1. Security of a Remote Users Authentication Scheme Using Smart Cards
Author: Her-Tyan Yeh, Hung-Min Sun, Bin-Tsan Hsieh
Source: IEICE transactions on Communications, Vol. E87-B, No.1, Jan
Speaker: Chih-Chiang Tsou
Date:

2. Outline Introduction Elgamal’s public key cryptosystem
Hwang and Li’s scheme
Chan and Cheng’s attack
Proposed attack
Conclusions

3. Introduction Remote password authentication User System Login
Insecure channel

4. Elgamal’s public key cryptosystem
P is a prime number, (P-1) has a large prime factor.
g is the primitive element in GF(P).
Ui has a secret key xi and a public key yi ,
If A wants to send M to B, A selects a random number r, and calculates
Then A uses the public key yb of B and a random number r to encipher M:

5. Elgamal’s public key cryptosystem
A sends (C1,C2) to B
B can decipher M:

6. Hwang and Li’s scheme 1. Registration 2. Login x : System secret key
P : Large prime
f: one-way function
S: Smart card ( f , P )
1. Registration
IDi
(PWi ,S)
Secure channel
User (Ui)
2. Login
System
. random number r .
After receive the Authentication message at time T’
Check the validity of IDi
Check if
(IDi ,C1 , C2 ,T)

7. Hwang and Li’s scheme (example)
f: one-way function
S: Smart card ( f , 17 )
1. Registration
IDi=10
(14 ,S)
Secure channel
User (Ui)
2. Login
System
. random number 5 .
After receive the Authentication message at time T’
Check the validity of IDi
Check
(10 ,6 , 8 ,T)

8. Chan and Cheng’s attack
Bob is a legitimate user.
Bob has a smart card, IDb and PWb
He wants to create a valid pair (IDf , PWf)
He computes
computes

9. Chan and Cheng’s attack (example)
Bob has a smart card, IDb=10 and PWb=14
He wants to create a valid pair (IDf , PWf)
He computes
Computes
System checks if

10. Proposed attack If Bob wants to impersonate the legal user Ui .
Computes
Submits IDE to the system for registration and then receives PWE and a smart card.

11. Proposed attack
Because P is a large prime and gcd( PWE , P )=1. By quadratic residues, PWi can be easily found.

12. Proposed attack (example)
If Bob wants to impersonate the legal user Ui .(IDi = 10)
Computes
Submits IDE =15 to the system for registration and then receives PWE = 9 and a smart card.

13. Conclusions
The authors proposed another impersonation attack to show that Hwang and Li’s scheme is not secure.
This attack is more powerful than the Chan and Chen’s attack that was proposed in 2000.