1. Biometrics-based RSA Cryptosystem for Securing Real-Time Communication
Source : sustainability, Vol. 10, Nol. 10 , pp. 1-15, Oct. 2018
Authors : Xiao-long Liu, Wei-Bin Lee, Quy-Anh Bui, Chia-Chen Lin
Speaker : Feng-yu Chiu
Date : 2019/4/25
1.福建農林大學 逢甲大學 4.靜宜大學

2. Outline Introduction Related works Proposed scheme Security analysis
Conclusions

3. Introduction(1/2)

4. Introduction(2/2)

5. Related works – RSA and unbalanced RSA(1/2)
Generate large prime p, q
G(generator)
t = G(u) (5000bits)
Compute N = pq, φ(N) = (p-1)(q-1)
p (500 bits)
Select e
q ([a, a ]), a ≥ t/p (4500bits)
Compute d, ed = 1(mod φ(N))
s = N – t , publish s
Public key (N, e) ; private key d
C = 𝑀 𝑒 (mod 𝑁)
M = 𝐶 𝑑 (mod 𝑁)

6. Related works –Fuzzy extractors(2/2)
Gen.
𝑃 ∈ {0,1} ∗ 𝑏
R ∈ {0,1} 𝑙 𝑏′
Rep.
If d𝑖𝑠 𝑏, 𝑏 ′ ≤𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑
R ∈ {0,1} 𝑙
𝑃 ∈ {0,1} ∗

7. Proposed scheme -Notation
Notion
Description
Gen.
Generator of Fuzzy Extractors
Rep.
Reproduction of Fuzzy Extractors b
Biometric information P
A helper string for Fuzzy Extractors R
An extracted string for Fuzzy Extractors
p, q
The prime numbers for RSA N
A modules for RSA 𝛼
A security parameter

8. Proposed scheme –Initialization phase
2-1) Capture 𝑏 𝐵
1-1) Capture 𝑏 𝐴
Alice
1-2) Gen( 𝑏 𝐴 ) = 𝑃 𝐴 , 𝑅 𝐴
Bob
2-2) Gen( 𝑏 𝐵 ) = 𝑃 𝐵 , 𝑅 𝐵
1-3) 𝑡 𝐴 = G( 𝑅 𝐴 )
𝑃 𝐴 , 𝑠 𝐴
2-3) 𝑡 𝐵 = G( 𝑅 𝐵 )
1-4) Choose 𝑝 𝐴
2-4) Choose 𝑝 𝐵
𝑃 𝐵 , 𝑠 𝐵
1-5) 𝑎 𝐴 = 𝑡 𝐴 / 𝑝 𝐴
2-5) 𝑎 𝐵 = 𝑡 𝐵 / 𝑝 𝐵
1-6) Choose 𝑞 𝐴 in [ 𝑎 𝐴 , 𝑎 𝐴 + 2 ∝ ]
2-6) Choose 𝑞 𝐵 in [ 𝑎 𝐵 , 𝑎 𝐵 + 2 ∝ ]
1-7) 𝑁 𝐴 = 𝑝 𝐴 ∗ 𝑞 𝐴
2-7) 𝑁 𝐵 = 𝑝 𝐵 ∗ 𝑞 𝐵
2-8) 𝑠 𝐵 = 𝑁 𝐵 − 𝑡 𝐵
1-8) 𝑠 𝐴 = 𝑁 𝐴 − 𝑡 𝐴

