suitable.