muthuramakrishnan venkitasubramaniam workshop: theory and practice of secure multiparty computation...
TRANSCRIPT
Muthuramakrishnan Venkitasubramaniam
WORKSHOP: THEORY AND PRACTICE OF SECURE MULTIPARTY COMPUTATION
Adaptive UC from New Notions of Non-Malleability15 years of UC-Security [Canetti00]
25 years of Adaptive Security [Beaver89]
dynamic
Joint with Dana Dachman-Soled, Maryana Raykova, Tal Malkin
How can we achieve semi-honest2-party computation?
Y A O
O(1)-rnd
^
IDEALREAL
AR
AI
x2 y2 x2y2
Security by Comparison
x1 y1 x1 y1
“as correct & private as”Correctness: The output of every player is the same in real and ideal
Mesgs
Privacy: Mesgs can be generated from the simulator’s input & output
Simulator
IDEALREALConcurrent Security
many executions ofdifferent protocols
many executions with
independent trusted parties
Arbitrary network Arbitrary network
REAL WORLD IDEAL WORLD
Universal Composability [C]
ARAI
Simulate messages without honest input Independence of executions
Theorem [CF, CKL, L]: It is impossible to achieve UC-security for all “non-trivial functionalities”
What can we implement with UC- Security?
SOLUTION: Get some “limited” help from a trusted party
ORRelax definition of security
……
Static Corruption
Adaptive Corruption
corrupt in the beginning
corrupt adaptivelyduring execution
• Stronger definition of security Static security does not imply adaptive security
• Implies leakage resilience* [BCH12,NVZ13]
• Relevant to cloud security [RTSS09] Adaptively co-locate VMs Side channel attacks
Why Adaptive Security?
— Common Reference String [CLOS02,DN02,DG03,CPS07]
— Public Key Registration [BCNP04]
Trusted Setups
General Results in Adaptive UC-Security?
Relaxed Security— Super-Poly Time Simulation (SPS) [BS05]
What about Static UC-Security?
— Common Reference String [CLOS02,DN02,DG03,CPS07,DNO10]
— Public Key Registration [BCNP04,DNO10]
— Tamper-Proof Hardware [Kat07,CGS08,GISVW10]
— Timing Model [DNS98,KLP05]
Trusted Setups
What about Static UC-Security?
Relaxed Security— Super-Poly Time Simulation (SPS) [Pas03, BS05, GGJS12]
— Angel-based Security Model [PS04, MMY06,CLP10]
— Bounded (Player) Concurrent[Barak]
— Non-Uniform Simulation [LPV09]
— A unified framework to achieve security in any setup under minimal trusted infrastructure [LPV09]
— Can achieve security assuming only SA-OT [DNO10,LPV12]
Static Security :
State of the Art
Adaptive Security : — Construction only in a few trusted setups— Constructions based on specific assumptions such as dense
cryptosystems, trapdoor simulatable PKE— Require independent setups for every pair of parties, e.g
sunspots [CPS07]
UC-puzzleSimulation
Trusted SetupStand-Alone
Non-malleabiltyOne-Way Functions
Non-malleability
UC-Security
Achieving UC-Security - Static Case [LPV09]
Puzzle
Static Security :
Static OT Puzzle Static
UC
This work: When, and at what cost, can Adaptive UC security be acheived?
Achieving UC-Security - Static Case [LPV09,LPV12]
NMC
Static Security :
Ideally…
Adaptive Security :
Static OT Puzzle Static
UC
Adap. OT
Adap.Puzzle
Adap.UC
NMC
?
Static Security :
Our Work
Adaptive Security :
Static OT Puzzle Static
UC
Adap. OT
Adap.Puzzle
Adap.UC
NMC
?
Static Security :
Adaptive Security :
Static OT Puzzle Static
UC
Adap. OT
Adap.Puzzle
Adap.UC
Simul. PKE
Our Work
NMC
?
Static Security :
Adaptive Security :
Static OT Puzzle Static
UC
Adap. OT
Adap.Puzzle
Adap.UC
Simul. PKE
Our Work
NMC
NM*
Adaptive Security :
Adap. OT
Adap.Puzzle
Adap.UC
Simul. PKE
Our Work
Simulatable Public Key Encryption [DN00]• Oblivious Sampling of Public Keys/Ciphertexts• Invertable randomness for oblivious algs.=> Non-commiting Encryption [CFGN96,DN00]
NM*
Assuming existence of simulatable PKE, Adaptive UC-security is achievable in any
setup that admits an Adaptive Puzzle
Main Theorem
Previous results - simple corollaries Improved complexity assumptions
New models – non-uniform, bounded conc.
