MPC across the wire: There is something you require Dragos Rotaru - PowerPoint PPT Presentation

TPMPC 2018 MPC across the wire: There is something you require Dragos Rotaru KU Leuven, University of Bristol 1 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

$6.3M question – Brandeis program Enc( K , ) K 2 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

$6.3M question – Brandeis program K 3 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

$6.3M question – Brandeis program C = Enc( K , ) K 4 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

MPC and Long-term storage some research shortage… 5 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage 42 𝑁 1 6 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage 42 + + = 𝑁 1 𝑁 2 𝑁 3 42 𝑁 1 𝑁 3 𝑁 2 7 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage + + = 𝑁 1 𝑁 2 𝑁 3 42 𝑁 1 𝑁 3 𝑁 2 8 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage K + + = 𝑁 1 𝑁 2 𝑁 3 42 𝑁 1 𝑁 3 𝑁 2 9 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage K + + = 𝑁 1 𝑁 2 𝑁 3 42 𝑁 1 𝑁 3 𝑁 2 10 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage + + = 𝑁 1 𝑁 2 𝑁 3 42 + + = 𝐿 1 𝐿 2 𝐿 3 K 𝑁 1 𝐿 1 𝑁 3 𝐿 3 𝑁 2 𝐿 2 11 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage + + = 𝑁 1 𝑁 2 𝑁 3 42 + + = 𝐿 1 𝐿 2 𝐿 3 K 𝑁 1 𝐿 1 𝑁 3 𝐿 3 Enc( 𝐿 1 , 𝑁 1 ) Enc( 𝐿 3 , 𝑁 3 ) 𝑁 2 𝐿 2 Enc( 𝐿 2 , 𝑁 2 ) 12 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage Too many keys! + + + + Let’s keep it simple. = 𝑁 1 𝑁 1 𝑁 2 𝑁 2 𝑁 3 𝑁 3 42 + + = 𝐿 1 𝐿 2 𝐿 3 K 𝑁 1 𝑁 1 𝐿 1 𝐿 1 𝑁 3 𝑁 3 𝐿 3 𝐿 3 Enc( 𝐿 1 , 𝑁 1 ) Enc( 𝐿 3 , 𝑁 3 ) 𝑁 2 𝑁 2 𝐿 2 𝐿 2 Enc( 𝐿 2 , 𝑁 2 ) 13 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage + + = 𝑁 1 𝑁 2 𝑁 3 42 + + = 𝐿 1 𝐿 2 𝐿 3 K 𝑁 1 𝐿 1 𝑁 3 𝐿 3 𝑁 2 𝐿 2 14 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage I can also detect whether parties used incorrect keys. K Enc(K,42) Tag(Enc(K,42)) 15 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Long-term storage I can also detect whether parties • Can be used to remove interaction used incorrect keys. when providing inputs to SPDZ [DDN+15]. K Enc(K,42) Tag(Enc(K,42)) 16 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Tricks to get a PhD in crypto* 17 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Line of work - mod p Tag(Enc(42)) Enc(42) PRFs: NR, MiMC, Leg. AE: OTR, PMAC. CCS’16 FSE’18 [GRRSS] [RSS] Generalized MiMC, Fewer triples per message block. ?’18 [AGPRRRRS] 18 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Authenticated Encryption in MPC [42] Enc(42) Tag(42) • Useful MPC happens in Fp => Need AE and PRFs modp. • Look for parallel AE: CTR+PMAC, OTR. • MPC framework splits computation in 2 phases: • Input independent pre-processing. • Online phase where inputs are used. 19 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Tweak your encryption to MPC 20 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

And the winner is… CTR+HtMAC Ciphertexts can be revealed. 21 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

And the winner is… CTR+HtMAC Ciphertexts can be revealed. Would be cool to have a formal security model: - What we can reveal. - What we should hide. 22 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

When ideal meets real 23 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

When ideal meets real – surprise! 24 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

When ideal meets real – surprise! Legendre MiMC 25 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Can we cripple…the triple(s)? • Pre-processing cost scales linearly with the number of blocks. 26 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

MiMC 𝑌 1 𝑌 2 𝑌 2 𝑌 3 𝑌 3 𝑌 4 𝑌 4 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 … … … … … … … 73 * L 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐺 𝑙 𝐷 1 𝐷 2 𝐷 1 𝐷 1 𝐷 3 𝐷 1 𝐷 4 27 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

GMiMC 𝑌 1 𝑌 2 𝑌 3 𝑌 4 1.262*128 + 2*L - 1 28 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Putting the (GMi)MC into MPC 29 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Putting the (GMi)MC into MPC 30 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Putting the (GMi)MC into MPC 31 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Putting the (GMi)MC into MPC 32 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

Putting the (GMi)MC into MPC Trust no one. Do your experiments. 33 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

My lyrics get stolen by MiMCs, I gotta ‘tag’ my rhymes with MPC; But I keep on generatin' like a PRG 'Cause there's so much drama in the PhD. * * Adapted from ‘So Much Drama in the PhD’ by Monzy 34 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering

My lyrics get stolen by miMCs, I gotta ‘tag’ my rhymes with MPC; But I keep on generatin' like a PRG 'Cause there's so much drama in the PhD. * Thank you! * Adapted from ‘So Much Drama in the PhD’ by Monzy 35 Dragos Rotaru imec-Cosic, Dept. Electrical Engineering