Introduction RSM: Rotating Sboxes Masking Information Theoretic Evaluation of RSM Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives Formal Analysis of the Entropy / Security Trade-off in First-Order Masking Countermeasures against Side-Channel Attacks Maxime Nassar, Sylvain Guilley and Jean-Luc Danger Bull TrustWay, Rue Jean Jaur` es, B.P. 68, 78 340 Les Clayes-sous-Bois, France. Institut TELECOM / TELECOM ParisTech, 46 rue Barrault, 75 634 Paris Cedex, France. Secure-IC S.A.S., 80 avenue des Buttes de Co¨ esmes, 35700 Rennes, France. Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 1
Introduction RSM: Rotating Sboxes Masking Information Theoretic Evaluation of RSM Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives Introduction 1 Side-Channel Analysis (SCA) Countermeasures Goal of the Presentation RSM: Rotating Sboxes Masking 2 Rationale of the Countermeasure RSM Modelization Information Theoretic Evaluation of RSM 3 Security Evaluation of RSM against CPA and 2O-CPA 4 Optimal HO-CPA Expression of ρ (1 , 2) opt Conclusions and Perspectives 5 Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 2
Introduction RSM: Rotating Sboxes Masking Side-Channel Analysis (SCA) Information Theoretic Evaluation of RSM Countermeasures Security Evaluation of RSM against CPA and 2O-CPA Goal of the Presentation Conclusions and Perspectives Introduction 1 Side-Channel Analysis (SCA) Countermeasures Goal of the Presentation RSM: Rotating Sboxes Masking 2 Rationale of the Countermeasure RSM Modelization Information Theoretic Evaluation of RSM 3 Security Evaluation of RSM against CPA and 2O-CPA 4 Optimal HO-CPA Expression of ρ (1 , 2) opt Conclusions and Perspectives 5 Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 3
Side-channel measurement cryptographic Encryption system requests containing a secret key 0110100010010010011 Energy on-duty Timing reference
Side-channel measurement Encryption requests Energy Timing reference
Electromagnetic probe I/Os: USB socket Power supply Ground Trigger probe
Introduction RSM: Rotating Sboxes Masking Side-Channel Analysis (SCA) Information Theoretic Evaluation of RSM Countermeasures Security Evaluation of RSM against CPA and 2O-CPA Goal of the Presentation Conclusions and Perspectives Protection against side-channel attacks Extrinsic countermeasures Noise addition . . makes the attack difficult but not impossible Internal powering . . . . . . . . . . . . . . . . . . . . .can be tampered with Internal countermeasures Make the power constant . . require design skills [DGBN09] ✖ Masking the power . . . . . . . . . . . . . . . susceptible to HO-SCA ✔ Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 7
Introduction RSM: Rotating Sboxes Masking Side-Channel Analysis (SCA) Information Theoretic Evaluation of RSM Countermeasures Security Evaluation of RSM against CPA and 2O-CPA Goal of the Presentation Conclusions and Perspectives Security Evaluation of Countermeasures Off-the-shelf platforms, e.g. the Smart-SIC Analyzer Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 8
Introduction RSM: Rotating Sboxes Masking Side-Channel Analysis (SCA) Information Theoretic Evaluation of RSM Countermeasures Security Evaluation of RSM against CPA and 2O-CPA Goal of the Presentation Conclusions and Perspectives Context + Security � = ⇒ + Costs � Trade-offs? Maximal security within a given budget Minimal spendings for a target security level (CC EALx?) Formal analysis: sound and realistic metrics for both security and cost. Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 9
Introduction RSM: Rotating Sboxes Masking Side-Channel Analysis (SCA) Information Theoretic Evaluation of RSM Countermeasures Security Evaluation of RSM against CPA and 2O-CPA Goal of the Presentation Conclusions and Perspectives Context − Costs � = ⇒ − Security � Trade-offs? Maximal security within a given budget Minimal spendings for a target security level (CC EALx?) Formal analysis: sound and realistic metrics for both security and cost. Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 9
