Reverse Engineering of a Secret AES-like Cipher by Ineffective Fault - PowerPoint PPT Presentation

Introduction Scope of the Attack Attack Steps Conclusion Reverse Engineering of a Secret AES-like Cipher by Ineffective Fault Analysis Antoine Wurcker Christophe Clavier antoine.wurcker@xlim.fr christophe.clavier@unilim.fr Universit´ e de Limoges FDTC 2013 20-08-2013 Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 1 / 33

Introduction Scope of the Attack Attack Steps Conclusion Outline Introduction 1 Advanced Encryption Standard Ineffective Fault Analysis Scope of the Attack 2 Modifications on AES Constraints on Attacker Attack Steps 3 Conclusion 4 Global Results Future Works Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 2 / 33

Introduction Scope of the Attack Attack Steps Conclusion Outline Introduction 1 Advanced Encryption Standard Ineffective Fault Analysis Scope of the Attack 2 Modifications on AES Constraints on Attacker Attack Steps 3 Conclusion 4 Global Results Future Works Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 3 / 33

Introduction Scope of the Attack Attack Steps Conclusion AES AES Datapath S r − 1 S 9 M SubBytes SubBytes ShiftRows ShiftRows MixColumns AddRoundKey ( K 0 ) AddRoundKey ( K r ) AddRoundKey ( K 10 ) S 0 S r C r = 1 , . . . , 9 r = 0 r = 10 Figure: The AES encryption path. Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 4 / 33

Introduction Scope of the Attack Attack Steps Conclusion AES AES KeySchedule K r − 1 RotWord SubWord � Rcon ( r ) � � � � K r Figure: The AES key schedule. Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 5 / 33

Introduction Scope of the Attack Attack Steps Conclusion IFA Ineffective Fault Analysis Fault Model: Stuck at 0 a precise byte. Fault effect: Ciphertext not modified ⇒ the value was already 0. Ciphertext modified ⇒ the value was not 0. Remark: IFA by-pass dual-execution countermeasure. Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 6 / 33

Introduction Scope of the Attack Attack Steps Conclusion IFA M M ⇓ ⇓ . . . . . . 45 00 98 34 44 98 34 44 AF 13 9C 59 AF 13 9C 59 23 77 08 B6 23 77 08 B6 E5 75 1A EE E5 75 1A EE . . . . . . ⇓ ⇓ � = C ′ C Figure: Example of no-occurrence of IFA. Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 7 / 33

Introduction Scope of the Attack Attack Steps Conclusion IFA M M ⇓ ⇓ . . . . . . 00 00 C6 67 34 C6 67 34 31 DE 90 58 31 DE 90 58 5F 4C 58 78 5F 4C 58 78 AB 45 11 6F AB 45 11 6F . . . . . . ⇓ ⇓ = C C Figure: Example of occurrence of IFA. Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 7 / 33

Introduction Scope of the Attack Attack Steps Conclusion Notations Notations m i : Byte number i of the input plaintext M . c i : Byte number i of the output ciphertext C . K r : 128-bit Key of round number r . k r , i : Byte number i of the round key K r . S (): Function SubBytes . S − 1 (0) : Preimage of 0 value by S-Box table µ i = k 0 , i ⊕ S − 1 (0) X r = { x r , 0 , . . . , x r , 15 } : Input state of SubBytes step of round r Y r = { y r , 0 , . . . , y r , 15 } : Input state of ShiftRows step of round r Z r = { z r , 0 , . . . , z r , 15 } : Input state of MixColumns step of round r T r = { t r , 0 , . . . , t r , 15 } : Input state of AddRoundKey step of round r Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 8 / 33

Introduction Scope of the Attack Attack Steps Conclusion Outline Introduction 1 Advanced Encryption Standard Ineffective Fault Analysis Scope of the Attack 2 Modifications on AES Constraints on Attacker Attack Steps 3 Conclusion 4 Global Results Future Works Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 9 / 33

Introduction Scope of the Attack Attack Steps Conclusion Modifications on AES Modifications on AES The modifications allowed have to respect the constraints from the NIST document describing the AES: The SBOX operation is a permutation table. 1 ⇒ 256! possible SBOX ( ≃ 2 1684 ). The ShiftRows operation keeps shifting rows. 2 ⇒ 2 8 possible ShiftRows. The MixColumns matrix stays circulant with four parameters ( � = 0). 3 ⇒ 255 4 possible MixColumns ( ≃ 2 32 ). The RotWord operation keeps shifting word. 4 ⇒ 2 2 possible RotWord. The Rcon vectors keeps the form [ ρ r − 1 , 0 , 0 , 0]. 5 ⇒ 2 8 possible sets of Rcon vectors. Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 10 / 33

