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Security Analysis of BLAKE2's Modes of Operation

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Security Analysis of BLAKE2's Modes of Operation Security Analysis of BLAKE2's Modes of Operation Atul Luykx, Bart Mennink, Samuel Neves KU Leuven (Belgium) and Radboud University (The Netherlands) FSE 2017 March 7, 2017 1 / 14 BLAKE2 m1 m2 m3 m 0∗ `k IV PB F F F F H(m) ⊕ t1 f1 t2 f2 t3 f3 t` f` Cryptographic hash function • Aumasson, Neves, Wilcox-O'Hearn, Winnerlein (2013) • Simplication of SHA-3 nalist BLAKE • 2 / 14 BLAKE2 Use in Password Hashing Argon2 (Biryukov et al.) • Catena (Forler et al.) • Lyra (Almeida et al.) • Lyra2 (Simplício Jr. et al.) • Rig (Chang et al.) • Use in Authenticated Encryption AEZ (Hoang et al.) • Applications Noise Protocol Framework (Perrin) • Zcash Protocol (Hopwood et al.) • RAR 5.0 (Roshal) • 3 / 14 BLAKE2 Guo et al. 2014 Hao 2014 Khovratovich et al. 2015 Espitau et al. 2015 ??? Even slight modications may make a scheme insecure! Security Inheritance? BLAKE cryptanalysis Aumasson et al. 2010 Biryukov et al. 2011 Dunkelman&K. 2011 generic Andreeva et al. 2012 Chang et al. 2012 4 / 14 ??? Even slight modications may make a scheme insecure! Security Inheritance? BLAKE BLAKE2 cryptanalysis Aumasson et al. 2010 Guo et al. 2014 Biryukov et al. 2011 Hao 2014 Dunkelman&K. 2011 Khovratovich et al. 2015 Espitau et al. 2015 generic Andreeva et al. 2012 Chang et al. 2012 4 / 14 Even slight modications may make a scheme insecure! Security Inheritance? BLAKE BLAKE2 cryptanalysis Aumasson et al. 2010 Guo et al. 2014 Biryukov et al. 2011 Hao 2014 Dunkelman&K. 2011 Khovratovich et al. 2015 Espitau et al. 2015 generic Andreeva et al. 2012 ??? Chang et al. 2012 4 / 14 Security Inheritance? BLAKE BLAKE2 cryptanalysis Aumasson et al. 2010 Guo et al. 2014 Biryukov et al. 2011 Hao 2014 Dunkelman&K. 2011 Khovratovich et al. 2015 Espitau et al. 2015 generic Andreeva et al. 2012 ??? Chang et al. 2012 Even slight modications may make a scheme insecure! 4 / 14 No structural design aws • Well-suited for composition • Indierentiability real world simulated world IC C idealPrandom Rsimulator S function primitive for oracle P distinguisher D Indierentiability of function from a random oracle • C P is indierentiable from if simulator such that • C R 9 S ( ; ) and ( ; ) indistinguishable C P R S 5 / 14 1 Indierentiability real world simulated world IC C idealPrandom Rsimulator S function primitive for oracle P distinguisher D Indierentiability of function from a random oracle • C P is indierentiable from if simulator such that • C R 9 S ( ; ) and ( ; ) indistinguishable C P R S No structural design aws • Well-suited for composition • 5 / 14 1 (i) First hash-function indierentiability results • Chop-/PF-MD with ideal F indierentiable −! (ii) Most obvious second step (composition) • But (e.g.) Davies-Meyer with ideal E dierentiable −! (iii) Researchers focused on direct proofs • Chop-/PF-MD with Davies-Meyer and ideal E indierentiable −! Composition1 indiff-compose-0 H E F H 6 / 14 (ii) Most obvious second step (composition) • But (e.g.) Davies-Meyer with ideal E dierentiable −! (iii) Researchers focused on direct proofs • Chop-/PF-MD with Davies-Meyer and ideal E indierentiable −! Composition2 indiff-compose-1 H (i) E F (i) H (i) First hash-function indierentiability results • Chop-/PF-MD with ideal F indierentiable −! 