Introduction RSM: Rotating Sboxes Masking Rationale of the Countermeasure Information Theoretic Evaluation of RSM RSM Modelization Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives Introduction 1 Side-Channel Analysis (SCA) Countermeasures Goal of the Presentation RSM: Rotating Sboxes Masking 2 Rationale of the Countermeasure RSM Modelization Information Theoretic Evaluation of RSM 3 Security Evaluation of RSM against CPA and 2O-CPA 4 Optimal HO-CPA Expression of ρ (1 , 2) opt Conclusions and Perspectives 5 Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 10
Introduction RSM: Rotating Sboxes Masking Rationale of the Countermeasure Information Theoretic Evaluation of RSM RSM Modelization Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives Masking with two (or more) paths Message k i IP IP Left Left Right Right masked mask mask masked data ( L i ) ( ML i ) ( MR i ) data ( R i ) Feistel function f m m ′ P S’ E x m S ( x ⊕ k c ) P S E ⊕ m ′ k c FP Ciphertext Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 11 This operation is costly in general [SRQ06], especially for the
Introduction RSM: Rotating Sboxes Masking Rationale of the Countermeasure Information Theoretic Evaluation of RSM RSM Modelization Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives Masking with one path: Z → Z ⊕ M (ex. AES) Pool of masks Base masks M 0 − 15 MC(SR( M i )) ⊕ M i MMS 0 − 15 SR( M i ) MS 0 − 15 1280 bytes InvMC(InvSR( M i )) ⊕ M i IMMS 0 − 15 InvSR( M i ) IMS 0 − 15 Homomorphic computation. This masking is the less costly in the litterature [NGDS12]. Requires leak-free ROMs (well suited for ASIC & FPGA). Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 12
Introduction RSM: Rotating Sboxes Masking Rationale of the Countermeasure Information Theoretic Evaluation of RSM RSM Modelization Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives Performances Table: Implementation results for reference and protected AES Unprotected RSM Overhead Number of ALUTs (%) 2136 (8%) 2734 (10%) 28% Number of M4K ROM Blocs (%) 20 (14%) 24 (17%) 20% Frequency (MHz) 133 88 34% Setting: n = 8 bit, 16 masks only, and (Price metric) provable security up to 2nd-order attacks (Security metric) Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 13
Introduction RSM: Rotating Sboxes Masking Rationale of the Countermeasure Information Theoretic Evaluation of RSM RSM Modelization Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives RSM mode of operation SB ′ 0 128 4 Barrel shifter j ∈ { 0 − 15 } S ′ S ′ S ′ 0 1 15 m 0 m 1 m 15 M 0 . . . SubBytes SubBytes SubBytes m 1 m 2 m 0 M 1 Barrel shifter j ∈ { 0 − 15 } 4 128 Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 14
Introduction RSM: Rotating Sboxes Masking Rationale of the Countermeasure Information Theoretic Evaluation of RSM RSM Modelization Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives RSM leakage Masked sboxes Z �→ M out ⊕ S ( Z ⊕ M in ). L ( Z , M ) = L ( Z ⊕ M ) . In this expression, Z and M are n -bit vectors, i.e. live in F n 2 . The leakage function L : F n 2 → R depends on the hardware. In a conservative perspective, L is assumed to be bijective. In a realistic perspective, L is assumed to non-injective. Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 15
Introduction RSM: Rotating Sboxes Masking Rationale of the Countermeasure Information Theoretic Evaluation of RSM RSM Modelization Security Evaluation of RSM against CPA and 2O-CPA Conclusions and Perspectives Metrics 1 Cost : Card[ M ] ∈ { 1 , · · · , 2 n } . 2 Security : Leakage: mutual information. Attack: resistance against HO-CPA. Modelization that bridges both notions: � 1 / Card[ M ] if m ∈ M , and P[ M = m ] = 0 otherwise. Sylvain Guilley, < sylvain.guilley@TELECOM-ParisTech.fr > Entropy / Security Trade-off | INDOCRYPT’2011 | 16
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