Introduction Scope of the Attack Attack Steps Conclusion Modifications on AES ⊳ σ 0   α 0 α 1 α 2 α 3 ⊳ σ 1 α 3 α 0 α 1 α 2   ⊳ σ 2   α 2 α 3 α 0 α 1   ⊳ σ 3 α 1 α 2 α 3 α 0 Figure: ShiftRows parameters. Figure: MixColumns matrix. ⊕ ρ r − 1 △ η Figure: RotWord parameter. Figure: Rcon [ r ] parameter. Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 11 / 33

Introduction Scope of the Attack Attack Steps Conclusion Constraints Constraints on Attacker We placed main constraints on an attacker: The SBOX table is unknown. 1 The MixColumns coefficients are unknown. 2 The ShiftRows coefficients are unknown. 3 The fault can only be applied on SBOX output. 4 The key K is unknown. 5 The Key-Schedule operation is also constrained: RotWord coefficient is unknown. 1 Rcon parameter is unknown. 2 Unavailable to fault injection (e.g. pre-computation). 3 Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 12 / 33

Introduction Scope of the Attack Attack Steps Conclusion Outline Introduction 1 Advanced Encryption Standard Ineffective Fault Analysis Scope of the Attack 2 Modifications on AES Constraints on Attacker Attack Steps 3 Conclusion 4 Global Results Future Works Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 13 / 33

Introduction Scope of the Attack Attack Steps Conclusion Retrieving K 0 up to a Constant Byte Retrieving K 0 up to a Constant Byte Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 14 / 33

Introduction Scope of the Attack Attack Steps Conclusion Retrieving K 0 up to a Constant Byte Retrieving K 0 up to a Constant Byte We obtain µ i = k 0 , i ⊕ S − 1 (0) by exhausting m i while faulting the output of i th S-Box of first round. Eventually an IFA occurs and we obtain the equation: S ( m i ⊕ k 0 , i ) = 0 m i ⊕ k 0 , i = S − 1 (0) m i = k 0 , i ⊕ S − 1 (0) m i = µ i We retrieve every µ i values by applying this method on each position. ⇒ The set of candidates for K 0 is reduced from 2 128 to 2 8 . Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 14 / 33

Introduction Scope of the Attack Attack Steps Conclusion Lemma: ”Choosing” S-Box Input Lemma: ”Choosing” S-Box Input Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 15 / 33

Introduction Scope of the Attack Attack Steps Conclusion Lemma: ”Choosing” S-Box Input Lemma: ”Choosing” S-Box Input Lemma The knowledge of µ i values allows us to choose any value x 1 , i up to the constant value S − 1 (0) . Proof. Playing value m i = v ⊕ µ i implies that: x 1 , i = m i ⊕ k 0 , i x 1 , i = v ⊕ µ i ⊕ k 0 , i x 1 , i = v ⊕ S − 1 (0) ⊕ k 0 , i ⊕ k 0 , i x 1 , i = v ⊕ S − 1 (0) Remark: if v = 0 it implies x 1 , i = S − 1 (0) ⇒ y 1 , i = 0 Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 15 / 33

Introduction Scope of the Attack Attack Steps Conclusion Reversing ShiftRows Operation Reversing ShiftRows Operation Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 16 / 33

Introduction Scope of the Attack Attack Steps Conclusion Reversing ShiftRows Operation Reversing ShiftRows Operation Fault position: first S-Box of second round. First step: Playing random messages until an IFA occurs. Second step: Playing previous message with only one byte modified each time. On each row 1 position will break the IFA when 3 will not. We play the second step until we get the 4 values that break IFA, revealing the 4 ShiftRows parameters. ⇒ The ShiftRows operation is reversed. Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 16 / 33

Introduction Scope of the Attack Attack Steps Conclusion Reversing ShiftRows Operation Reversing ShiftRows Operation ⊕ K 0 SB SR ⇒ ⇒ ⇒ MC ⇓ ⊕ K 1 SB ⇐ ⇐ Figure: Position of IFA Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 17 / 33

Introduction Scope of the Attack Attack Steps Conclusion Reversing ShiftRows Operation Reversing ShiftRows Operation � = � = � = � = ⊕ K 0 SB SR ⇒ ⇒ ⇒ MC ⇓ � = � = � = � = � = � = SB ⊕ K 1 ⇐ ⇐ � = � = � = � = � = � = Figure: Proof: shift parameter of second row is not 0 Antoine Wurcker (Universit´ e de Limoges) Reverse AES by IFA FDTC 2013 17 / 33