6 / 14 (iii) Researchers focused on direct proofs • Chop-/PF-MD with Davies-Meyer and ideal E indierentiable −! Composition3 indiff-compose-2 H (i) E (ii) F (i) H (i) First hash-function indierentiability results • Chop-/PF-MD with ideal F indierentiable −! (ii) Most obvious second step (composition) • But (e.g.) Davies-Meyer with ideal E dierentiable −! 6 / 14 Composition4 indiff-compose-3 (iii) H (i) E (ii) F (i) (iii) H (i) First hash-function indierentiability results • Chop-/PF-MD with ideal F indierentiable −! (ii) Most obvious second step (composition) • But (e.g.) Davies-Meyer with ideal E dierentiable −! (iii) Researchers focused on direct proofs • Chop-/PF-MD with Davies-Meyer and ideal E indierentiable −! 6 / 14 Composition5 indiff-compose-4 (iii) H (i) E (ii) F (i) (iii) H (i) First hash-function indierentiability results • Chop-/PF-MD with ideal F indierentiable −! (ii) Most obvious second step (composition) • But (e.g.) Davies-Meyer with ideal E dierentiable −! (iii) Researchers focused on direct proofs • Chop-/PF-MD with Davies-Meyer and ideal E indierentiable −! 6 / 14 Weakly Ideal Cipher Model BLAKE2 cipher has known, but harmless, properties • Analysis tolerates these properties • Our Results Compression Level Indierentiability BLAKE2 indierentiable at compression function level • Immediately implies • • indierentiability of sequential hash mode • indierentiability of tree/parallel hash mode • multi-key PRF security of keyed BLAKE2 mode One proof ts all! • 7 / 14 Our Results Compression Level Indierentiability BLAKE2 indierentiable at compression function level • Immediately implies • • indierentiability of sequential hash mode • indierentiability of tree/parallel hash mode • multi-key PRF security of keyed BLAKE2 mode One proof ts all! • Weakly Ideal Cipher Model BLAKE2 cipher has known, but harmless, properties • Analysis tolerates these properties • 7 / 14 BLAKE2 Compression Function n \ m 2n \ n h \ n \ n/2 2n n \ \ \ 0 h0 E \ n/4 n n \ t \ n/4 \ f n \ IV h is state, m is message, t is counter, f is ag • IV is initialization value • 8 / 14 Weak- and strong-subspace invariance for weak keys • Evaluation of E in BLAKE2 is never weak • (as left half of IV is not of the form cccc) Weakly Ideal Cipher Model E is an ideal cipher modulo above property • Underlying Block Cipher k k k k k k k k k k k k k k k k \ 2n a a a a a a a a 2n 2n 0 0 0 0 \ b b b b \ b0 b0 b0 b0 c c c c E c0 c0 c0 c0 ! ! d d d d d0 d0 d0 d0 9 / 14 Weak- and strong-subspace invariance for weak keys • Evaluation of E in BLAKE2 is never weak • (as left half of IV is not of the form cccc) Underlying Block Cipher k k k k k k k k k k k k k k k k \ 2n a a a a a a a a 2n 2n 0 0 0 0 \ b b b b \ b0 b0 b0 b0 c c c c E c0 c0 c0 c0 ! ! d d d d d0 d0 d0 d0 Weakly Ideal Cipher Model E is an ideal cipher modulo above property • 9 / 14 Evaluation of E in BLAKE2 is never weak • (as left half of IV is not of the form cccc) Underlying Block Cipher k k k k k k k k k k k k k k k k \ 2n a a a a a a a a 2n 2n 0 0 0 0 \ b b b b \ b0 b0 b0 b0 c c c c E c0 c0 c0 c0 ! ! d d d