1. Anonymous Wireless Authentication on a Portable Cellular Mobile System
Source: IEEE TRANSACTIONS ON COMPUTERS, Vol. 53, NO , OCTOBER 2004
Authors: Shiuh-Jeng Wang, Member, IEEE
Speaker: Pen-Yi Chang, 2004/10/18

2. Outline Introduction Cryptographic Knapsack System
Call Set-Up Authentication Protocol
Hand-Off Authentication Protocol
Anonymous Conference Call Protocol
Conclusion

3. Introduction
Author have proposed a secure and anonymous conference call set-up scheme for a group of mobile units using an identity-based concept as well as a knapsack-like cipher mechanism.

4. Cryptographic Knapsack System
Without loss of generality, the 0/1 knapsack problem of larger vector length is subject to the NP-complete problem
0/1 Knapsack Problem.
C : positive integer
A : a vector (a1, a2, …, an) of positive integer
M : a binary vector (m1, m2, …, mn)
Such that

5. Cryptographic Knapsack System-cont.1
The knapsack variant incorporated into our scheme:
Definition1:
A vector A=(a1, a2 , ai, …, an) is said to be volume-increasing on i, 1≦ i ≦ n iff
If the vector A given in the 0/1 knapsack problem is volume-increasing on i, then
If C≧ai, then mi=1, otherwise, mi=0

6. Cryptographic Knapsack System-cont.2
Problem1:
Find a vector A=(a1, a2, … ,ai …, an) and a set of n constant {λ1, λ2, …, λi, …, λn} such that
λ1*A mod p = (λ1* a1 mod p, λ1*a2 mod p, …, λ1*an mod p)
λ2*A mod p = (λ2* a1 mod p, λ2*a2 mod p, …, λ2*an mod p) …
λn*A mod p = (λn* a1 mod p, λn*a2 mod p, …, λn*an mod p)
are volume-increasing on I for each (λi*A mod p) 1≦i≦n, where p is a large prime and

7. Cryptographic Knapsack System-cont.3

8. Notations MUi : the ith mobile unit BSi : the ith base station
RC : random check number, generate by MSC
Kc : the conference key used by MUi
Ks : the session generate by MUi, used to participate in the construction of Kc
PKC : public key cryptosystem
h : a secure one-way hash function
Ek : Encryption algorithm with private key k

9. Call Set-Up Authentication Protocol
MSC
ARC DB
MUi
BSi
Compute

10. Hand-Off Authentication Protocol
MSC
ARC DB
MUi
BSi
BSi-new

11. Anonymous Conference Call Protocol
Assume that there are at most m+1 mobile units MU0, MU1, …, Mum in a communicating group of our system
Let n=m+l, according to Problem 1, it is then solved to obtain the vector A= (a1, a2, …, an) and the n constants λis.
yi, 1 ≤ i ≤ n, yi=λiai mod p
A, p : public
ai : the public key of the ith mobile.
(λi, yi) : the private keys for the ith mobile

12. Anonymous Conference Call Protocol-cont.1
MSC
ARC DB
MU0
If authentication is successfully completed, then MSC broadcast Z
MUi

13. Anonymous Conference Call Protocol-cont.2
MSC
ARC DB
Check list
Collects the coordinate points ()

14. Example There are six mobiles in the mobile system form Problem 1
A=(a1, a2, a3, a4, a5, a6)
=(1341,5239,13954,2490,15341,4662)
p=54401
(λ1, y1)=(37341,25361), (λ2, y2)=(5965,24461)
(λ3, y3)=(52699,23529), (λ4, y4)=(6979,23791)
(λ5, y5)=(11973,20017), (λ6, y6)=(2316,25794)
assume that the participating mobiles in a conference call are {MU2, MU4, MU6} that is, R=(0,1,0,1,0,1)

15. Example-cont.1 Z=(A)(R)=12391 λ1*Z mod 54401=11826<25361, r1=0

16. Conclusion
We have proposed an anonymous identity-based mutual authentication scheme for holding a conference call.
This so-called anonymity is accomplished by the aspect of a knapsack-like cipher mechanism among the communicating mobile.