FSE 2018 Modes of operations for computing on encrypted data Dragos Rotaru, N.P. Smart, and Martijn Stam KU Leuven, University of Bristol 1 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Multiparty computation hijacks FSE’18 a c b Goal : Compute F(a, b, c) Dragos Rotaru 2 2 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
What is the problem? 3 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
What is the problem? 42 42 42 42 4 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
What is the problem? 42 42 42 42 Enc Enc Enc 5 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
What is the problem? 42 42 42 Enc(42) 6 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
What is the problem? 42 42 42 Enc(42) 7 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
What is the problem? 42 42 42 Tag(E(42)) Enc(42) 8 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
What is the problem? For free: detect malicious encryption keys. Tag(E(42)) Enc(42) 9 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Prior work – PRFs in MPC (CCS’16) Tag(Enc(42)) Enc(42) - MiMC - Legendre PRF 10 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Prior work – PRFs in MPC (CCS’16) Tag(Enc(42)) Enc(42) M[1] Enc 11 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Prior work – PRFs in MPC (CCS’16) Tag(Enc(42)) Enc(42) M[1] M[2] + Enc Enc 12 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Prior work – PRFs in MPC (CCS’16) Tag(Enc(42)) Enc(42) M[1] M[2] M[3] + + Enc Enc Enc 13 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Prior work – PRFs in MPC (CCS’16) Tag(Enc(42)) Enc(42) M[1] M[2] M[3] M[4] + + + Tag Enc Enc Enc Enc 14 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
What we have done [42] Enc(42) Tag(42) • Analyze AE in Multiparty Computation (MPC). • Useful MPC happens in Fp => Need AE and PRFs modp. • Look for parallel AE: CTR+PMAC, OTR. 15 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
The story This Photo by Unknown Author is licensed under CC BY-NC-ND 16 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
The story ‘You take the blue pill— the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill — you stay in Wonderland, and I show you how deep the rabbit hole goes.’ 17 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
The story ‘You take the blue pill— the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill — you stay in Wonderland, and I show you how deep the rabbit hole goes.’ 18 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Down the rabbit hole - MPC with Secret Sharing 𝑦 ← 𝑦 2 𝑦 = 𝑦 1 + ⋯ + 𝑦 𝑜 𝑦 ← 𝑦 1 Each 𝑄 𝑗 has 𝑦 ← 𝑦 𝑗 𝑦 ← 𝑦 3 19 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Preprocessing Phase Generate triples [c] = [a][b] 20 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Preprocessing Phase Generate triples [c] = [a][b] 21 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Preprocessing Phase 22 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Preprocessing Phase 23 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Online Phase Use Triples. 24 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Online Phase Use Triples. 25 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Circuit Evaluation X Z Y Z X Y 26 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Circuit Evaluation Z X Y 27 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Circuit Evaluation Z X Y 28 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Circuit Evaluation Z X Y 29 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
MPC Circuit Evaluation 3 triples. 2 comm. rounds Z X Y 30 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Tweak your encryption to MPC Reveal 31 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Tweak your encryption to MPC 32 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Tweak your encryption to MPC 33 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
How-to compute PMAC 34 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Let’s do AE with CTR+pPMAC 35 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Let’s do AE with CTR+pPMAC 36 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
When ideal meets real 37 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
When ideal meets real – surprise! 38 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
When ideal meets real – surprise! Legendre MiMC 39 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Other competitive modes 40 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Other competitive modes 41 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Some open problems • Preprocessing scales linearly in terms of number of message blocks - roughly n PRFs for n messages. • Number of rounds of a cipher vs. multiplicative depth in MPC. 42 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Thank you! 43 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
Thank you! • Questions? 44 Dragos Rotaru , N.P. Smart, M. Stam imec-Cosic, Dept. Electrical Engineering
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