d d0 d0 d0 d0 Weakly Ideal Cipher Model E is an ideal cipher modulo above property • Weak- and strong-subspace invariance for weak keys • 9 / 14 Underlying Block Cipher k k k k k k k k k k k k k k k k \ 2n a a a a a a a a 2n 2n 0 0 0 0 \ b b b b \ b0 b0 b0 b0 c c c c E c0 c0 c0 c0 ! ! d d d d d0 d0 d0 d0 Weakly Ideal Cipher Model E is an ideal cipher modulo above property • Weak- and strong-subspace invariance for weak keys • Evaluation of E in BLAKE2 is never weak • (as left half of IV is not of the form cccc) 9 / 14 inverse query−−! hits 0-block −−−−! collision in uniformly random−−! responses q Indiff E (q) = Θ F ;S 2n=2 input matches legitimate F -call? yes no consult R input weak? yes no reply like weak reply uniformly permutation at random Proof Idea E Construction : n Simulator : F \ S m 2n \ n h \ n \ n/2 2n n \ \ \ 0 h0 E \ n/4 n n \ t \ n/4 \ f n \ IV 10 / 14 inverse query−−! hits 0-block −−−−! collision in uniformly random−−! responses q Indiff E (q) = Θ F ;S 2n=2 Proof Idea E Construction : n Simulator : F \ S m input matches \ legitimate F -call? 2n n h \ yes no n \ n/2 2n n \ \ \ consult input weak? 0 R h0 E \ n/4 n n \ t \ yes no n/4 \ f n \ reply like weak reply uniformly permutation at random IV 10 / 14 inverse query−−! hits 0-block −−−−! collision in uniformly random−−! responses q Indiff E (q) = Θ F ;S 2n=2 Proof Idea E Construction : n Simulator : F \ S m input matches \ legitimate F -call? 2n n h \ yes no n \ n/2 2n n \ \ \ consult input weak? 0 R h0 E \ n/4 n n \ \ yes no t n/4 \ f n \ reply like weak reply uniformly permutation at random IV 10 / 14 inverse query−−! hits 0-block q Indiff E (q) = Θ F ;S 2n=2 Proof Idea E Construction : n Simulator : F \ S m input matches \ legitimate F -call? 2n n h \ yes no n \ n/2 2n n \ \ \ consult input weak? 0 R h0 E \ n/4 n n \ \ yes no t n/4 \ f n \ reply like weak reply uniformly permutation at random IV −−−−! collision in uniformly random−−! responses 10 / 14 q Indiff E (q) = Θ F ;S 2n=2 Proof Idea E Construction : n Simulator : F \ S m input matches \ legitimate F -call? 2n n h \ yes no n \ n/2 2n n \ \ \ consult input weak? 0 R h0 E \ n/4 n n \ \ yes no t n/4 \ f n \ reply like weak reply uniformly permutation at random IV inverse query−−! hits 0-block −−−−! collision in uniformly random−−! responses 10 / 14 Proof Idea E Construction : n Simulator : F \ S m input matches \ legitimate F -call? 2n n h \ yes no n \ n/2 2n n \ \ \ consult input weak? 0 R h0 E \ n/4 n n \ \ yes no t n/4 \ f n \ reply like weak reply uniformly permutation at random IV inverse query−−! hits 0-block −−−−! collision in uniformly random−−! responses q Indiff E (q) = Θ F ;S 2n=2 10 / 14 Prex-Free Merkle-Damgård? BLAKE2 Hashing Modes m1 m2 m3 m 0∗ `k IV PB F F F F H(m) ⊕ t1 f1 t2 f2 t3 f3 t` f` Message m padded into m1 m` • k · · · k t1 t` are counter values, f1 f` are ags • k · · · k k · · · k PB is a parameter block • 11 / 14 BLAKE2 Hashing Modes m1 m2 m3 m 0∗ `k IV PB F F F F H(m) ⊕ t1 f1 t2 f2 t3 f3 t` f` Message m padded into m1 m` • k · · · k t1 t` are counter values, f1 f` are ags • k · · · k k · · · k PB is a parameter block • Prex-Free Merkle-Damgård? 11 / 14 Captured by generalized design of Bertoni et al.
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