Biometric Verification Schemes for Gaussian Data

1. Biometric Verification Schemes for Gaussian Data V. Balakirsky and A.J. Han Vinck ISITA October 2010, Taichun, Taiwan University Duisburg-Essen

2. Biometrics used as a key/password I am Han, can I come in? • - verify claimed identity with stored information • problems: • Errors: false rejection (FRR)/ false acceptance (FAR) • Leakage: privacy / information about bio from Data Base • Attacks: generation of fake system inputs (wolves) A.J. Han Vinck 2

3. content • Gaussian assumptions of the biometric data • to go to binary gives loss • Verification algorithm • Data compression for privacy reasons • Attacks

4. Introduction to the problemsituation where verifier has to make the accept decision Enrolment channel W(x|z), σ2 verifier x W Acc Rej= false rejection  z W‘ y Verificationchannel W‘(y|z), ρ2 Enrolment channel and verification channel can be different - more measurements and different sensors

5. Introduction to the problemsituation where verifier has to make the reject decision Enrolment channel W(x|z), σ2 verifier x W Rej Acc= false acceptance  z  z‘ y W‘ Another user with the same probability distribution

6. Create an input („wolf“) and verifysituation where verifier has to make the reject decision Enrolment channel W(x|z), σ2 verifier x W Rej Acc= false acceptance  z 0 y W‘

7. Create a direct input („wolf“)situation where verifier has to make the reject decision Enrolment channel W(x|z), σ2 verifier x W Rej Acc= false acceptance  z y „wolf“ A sequence of direct inputs

8. PDF‘s for the model x W z W‘ y Enrolment channel and verification channel can be different - more measurements and different sensors

9. Example of the PDFs V(y|x) σ2 x z μ2 y ρ2 Decision region False Reject y - x‘i + Note: the expected value of yi under the „acc“ hypothesis differs from xi

10. FAR, another user σ2 Decision region x z μ2 y z‘ ρ2 ФFAR(y i) y - x‘i + 10

11. FAR, input 0 vector („wolf“ 1) σ2 Decision region x z μ2 y 0 ρ2 ФFAR(y i) y - x‘i +

12. input 0 vector directly („wolf“ 2) σ2 2δ x z μ2 y 0 y x-i x‘i x+i Probability that „wolf“ inside decision region Assume input: 0 condition: x-i < 0 => xi < + δ ( μ 2 + σ2)/ μ 2 x+i > 0 => xi > - δ ( μ 2 + σ2)/μ 2 Therefore: FAR(„wolf“)=

13. Summary so FAR σ2 x z μ2 y z‘ other user ρ2 σ2 x z μ2 y 0 wolf-1 ρ2 σ2 x μ2 z y 0 wolf-2

14. Change strategy to improve privacystore only average of n components System: G(n1, 0, σ2) enrolment G(z, 0, μ2) z + n1 Aaron Wyner verification z + n2 G(n2, 0, ρ2) G(n1, 0, σ2) G(z, 0, μ2) ∑ verification ∑ G(n2, 0, ρ2)

15. Change strategy to improve privacystore only average of n components System: enrolment verification G(n1, 0, σ2) G(z, 0, μ2) ∑ verification ∑ G(n2, 0, ρ2) 15

16. Transformation of the dependencyfrom x => y to a => b (T blocks of length n) verifier a = pw(x) Rej Acc= false acceptance b =pw(y) Transformation of dependency

17. consequence • Same FAR - FRR if we change decision region from • but high privacy due to compression • Processing T blocks: • Accept: # of accepts > # of rejects • Otherwise Reject • Result: • improvement by looking at Euclidean distance 17

18. Gaussian Fuzzy Commitmentmasking the bio at enrollmentent R C Code word (n,k) code DCT Stored at enrollment G(n1, 0, σ2) c G(z, 0, μ2) c + n1 +z - observable by attacker z + n2 at verification G(n2, 0, ρ2) 18

19. Gaussian Fuzzy CommitmentEquivalent wiretappresentation Enrol - verify = decode R (c + n1 +z) - (z + n2)= c + n1 - n2 C decode c c + n1 - n2 DCT c Joint decoding c + n1 +z wiretap Encode given z There is an exchange between security and privacy 19

20. conclusions • We presented a direct verification scheme for Gaussian data • To improve privacy (hiding): • we store a compressed biometric (average) • Same performance, but high expected privacy • Relation with „wire tapper“ • => Juels-Wattenberg fuzzy commitment scheme • => Exchange between privacy and security • Processing T blocks of length n improves performance

21. FAR, another user σ2 x z decision region μ2 y 0 ρ2 ФFAR(b i) y a-i a‘i a+i

22. LOW PRIVACY => Transformation into a password Enrolment channel W(x|z), σ2 verifier a = pw(x) x pw W 1 Rej Acc= false acceptance n  z b =pw(y) W‘ y pw Verificationchannel W‘(y|z), ρ2 Enrolment channel and verification channel can be different - more measurements and different sensors

23. Transformation into a passwordFAR for another user Enrolment channel W(x|z), σ2 verifier a = pw(x) x pw W 1 Rej Acc= false acceptance n  z b =pw(y)  z‘ y pw W‘ Enrolment channel and verification channel can be different - more measurements and different sensors

24. Wolf 1 Enrolment channel W(x|z), σ2 verifier a = pw(x) x pw W 1 Rej Acc= false acceptance n  z b =pw(y) 0 pw A sequence of direct inputs 24

25. „wolf“ 2 Enrolment channel W(x|z), σ2 verifier a = pw(x) x pw W 1 Rej Acc= false acceptance n  z y A sequence of direct inputs

26. Example of the PDFs V(b|a) σ2 x μ2 z acceptance region y ρ2 y a-i a‘i a+i

27. wolf 1 σ2 x z decision region μ2 y 0 ρ2 ФFAR(b i) y a-i a‘i a+i

28. wolf 2 σ2 x z decision region μ2 y 0 y a-i a‘i a+i