Statistical Fault Attacks on Nonce-Based Authenticated Encryption - - PowerPoint PPT Presentation

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Statistical Fault Attacks on Nonce-Based Authenticated Encryption - - PowerPoint PPT Presentation

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Statistical Fault Attacks on Nonce-Based Authenticated Encryption Schemes C. Dobraunig 1 , M. Eichlseder 1 , T. Korak 1 , V. Lomn e 2 , F. Mendel 1 AsiaCrypt 2016 1 Graz University of Technology, Austria 2 ANSSI, Paris, France

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Statistical Fault Attacks on Nonce-Based Authenticated Encryption Schemes

  • C. Dobraunig1, M. Eichlseder1, T. Korak1, V. Lomn´

e2, F. Mendel1 AsiaCrypt 2016

1 Graz University of Technology, Austria 2 ANSSI, Paris, France

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Overview

Fault attacks on AES-based AE-schemes

Nonce does not preclude fault attacks Based on Fuhr et al. (FDTC 2013) Faults influence distribution

Experiments to show practical relevance

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Statistical Fault Attack

SB SR AKequ SB SR AK MC C

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Application to Authenticated Encryption

Requirements for the Attack 1 The inputs need to be different for each fault 2 The block cipher output needs to be known

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Application to Authenticated Encryption

Authenticated encryption modes for block ciphers (ISO/IEC) CCM EAX GCM OCB

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Attack on CCM

NCTR0 ⊞ CTR1 · · · ⊞ CTRd 1 1 Ek Ek Ek S P1 ⊕ · · · Pd ⊕ C1 · · · Cd S V ⊕ · · · ⊕ ⊕ Ek Ek trunc T

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Attack on CCM

NCTR0 ⊞ CTR1 · · · ⊞ CTRd 1 1 Ek Ek Ek S P1 ⊕ · · · Pd ⊕ C1 · · · Cd S V ⊕ · · · ⊕ ⊕ Ek Ek trunc T

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Attack on OCB

P1 ∆1 ⊕ Ek ∆1 ⊕ C1 Pd−1 ∆d−1 ⊕ Ek ∆d−1 ⊕ Cd−1 . . . . . . . . . Pd0∗ ∆∗ Ek ⊕ Cd Mi ∆$ ⊕ Ek V ⊕ T

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Attack on OCB

P1 ∆1 ⊕ Ek ∆1 ⊕ C1 Pd−1 ∆d−1 ⊕ Ek ∆d−1 ⊕ Cd−1 . . . . . . . . . Pd0∗ ∆∗ Ek ⊕ Cd Mi ∆$ ⊕ Ek V ⊕ T

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Application to other schemes

rand rand rand ∆k ⊕ Ek Ek Et

k

∆k ⊕ C C C

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XEX-like Construction

Output masked by ∆k

∆k := δk ∆k := δk + δn ∆k := δk,n

Example: COPA rand ∆k ⊕ Ek ∆k ⊕ C

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Attack on COPA

P1 P2 Pd Pi 3L ⊕ 2 · 3L ⊕ 2d−13L ⊕ 2d−132L ⊕ Ek Ek Ek Ek V ⊕ ⊕ · · · ⊕ ⊕ L Ek Ek Ek Ek 2L ⊕ 22L ⊕ 2dL ⊕ 2d7L ⊕ C1 C2 Cd T L = Ek(0)

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Attack on COPA

P1 P2 Pd Pi 3L ⊕ 2 · 3L ⊕ 2d−13L ⊕ 2d−132L ⊕ Ek Ek Ek Ek V ⊕ ⊕ · · · ⊕ ⊕ L Ek Ek Ek Ek 2L ⊕ 22L ⊕ 2dL ⊕ 2d7L ⊕ C1 C2 Cd T L = Ek(0)

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Attack on COPA

Idea: Consider 2L as part of the last subkey

SK ′

10 := SK10 ⊕ 2L

Apply SFA to recover SK ′

10

Repeat attack to either recover

SK9 (in round 9) or SK ′′

10 := SK10 ⊕ 22L of the next block the get SK10

⇒ Attack complexity (number of needed faults) is doubled

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XEX-like Construction

Output masked by ∆k

∆k := δk ∆k := δk + δn ∆k := δk,n

rand ∆k ⊕ Ek ∆k ⊕ C

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Tweakable Block Cipher

TWEAKEY framework

Deoxys KIASU . . .

rand Et

k

C

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Attack on Deoxys=

P1 Pd Pi E0,N,0

k

· · · E0,N,d−1

k

E1,N,d−1

k

⊕ V C1 Cd T Similar to OCB

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Attack on Deoxys=

P1 Pd Pi E0,N,0

k

· · · E0,N,d−1

k

E1,N,d−1

k

⊕ V C1 Cd T Similar to OCB

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Attack on Deoxys=

Deoxys-BC-256

k h 2 h · · · h 2 t h h · · · h ⊕ RC0 ⊕ RC1 ⊕ RC13 ⊕ RC14 SK0 SK1 SK13 SK14 P ⊕ f ⊕ f · · · ⊕ f ⊕ C

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Summary of Results

Primitive Classification Comments CCM basic CTR GCM basic CTR EAX basic CTR OCB basic XE Cloc/Silc∗ basic CFB OTR∗ basic XE COPA∗ XEX ELmD∗ XEX SHELL∗ XEX KIASU∗ TBC Deoxys∗ TBC

∗ CAESAR candidates 15 / 21

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Practical Verification/Implementation

Clock glitches

General-purpose microcontroller AES software implementation AES hardware co-processor

Laser fault injection

Smartcard microcontroller AES hardware co-processor

⇒ Key-recovery with a small number of faulty ciphertexts

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ATxmega 256A3

10 20 30 40 50 60 70 80 2−5 2−4 2−3 2−2 2−1 number of faulty encryptions SEI correct key wrong keys Software implementation Single clock glitch

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ATxmega 256A3

10 20 30 40 50 60 70 80 2−5 2−4 2−3 2−2 2−1 number of faulty encryptions SEI correct key wrong keys Software implementation Multiple clock glitches

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Smartcard Microcontroller

10 20 30 40 50 60 70 80 2−5 2−4 2−3 2−2 2−1 number of faulty encryptions SEI correct key wrong keys AES co-processor Laser

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Summary

SFA is a powerful tool Nonce is not enough Attacks are not limited to AES-based modes

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Thank you

http://eprint.iacr.org/2016/616

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References

  • E. Biham and A. Shamir

Differential Fault Analysis of Secret Key Cryptosystems CRYPTO 1997

  • D. Boneh, R. A. DeMillo, and R. J. Lipton

On the Importance of Checking Cryptographic Protocols for Faults EUROCRYPT 1997

  • J. Bl¨
  • mer and V. Krummel

Fault Based Collision Attacks on AES FDTC 2006

  • T. Fuhr, ´
  • E. Jaulmes, V. Lomn´

e, and A. Thillard Fault Attacks on AES with Faulty Ciphertexts Only FDTC 2013

  • C. Dobraunig, M. Eichlseder, T. Korak, V. Lomn´

e, and F . Mendel Statistical Fault Attacks on Nonce-Based Authenticated Encryption Schemes ASIACRYPT 2016