Error Correction for Physical Unclonable Functions Using Generalized - PowerPoint PPT Presentation

Ulm University Communications Engineering Error Correction for Physical Unclonable Functions Using Generalized Concatenated Codes uelich ∗ , Sven Puchinger ∗ , Martin Bossert ∗ , Sven M¨ Matthias Hiller ⋄ , Georg Sigl ⋄ ∗ Institute of Communications Engineering, Ulm University, Germany ⋄ Institute for Security in Information Technology, TU Munich, Germany ITG Fachgruppe ”Angewandte Informationstheorie” Munich, October 9, 2014 Sven M¨ uelich Error Correction for Physical Unclonable Functions 1

Ulm University Communications Engineering A Outline NACHRICHTENTECHNIK Motivation 1 Physical Unclonable Functions (PUFs) 2 Example Code Construction 3 Conclusion 4 Sven M¨ uelich Error Correction for Physical Unclonable Functions 2

Ulm University Communications Engineering A Motivation NACHRICHTENTECHNIK Challenges when implementing a cryptosystem: Secure key generation Random, unique and unpredictable keys Satisfying these properties is hard to achieve Secure key storage Key bits in a non-volatile memory Adversaries can gain physical access to (protected) memories Physical Unclonable Functions (PUFs) can be used to realize secure key generation and secure key storage Sven M¨ uelich Error Correction for Physical Unclonable Functions 4

Ulm University Communications Engineering A Physical Unclonable Functions (PUFs) NACHRICHTENTECHNIK What is a PUF? Physical entity with challenge-response behavior Properties: Uniqueness Reproducibility 10111001 0 1 1 1 0 0 1 1 10111001 0 1 1 1 0 0 1 1 PUF 1 PUF 1 10111001 PUF 2 1 0 0 1 1 1 0 1 10111001 PUF 1 0 1 1 0 1 0 1 1 Uniqueness Reproducibility Sven M¨ uelich Error Correction for Physical Unclonable Functions 6

Ulm University Communications Engineering A Physical Unclonable Functions (PUFs) NACHRICHTENTECHNIK Example: SRAM PUFs device with memory cells random initialization when powering on randomness static over lifetime Challenge: Subset of memory cells 0 0 1 1 1 1 0 0 1 1 0 0 · · · Response: Values in selected m m 1 1 2 2 3 3 4 4 5 5 memory cells Sven M¨ uelich Error Correction for Physical Unclonable Functions 7

Ulm University Communications Engineering A Physical Unclonable Functions (PUFs) NACHRICHTENTECHNIK Why coding theory? Responses are not perfectly reproducible and hence cannot be used as key directly Helper r = c + e Sketch e PUF Data Function Storage r ′ = c + e + e ′ e ˆ r = ˆ c + e Recover Key Hash Function Sven M¨ uelich Error Correction for Physical Unclonable Functions 8

Ulm University Communications Engineering A Example Code construction NACHRICHTENTECHNIK Challenge: Find good codes for Secure Sketches Constraints: Time and area consumption Binary codes Dimension ≥ key length Codelength as small as possible Sven M¨ uelich Error Correction for Physical Unclonable Functions 10

Ulm University Communications Engineering A Example Code construction NACHRICHTENTECHNIK Existing scheme given in [Maes2012] 1 : Binary Symmetric Channel with p = 0 . 14 Generate 128 bit key with block error probability P err = 10 − 9 Concatenation of (318 , 174 , 35) BCH code and (7 , 1 , 7) code What is our goal? Generate 128 bit key with block error probability P err < 10 − 9 Improve existing scheme in Codelength Block error probability Simple implementation 1 R. Maes, A. Herrewege, I. Verbauwhede, ”PUFKY: A Fully Functional PUF-Based Cryptographic Key Generator”, CHES, 2012 Sven M¨ uelich Error Correction for Physical Unclonable Functions 11

Ulm University Communications Engineering A Reed-Muller Example Code Construction NACHRICHTENTECHNIK Partitioning: B (1) (16 , 5 , 8) Level 1 . . . − A (1) (128 , 8 , 64) 0000 1111 ← B (2) B (2) . . . 0000 (16 , 1 , 16) 1111 (16 , 1 , 16) Level 2 . . . − A (2) (128 , 99 , 8) 0 1 0 1 ← B (3) B (3) B (3) B (3) . . . Level 3 0000 , 0 0000 , 1 1111 , 0 1111 , 1 Sven M¨ uelich Error Correction for Physical Unclonable Functions 12

Ulm University Communications Engineering A Reed-Muller Example Code Construction NACHRICHTENTECHNIK Used decoding methods: Generalized Concatenated Codes (GC Codes) RM Error Erasure Decoding Generalized Minimum Distance (GMD) Decoding Sven M¨ uelich Error Correction for Physical Unclonable Functions 13

Ulm University Communications Engineering A Conclusion NACHRICHTENTECHNIK How good is our code construction? Code P err Length Largest Field [Maes2012] ≈ 10 − 9 2226 F 2 8 (BCH) ≈ 5 . 37 · 10 − 10 New 2048 F 2 Sven M¨ uelich Error Correction for Physical Unclonable Functions 15

Ulm University Communications Engineering Thank you for your attention. Sven M¨ uelich Error Correction for Physical Unclonable Functions 16