9. Proposed scheme –Authentication and key agreement phase
3-1) Capture 𝑏 𝐵 ′
Rep( 𝑏 𝐵 ′, 𝑃 𝐵 )= 𝑅 𝐵
4-1) Capture 𝑏 𝐴 ′
Rep( 𝑏 𝐴 ′, 𝑃 𝐴 )= 𝑅 𝐴
Alice
Bob
3-2) 𝑡 𝐵 = G(𝑅 𝐵 )
𝐶 𝐴 1 , 𝐶 𝐴 2
4-2) 𝑡 𝐴 = G(𝑅 𝐴 )
3-3) 𝑁 𝐵 = 𝑡 𝐵 + 𝑠 𝐵
4-3) 𝑁 𝐴 = 𝑡 𝐴 + 𝑠 𝐴
3-4) Choose 𝐾 𝐴 , 𝑁 𝑎
𝐶 𝐴 1 = 𝐾 𝐴 𝑒 𝐵 mod 𝑁 𝐵
𝐶 𝐴 2 = ( 𝑁 𝑎 ||ℎ 𝐶 𝐴 1 ) 𝑑 𝐴 mod 𝑁 𝐴
4-4) 𝐾 𝐴 = ( 𝐶 𝐴 1 ) 𝑑 𝐵 mod 𝑁 𝐵
𝑁 𝑎 ||ℎ 𝐶 𝐴 1 = ( 𝐶 𝐴 2 ) 𝑒 𝐴 mod 𝑁 𝐴
4-5) Choose 𝐾 𝐵 , 𝑁 𝑏
𝐶 𝐵 1 = 𝐾 𝐵 𝑒 𝐴 mod 𝑁 𝐴
𝐶 𝐵 2 = ( 𝑁 𝑏 ||ℎ 𝐶 𝐵 1 ) 𝑑 𝐵 mod 𝑁 𝐵
𝐾 𝐴𝐵 =H( 𝐾 𝐴 || 𝐾 𝐵 ) = K
5-1) 𝐾 𝐵 = ( 𝐶 𝐵 1 ) 𝑑 𝐴 mod 𝑁 𝐴
𝑁 𝑏 ||ℎ 𝐶 𝐵 1 = ( 𝐶 𝐵 2 ) 𝑒 𝐵 mod 𝑁 𝐵
𝐾 𝐵𝐴 =H( 𝐾 𝐴 || 𝐾 𝐵 ) = K
𝐶 𝐵 1 , 𝐶 𝐵 2

10. Security analysis(1/3)
Comparisons of Attack resistance for various cryptosystem schemes.
[26] Younsung Choi, Youngsook Lee, Jongho Moon ,Dongho Won, “security enhanced multi-factor biometric authentication scheme using bio-hash function,” PLOS ONE, Vol. 12, Nol. 5, May 2017
[27] Ashok Kumar Das, “secure and effective biometric-based user authentication scheme for wireless sensor networks
using smart card and fuzzy extractor,” International Journal of Communication System, Vol. 30, Nol. 1, Jan. 2017

11. Security analysis(2/3) Replay attack 3-4) Choose 𝐾 𝐴 , 𝑁 𝑎
𝐶 𝐴 1 = 𝐾 𝐴 𝑒 𝐵 mod 𝑁 𝐵
𝐶 𝐴 2 = ( 𝑁 𝑎 ||ℎ 𝐶 𝐴 1 ) 𝑑 𝐴 mod 𝑁 𝐴
Server masquerading attack
4-4) 𝐾 𝐴 = ( 𝐶 𝐴 1 ) 𝑑 𝐵 mod 𝑁 𝐵
𝑁 𝑎 ||ℎ 𝐶 𝐴 1 = ( 𝐶 𝐴 2 ) 𝑒 𝐴 mod 𝑁 𝐴
Mutual authentication
Biometric recognition error
User impersonation attack

12. Security analysis(3/3) Database capture attack 3-4) Choose 𝐾 𝐴 , 𝑁 𝑎
𝐶 𝐴 1 = 𝐾 𝐴 𝑒 𝐵 mod 𝑁 𝐵
𝐶 𝐴 2 = ( 𝑁 𝑎 ||ℎ 𝐶 𝐴 1 ) 𝑑 𝐴 mod 𝑁 𝐴
Smart card attack
Man-in-the-middle attack
4-4) 𝐾 𝐴 = ( 𝐶 𝐴 1 ) 𝑑 𝐵 mod 𝑁 𝐵
𝑁 𝑎 ||ℎ 𝐶 𝐴 1 = ( 𝐶 𝐴 2 ) 𝑒 𝐴 mod 𝑁 𝐴
Vulnerability to a DoS attack
Session key agreement
𝐾 𝐴𝐵 =H( 𝐾 𝐴 || 𝐾 𝐵 ) = K

13. Conclusions
Biometrics-based
Without Public Key Infrastructure(PKI)