Background Correlation Analysis Results Conclusion Side-channel analysis of six SHA-3 candidates in HMAC scheme Olivier Benoˆ ıt and Thomas Peyrin CHES 2010 Workshop Santa Barbara - August 18, 2010
Background Correlation Analysis Results Conclusion Outline Background Correlation Analysis Theory Practice Results AES-bases candidates Others Candidates Conclusion
Background Correlation Analysis Results Conclusion Outline Background Correlation Analysis Theory Practice Results AES-bases candidates Others Candidates Conclusion
Background Correlation Analysis Results Conclusion Introduction • NIST launched the SHA-3 competition in order to replace the collision-broken SHA-1 function • 14 candidates are still in the race, the winner will be determined in 2012 • it makes sense to consider side-channel attack on these SHA-3 candidates in the HMAC scheme • Retrieving the key would lead to the ability to forge correct MAC • We will therefore analyse a panel of six candidates deemed representative ECHO Grøstl SHAvite-3 HAMSI BLAKE CubeHash
Background Correlation Analysis Results Conclusion Prior works • DPA on n-bit sized boolean and arithmetic operations and its application to IDEA, RC6, and HMAC construction (CHES 2005), Lemke et al. • Side channel attacks against HMAC based on block-cipher based hash functions (ACISP 2006), Okeya et al. • DPA of HMAC based on SHA-2, and countermeasures (WISA2007), McEvoy et al. • An update on the side channel cyrptanalysis of MAC based on crytopgaphic hash functions (INDOCRYPT 2007), Gauravaram et al. • Practical Electromagnetic Template Attack on HMAC (CHES 2009), Fouque et al.
Background Correlation Analysis Results Conclusion HMAC HMAC ( K , M ) = H (( K ⊕ opad ) || H (( K ⊕ ipad ) || M )) K ⊕ ipad M 1 M k CV in H in CV in 1 0 h h h K ⊕ opad CV out CV out 1 0 H out h h • The possible targets of a side-channel analysis attack are: K , CV in 1 and CV out 1
Background Correlation Analysis Results Conclusion Outline Background Correlation Analysis Theory Practice Results AES-bases candidates Others Candidates Conclusion
Background Correlation Analysis Results Conclusion Correlation • A selection function is defined as w = f ( cv , m ) • The theoretical correlation between a data set x i for a key guess j and the data set y i for an arbitrary real key r is: � ( x i − x )( y i − y ) c ( j , r ) = �� ( x i − x ) 2 . �� ( y i − y ) 2 • Assumming a leakage in the Hamming Weight model: x i = HW ( f ( j , m i )) and y i = HW ( f ( r , m i )) • Given a selection function, it is possible to compute c ( j , r ) for all key guess and look a the correlation contrast between the real key and the wrong keys
Background Correlation Analysis Results Conclusion SHA-3 Selection functions The typical selection functions that will be found in SHA-3 candidates are: • AES sbox (256 → 256 substitution): w = SBOX AES ( cv ⊕ m ) • Modular addition: w = ( cv ⊞ m ) mod 256 • Exclusive OR logic operation: w = cv ⊕ m • HAMSI sbox ( 16 → 16 substitution): w = SBOX HAMSI ( cv i + 1 || m i + 1 || cv i || m i )
Background Correlation Analysis Results Conclusion SHA-3 Selection functions The typical selection functions that will be found in SHA-3 candidates are: • AES sbox (256 → 256 substitution): w = SBOX AES ( cv ⊕ m ) • Modular addition: w = ( cv ⊞ m ) mod 256 • Exclusive OR logic operation: w = cv ⊕ m • HAMSI sbox ( 16 → 16 substitution): w = SBOX HAMSI ( cv i + 1 || m i + 1 || cv i || m i )
Background Correlation Analysis Results Conclusion SHA-3 Selection functions The typical selection functions that will be found in SHA-3 candidates are: • AES sbox (256 → 256 substitution): w = SBOX AES ( cv ⊕ m ) • Modular addition: w = ( cv ⊞ m ) mod 256 • Exclusive OR logic operation: w = cv ⊕ m • HAMSI sbox ( 16 → 16 substitution): w = SBOX HAMSI ( cv i + 1 || m i + 1 || cv i || m i )
Background Correlation Analysis Results Conclusion SHA-3 Selection functions The typical selection functions that will be found in SHA-3 candidates are: • AES sbox (256 → 256 substitution): w = SBOX AES ( cv ⊕ m ) • Modular addition: w = ( cv ⊞ m ) mod 256 • Exclusive OR logic operation: w = cv ⊕ m • HAMSI sbox ( 16 → 16 substitution): w = SBOX HAMSI ( cv i + 1 || m i + 1 || cv i || m i )
Background Correlation Analysis Results Conclusion Selection function efficiency, r = 8 1 correlation ( AES Sbox) j correlation (modular addition) 1 j − 0 . 5 correlation (XOR) 1 j − 1
