11 th October 2017 Leakage Resilience from Lattices Marco Martinoli ( ESR10 ) Supervised by Prof. Elisabeth Oswald and Dr. Martijn Stam University of Bristol
Leaky Lattices 11 th October 2017 HIGHLIGHTS 09/16 – 09/17 I went to NXP for my secondment; I started to write a draft of my long-lasting project; I presented my first paper. Marco 3 - 0 ∗ PhD ∗ Events that might have increased this score are out of scope.
Leaky Lattices 11 th October 2017 Frodo meets ELMO Joint work with Joppe Bos, Simon Friedberger ( ESR12 ), Martijn Stam and Elisabeth Oswald. (a) Frodo (b) ELMO
Leaky Lattices 11 th October 2017 Introducing: ELMO E mulator for power L eakages for the M0 is a tool for simulating power consumption for side-channel measurements; allows evaluating attacks on software running on an ARM Cortex-M0 without requiring a hardware measurement setup; simulates leakage with instruction accuracy; was checked against real leakage measured on an STM32F0 Discovery Board. Available at https://github.com/bristol-sca/ELMO .
Leaky Lattices 11 th October 2017 Introducing: Frodo Available at https://github.com/lwe-frodo/lwe-frodo .
Leaky Lattices 11 th October 2017 Profiling A [0 , 0] A [0 , 1] A [0 , 2] S [0 , 0] S [0 , 1] S [0 , 2] · A [1 , 0] A [1 , 1] A [1 , 2] S [1 , 0] S [1 , 1] S [1 , 2] A [2 , 0] A [2 , 1] A [2 , 2] S [2 , 0] S [2 , 1] S [2 , 2]
Leaky Lattices 11 th October 2017 Profiling A [0 , 0] A [0 , 1] A [0 , 2] S [0 , 0] S [0 , 1] S [0 , 2] · A [1 , 0] A [1 , 1] A [1 , 2] S [1 , 0] S [1 , 1] S [1 , 2] A [2 , 0] A [2 , 1] A [2 , 2] S [2 , 0] S [2 , 1] S [2 , 2]
Leaky Lattices 11 th October 2017 Profiling A [0 , 0] A [0 , 1] A [0 , 2] S [0 , 0] S [0 , 1] S [0 , 2] · A [1 , 0] A [1 , 1] A [1 , 2] S [1 , 0] S [1 , 1] S [1 , 2] A [2 , 0] A [2 , 1] A [2 , 2] S [2 , 0] S [2 , 1] S [2 , 2]
Leaky Lattices 11 th October 2017 Profiling A [0 , 0] A [0 , 1] A [0 , 2] S [0 , 0] S [0 , 1] S [0 , 2] · A [1 , 0] A [1 , 1] A [1 , 2] S [1 , 0] S [1 , 1] S [1 , 2] A [2 , 0] A [2 , 1] A [2 , 2] S [2 , 0] S [2 , 1] S [2 , 2]
Leaky Lattices 11 th October 2017 Attack techniques LWE-based key agreement protocol implies: weakly non-linear operations; internal secrets must be freshly regenerated at every invocation. DPA-style attacks need a lot of traces which are not provided. But secrets are small, hence there is a very small number of possible guesses to build template for.
Leaky Lattices 11 th October 2017 Template profiles q = 2 11 , n = 352 , S [0 , 0] ∈ { 0 , ± 1 , ± 2 , ± 3 } ← χ
Leaky Lattices 11 th October 2017 Template profiles: loading − 1 11111111111 − 2 11111111110 − 3 11111111101 +3 00000000011 +2 00000000010 +1 00000000001 0 00000000000 Depends on S [0 , 0] only, constant with varying A [0 , 0] .
Leaky Lattices 11 th October 2017 Template profiles: multiplication − 1 11111111111 − 3 11111111101 − 2 11111111110 +3 00000000011 +1 00000000001 +2 00000000010 0 00000000000 A [0 , 0] contributes to power consumption too.
Leaky Lattices 11 th October 2017 Signal variance
Leaky Lattices 11 th October 2017 SNR comparison
Leaky Lattices 11 th October 2017 SCA of Frodo Where we are: set up simulations and profiling; template matching in noiseless case; analysis of noise in PoI;
Leaky Lattices 11 th October 2017 SCA of Frodo Where we are: set up simulations and profiling; template matching in noiseless case; analysis of noise in PoI; template attack for first order recovery; alternative implementations;
Leaky Lattices 11 th October 2017 SCA of Frodo Where we are: set up simulations and profiling; template matching in noiseless case; analysis of noise in PoI; template attack for first order recovery; alternative implementations; shuffling; including leakage in BKZ to boost lattice attacks.
Leaky Lattices 11 th October 2017 Totally non singular key update mechanism Joint work with Martijn Stam and Elisabeth Oswald. Setting is continuous d -probing model. ← KeyGen ( n ) s (˙ s 0 , ¨ s 0 ) ← Share ( s ) ˙ (˙ s i , O i ) ← Update (˙ s i − 1 ) ¨ ¨ s i ← Update (¨ s i − 1 , O i ) ← Recombine (˙ s i , ¨ s i ) s
Leaky Lattices 11 th October 2017 Totally non singular KU mechanism Target is LWE public key encryption scheme over Z q for a prime q , secret is s ∈ Z n q . Share ( s ) = (˙ s , ¨ s ) such that � � � = + � � � �� � � �� � � �� � � �� � s B s ˙ ¨ s B needs to be TNS to avoid linear dependencies among positions of the secret.
Leaky Lattices 11 th October 2017 TNS KU mechanism Where we are: Share is secure; leak-free Update is secure;
Leaky Lattices 11 th October 2017 TNS KU mechanism Where we are: Share is secure; leak-free Update is secure; Update is secure;
Leaky Lattices 11 th October 2017 TNS KU mechanism Where we are: Share is secure; leak-free Update is secure; Update is secure; composition of KU + Dec is secure;
Leaky Lattices 11 th October 2017 Future work and more ideas Finalise side-channel analysis of Frodo and TNS KU mechanism. Glitchtool, joint work with Erik Boss ( ESR6 ), Duˇ san Boˇ zilov ( ESR13 ), Miroslav Kneˇ zevi´ c, Ventzi Nikov. Involutory SBoxes, joint work with Erik Boss ( ESR6 ), Ralph Ankele ( ESR7 ). BKZ on leaky lattices, joint work with Matthias Minihold ( ESR5 ).
Leaky Lattices 11 th October 2017 Related activities Secondment: NXP Semiconductors, Leuven (BE) ; Outreach: Digimaker on 11 th November, Bristol; Teaching: Security 101, Cryptography A; Travels: SPACE16, RWC17, School on lattices in Oxford, Eurocrypt17, second London Crypto day. Subreviewer: Crypto17, Asiacrypt17, SPACE17, Transaction on Computers 2017, CT-RSA17.
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