Automatic Synthesis of Fault Attack Resistant Cipher Implementations - PowerPoint PPT Presentation

Automatic Synthesis of Fault Attack Resistant Cipher Implementations Chester Rebeiro IIT Madras

Side Channel Analysis Electro magnetic Radiation Fault injection Power consumption Timing channels

Preventing Side Channel Attacks is Difficult Programming Platform / Language overheads Compiler Specific Specific Naïve implementations can VHDL, Countermeasures need to have significant size or/and Assembly, be tuned based on performance overheads Java * device (IoT devices to server) * compilers may introduce further Vulnerabilities Cannot be implemented by your average Joe

Block Cipher Specification Language Specification- 1. h begin i 2. h lookups i 3. SBOX : { 0 x 63 , 0 x 7 c , 0 x 77, 0 x 7 b , · · · } HTML like language that captures basic 4. KEY : { 0 x 54, 0 x 68, 0 x 61, 0 x 74, · · · } 5. h /lookups i functionality of the cipher 6. h operations i 7. h func i h MUL2 ( a ) i 8. h h : { a : RS ( a, 7 ) } i - operations 9. h t : { a : LS ( a, 1 ) } i h n : { h : MUL ( h, 0 0 x 1 b0 ) } i 10. - information flow 11. h m : { ( n, t ) : XOR ( n, t ) } i 12. ret m 13. h / func i 14. · · · · · · · · · 15. h /operations i 16. · · · · · · · · · 17. h F 2 i h nonlinear i h SUBBYTE i h 18. h F 2[1] : { F 1[1] : LKUP ( F 1[1], SBOX ) } i 19. · · · · · · · · · Just need one per cipher 20. h F 2[16] : { F 1[16] : LKUP ( F 1[16], SBOX ) } i 21. / i 22. h F 3 i h linear i h PERMUTE i h Platform independent 23. h F 3[1] : { F 2[1] } i 24. · · · · · · · · · Programming language independent 25. h F 3[16] : { F 2[12] } i 26. / i 27. h F 4 i h linear i h MDS i h 28. h F 4[1] : { ( F 3[1], F 3[2], F 3[3], F 3[4] ) : XOR ( XOR ( MUL2 ( F 3[1] ), MUL3 ( F 3[2] ) ), XOR ( F 3[3], F 3[4] ) ) } i 29. · · · · · · · · · 30. h F 4[16] : { ( F 3[13], F 3[14], F 3[15], F 3[16] ) : XOR ( XOR ( MUL2 ( F 3[16] ), MUL3 ( F 3[23] ) ), XOR ( F 3[14], F 3[15] ) ) } i 31. / i 32. · · · · · · · · · 33. h end i

Synthesis Tools Source Code (Java / Assembly / RTL) uint8_t F1[ 16 ], F2[ 16 ], F2d[ 16 ]; uint8_t SBOX[ 256 ] = {S1, S2, · · · , S256} ; Synthesis tools F 2[ 0 ] = SBOX[ F 1[ 0 ]] ; F 2[ 1 ] = SBOX[ F 1[ 1 ]] ; Specification- · · · · · · · · · F 2[ 15 ] = SBOX[ F 1[ 15 ]] ; · · · · · · · · · 1. h begin i F 2 d [ 0 ] = SBOX[ F 1[ 0 ]] ; 2. h lookups i 3. SBOX : { 0 x 63 , 0 x 7 c , 0 x 77, 0 x 7 b , · · · } F 2 d [ 1 ] = SBOX[ F 1[ 1 ]] ; 4. KEY : { 0 x 54, 0 x 68, 0 x 61, 0 x 74, · · · } 5. h /lookups i · · · · · · · · · 6. h operations i Side-Channel F 2 d [ 15 ] = SBOX[ F 1[ 15 ]] ; · · · · · · · · · 7. h func i h MUL2 ( a ) i 8. h h : { a : RS ( a, 7 ) } i 9. h t : { a : LS ( a, 1 ) } i h n : { h : MUL ( h, 0 0 x 1 b0 ) } i if ( F 2[ 0 ] == F 2 d [ 0 ] && · · · && F 2[ 15 ] == F 2 d [ 15 ]) 10. 11. h m : { ( n, t ) : XOR ( n, t ) } i { Evaluation 12. ret m continue ; 13. h / func i 14. · · · · · · · · · } · · · · · · · · · 15. h /operations i else 16. · · · · · · · · · 17. h F 2 i h nonlinear i h SUBBYTE i h & { 18. h F 2[1] : { F 1[1] : LKUP ( F 1[1], SBOX ) } i exit( 0 ); 19. · · · · · · · · · 20. h F 2[16] : { F 1[16] : LKUP ( F 1[16], SBOX ) } i } 21. / i 22. h F 3 i h linear i h PERMUTE i h Synthesis 23. h F 3[1] : { F 2[1] } i 24. · · · · · · · · · 25. h F 3[16] : { F 2[12] } i 26. / i 27. h F 4 i h linear i h MDS i h 28. h F 4[1] : { ( F 3[1], F 3[2], F 3[3], F 3[4] ) : XOR ( XOR ( MUL2 ( F 3[1] ), MUL3 ( F 3[2] ) ), XOR ( F 3[3], F 3[4] ) ) } i 29. · · · · · · · · · 30. h F 4[16] : { ( F 3[13], F 3[14], F 3[15], F 3[16] ) : XOR ( XOR ( MUL2 ( F 3[16] ), MUL3 ( F 3[23] ) ), XOR ( F 3[14], F 3[15] ) ) } i 31. / i 32. · · · · · · · · · 33. h end i compiler Specification Side-channel secure Executable / design