Background Correlation Analysis Results Conclusion Selection function efficiency • Results for the HAMSI sbox selection function: real and guess key j = 0 j = 1 j = 2 j = 3 r = 0 + 1 . 00 − 0 . 17 − 0 . 56 − 0 . 87 r = 1 − 0 . 17 + 1 . 00 + 0 . 87 − 0 . 09 r = 2 − 0 . 56 + 0 . 87 + 1 . 00 + 0 . 17 r = 3 − 0 . 87 − 0 . 09 + 0 . 17 + 1 . 00
Background Correlation Analysis Results Conclusion Correlation Contrast • The correlation contrast is computed from the highest correlation for a wrong guess ( c w ) selection modular AES HAMSI XOR function Sbox addition Sbox c c = 1 −| c w | | c w | c w 0 . 23 0 . 75 0 . 87 − 1 c c 3 . 34 0 . 33 0 . 15 0 • The selection function efficiency E is linked to the correlation contrast E ( AES Sbox ) > E ( modular addition ) > E ( HAMSI Sbox ) > E ( XOR )
Background Correlation Analysis Results Conclusion Correlation Contrast • The correlation contrast is computed from the highest correlation for a wrong guess ( c w ) selection modular AES HAMSI XOR function Sbox addition Sbox c c = 1 −| c w | | c w | c w 0 . 23 0 . 75 0 . 87 − 1 c c 3 . 34 0 . 33 0 . 15 0 • The selection function efficiency E is linked to the correlation contrast E ( AES Sbox ) > E ( modular addition ) > E ( HAMSI Sbox ) > E ( XOR )
Background Correlation Analysis Results Conclusion Measurement platform • Xilinx Spartan FPGA • Software selection function running on a TSK3000 RISC CPU • 5 GS/s sampling frequency • Homemade EMA sensor • 30db Amplifier (1GHz BdW) • 100.000 curves • 10 curves per message
Background Correlation Analysis Results Conclusion Selection functions implementation
Background Correlation Analysis Results Conclusion CEMA results: correlation curves for correct and wrong guess
Background Correlation Analysis Results Conclusion CEMA results (5 best guess for each target byte)
Background Correlation Analysis Results Conclusion CEMA results versus number of curves
Background Correlation Analysis Results Conclusion Outline Background Correlation Analysis Theory Practice Results AES-bases candidates Others Candidates Conclusion
Background Correlation Analysis Results Conclusion ECHO side channel analysis • Internal state at the end of the first round: w i 0 [ b ] = α · cv ′ i 1 [ b ] ⊕ β · m ′ i 2 [ b ] ⊕ γ · m ′ i 3 [ b ] ⊕ δ · m ′ i 4 [ b ] • Internal state in second round, after AES Sbox operation: w ′ i [ b ] = Sbox ( w i [ b ] ⊕ t i [ b ]) • 64 AES Sbox side-channel attacks to retrieve CV • For each cv ′ i , four selection functions can be exploits
Background Correlation Analysis Results Conclusion Grøstl side channel analysis • Internal state after the AES Sbox operation during first round of P G w ′ [ b ] = Sbox ( m [ b ] ⊕ CV [ b ]) • In this case, CPA is straightforward • 64 AES Sbox side-channel attacks to retrieve CV • It is possible to speed up the attack by a factor 64 by choosing all m [ b ] equals
Background Correlation Analysis Results Conclusion SHAvite-3 side channel analysis • Internal state after the AES Sbox operation during first round of E S w ′ [ b ] = Sbox ( CV R [ b ] ⊕ m 1 0 [ b ]) • Internal state after the AES Sbox operation during second round of E S z ′ [ b ] = Sbox ( CV L [ b ] ⊕ w ′′ [ b ] ⊕ m 2 0 [ b ]) • 32 AES Sbox side-channel attacks to retrieve CV • In order to retrieve CV L , the right part CV R must be found without errors
Background Correlation Analysis Results Conclusion BLAKE description • Overview: CV i + 1 = final ( E B M i ( init ( CV i )) , CV i ) • E B is a block cipher composed of 10 rounds, each consisting of the application of eight 128-bit sub-functions G i Initialisation Finalization M i CV i cv 0 cv 1 cv 2 cv 3 cv 0 cv 1 cv 2 cv 3 cv 4 cv 5 cv 6 cv 7 E B cv 4 cv 5 cv 6 cv 7 t 0 t 1 t 2 t 3 t 4 t 5 t 6 t 7 CV i + 1
Background Correlation Analysis Results Conclusion BLAKE description • One round of E B computes: G 0 ( v 0 , v 4 , v 8 , v 12 ) G 1 ( v 1 , v 5 , v 9 , v 13 ) G 2 ( v 2 , v 6 , v 10 , v 14 ) G 3 ( v 3 , v 7 , v 11 , v 15 ) G 4 ( v 0 , v 5 , v 10 , v 15 ) G 5 ( v 1 , v 6 , v 11 , v 12 ) G 6 ( v 2 , v 7 , v 8 , v 13 ) G 7 ( v 3 , v 4 , v 9 , v 14 ) • The function G s ( a , b , c , d ) processes the following steps: ← ( a ⊞ b ) ⊞ ( m i ⊕ k j ) a d ← ( d ⊕ a ) ≫ 16 c ← ( c ⊞ d ) d ← ( b ⊕ c ) ≫ 12 a ← ( a ⊞ b ) ⊞ ( m j ⊕ k i ) d ← ( d ⊕ a ) ≫ 8 c ← ( c ⊞ d ) d ← ( b ⊕ c ) ≫ 7
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