Automatic Synthesis of Fault Attack Resistant Block Cipher Implementations

Fault Injection in Block Ciphers optical glitch in power Random single byte fault glitch in clock Memory Instructions injection 000000000000 load r1, #key 000000000000 add r0, r1, r2 000000000000 out r9,r1 out r9,r0 000000000000 sub r4, #23 000000000 88 0 mul r2, r1, r4 000000000000 cmp r3, #0 target device Logical Fault Effect 000000000000 Physical Fault Injection Secret Key Attack Outcome Fault Propagation Difficult

Differential Fault Attacks plaintext FAULT INJECTION ENCRYPTION ENCRYPTION ciphertext faulty ciphertext ANALYSIS

A Simple AES Fault Attack P P p 0 p 1 p 127 p 0 p 1 p 127 AES AES k 127 k 1 k 1 k 127 k 0 k 0 c 0 c 1 c 127 c’ 0 ’ c 1 c 127 C’ C ' k 0 = c 0 Many more stronger fault attacks are possible

Central Idea in DFA Fault attackers look to solve equations in one of the following form x Å x ' = d x - 1 ( y Å k ) Å S - 1 ( y ' Å k ) = d x ' S x x ' k where and are known and and are S S d unknown. k k Iterate over all possible values of and identify d y those that satisfy the above equations. y ' The number of solutions depends on the properties of the S-box.

Central Idea in DFA If multiple equations of this form are found, then the complexity is reduced considerably where are linear functions in d Only key tuples that satisfy all n equations are potential candidates Assuming is a byte, we can recover n bytes of key with a complexity of 2 8 d

summarize Linear functions Involving sbox More the better Inject Fault Solve Equations Online complexity : #faults are needed to retrieve the key Offline complexity : Search space for finding the keys

Differential Fault Attacks on AES Fault Injected #faults (online complexity) Offline complexity in first round requires 128 faults NIL in last round requires 128 faults NIL in 9 th round requires 4 faults 256 (each fault derives 32 bits of key) in 8 th round Requires 1 fault 256 all other rounds Not exploitable N/A A majority of the faults are unexploitable Naïve countermeasures do not consider the online or offline attack complexity requirements, thus significant overheads

SAFARI Automatic Synthesis of Fault Attack Resistant Block Cipher Implementations Block Cipher Specification (BCS) FaultDroid XFC Ranked list of Countermeas ure fault locations with corresponding offline Addition to complexity Specification Software (CAS) Implementation BCS ⇤ Synthes is Security RTL Implementation

XFC: Exploitable Fault Characterization Block Cipher Specification (BCS) FaultDroid XFC Ranked list of Countermeas ure fault locations with corresponding offline Addition to complexity Specification Software (CAS) Implementation BCS ⇤ Synthes is Security RTL Implementation DAC’17

XFC XFC

Fault Propagation Phase Linear Key Addition Non-Linear S-box S-box S-box S-box A Typical Block Cipher Diffusion Diffusion Linear Linear Key Addition Non-Linear S-box S-box S-box S-box Diffusion Diffusion Linear Linear Key Addition Non-Linear S-box S-box S-box S-box Diffusion Diffusion Linear Linear Key Addition Non-Linear S-box S-box S-box S-box Linear Key Addition

Fault Propagation Phase Linear Key Addition Non-Linear S-box S-box S-box S-box Diffusion Diffusion Linear Color the fault affected part. Propagate and color as follows. Linear Key Addition 1. When passing through a linear layer, Non-Linear S-box S-box S-box S-box retain same color Diffusion Diffusion Linear 2. When passing through a non-linear Linear Key Addition layer, change color Non-Linear S-box S-box S-box S-box 1. If two bytes of different colors are Diffusion Diffusion Linear combined, change the color. Linear Key Addition Same colors are linearly correlated Non-Linear S-box S-box S-box S-box Different colors are not correlated Linear Key Addition

Key Addition Key Determination Phase S-box S-box S-box S-box Diffusion Diffusion ' Å k 1 Å k 1 ) Å S S - 1 ( y - 1 ( y 1 ) = g 1 ( d ) 1 ' Å k 2 ) = g 2 ( d ) Key Addition - 1 ( y 2 Å k 2 ) Å S S - 1 ( y 2 S-box S-box S-box S-box For every possible value of d Diffusion Diffusion determine k 1 , k 2 that satisfy the equations. Key Addition The complexity is 2 4 ; the possible S-box S-box S-box S-box values can take. d Diffusion Diffusion Key Addition S-box S-box S-box S-box k k 2 k 3 k 4 1 y 3 y y 2 y 4 1

Key Addition Key Determination Phase S-box S-box S-box S-box Diffusion Diffusion Key Addition S-box S-box S-box S-box ' Å k 3 ) = g 3 ( d ) Diffusion Diffusion - 1 ( y 3 Å k 3 ) Å S S - 1 ( y 3 ' Å k 4 ) = g 4 ( d ) - 1 ( y 4 Å k 4 ) Å S S - 1 ( y 4 Key Addition Can be used to determine (k 3 , k 4 ) S-box S-box S-box S-box Diffusion Diffusion Key Addition S-box S-box S-box S-box k k 2 k 3 k 4 1 y 3 y y 2 y 4 1