UC-puzzleAdap. Simulation
Trusted Setup
Adap. Non-malleability
Adaptive UC-Security
Achieving UC-Security - Adaptive Case
Cannot decouple! stand alone adaptivity requires setup
UC-puzzleAdap. Simulation
Trusted Setup
Adap. Non-malleability
Adaptive UC-Security
Achieving UC-Security - Adaptive Case
Adap. UC-Puzzle[LPV09] TODAY
Commitment SchemeThe “digital analogue” of sealed envelopes.
Com(v)
Decommitmentphase
v
v
Sender/committer Receiver
Hiding: The commitment hides the committed value
Commitmentphase
d
Binding: The commitment can only open to one value
Com(u)
MIM Attack on Commitments[DDN91]
Receiver/SenderSender Receiver
Com(u+1)
Man in the Middle
MIM ”mauls” left commitmentinto another to a related value
Non-Malleable w.r.t commitment[DDN91, PR05, LPV08]
i j ≠ i
IDEAL
REAL
Ci(u) Cj(v)
Simulator
MIM
Output v’ = v
Cj(v’)
Can construct O(1) round concurrent NMC w.r.t commitmentbased on OWFs [LP12,Goy12]
Non-Malleable w.r.t opening[CIO98,FF00,PR05]
i j ≠ i
IDEAL
REAL
Ci(u) Cj(v)
MIM
Cj(v’)
u v
u v'
Simulator
Can construct O(1) round stand-alone NMC w.r.t openingbased on CRHs for sychronized adversaries [PR05]
What we need?
Ci3(w) Cj1(v)
MIMw
v
Ci1(u)
uCi2(t)
tCi4(x)
xCi5(y)
y
Cj2(v’)
v'
Cj3(u’)
u'
Concurrent Non-Malleable Commitments w.r.t opening
Adaptively Secure
Concurrent Non-Malleable Commitments w.r.t opening
Adaptively Secure
MIM
Ci1(u)
u
Ci2(w)
w
Cj(v’)
v'…
… Simulator
u
w
Cj(v’)
v'
……
v’
Relaxation: Left commitments are i.i.d samples
Main Lemma: Assuming OWFs and Puzzle, O(n)-round Adaptively-secure Conc. NMC w.r.t opening and i.i.d samples
No additional trusted infrastructure to achieve non-malleability!
A single CRS/URS/sunspot is sufficient same gains as static case
Relaxation: Left commitments are i.i.d samples
“What is a few rounds of communication between friends”
i.e., Receiving Green does not help giving Orange and vice versa
Non-Malleable Sub-protocols
Ingredient I – Scheduling [DDN]
Ingredient I – Scheduling [DDN]
Can rewind the right without rewinding the left!
Id = 0 Id = 1
Simulation
Soundness
Challenger Solver
No Malicious Solver can output trapdoor after interaction
TRAPDOOR
NP-statement
Concurrent Adversary Challenger A, Simulator S that simulates all puzzles indistinguishably while
extracting the trapdoor
Puzzle
NP-witness
UC-
Ingredient II – Instance Based Comm. [LZ09]
W/O Trapdoor: Commitment is bindingWith Trapdoor: Reveal it to 0 and 1
UC-PuzzleNP-statement
Hamiltonian Circuit
Scheme: Commit to adjacency matrix
Commit 0 : Commit to true adjacency matrixCommit 1 : Commit to a simple cycleEquivocate : Commit to true adjacency matrix
Application: Conc. NM Coin Tossing
ANMCOM(r)
r'
r
Coin toss output = r+r’
IDEA FOR UC-COM: Create two URSSender to Receiver (URS1) – equivocate (using OWF)Receiver to Sender (URS2) – extract (using sim PKE)
Main TheoremAssuming existence of sim. PKE and Adap.UC Puzzle,
Adaptive UC-security is achievable
Assuming existence of OWFs and Adap.UC Puzzle, O(n)-round Adaptively-secure
Concurrent NMC w.r.t opening and i.i.d samples
Main Lemma
UC-Puzzle: Hard for Adversary to solve in real worldEasy for Simulator to obtain trapdoor
— Common Reference String [CLOS02,CPS07,CDPW07,DNO10]
— Public Key Registration [BCNP04,DNO10]
— Tamper-Proof Hardware [Kat07,CGS08,GISVW10]
— Timing Model [DNS98,KLP05]
Trusted Setups
Corollaries
Relaxed Security— Super-Poly Time Simulation (SPS) [Pas03, BS05, GGJS12]
— Angel-based Security Model [PS04, MMY06,CLP10]
— Bounded (Player) Concurrent[Barak, Goyal1, Goyal2]
— Non-Uniform Simulation [LPV09]
✓✓✓✓
✓
✓✓
Adaptive UC Security
Sim. PKE and PuzzleO(nd)-rounds(d = depth(C))
Not Everything! [IKOS10]
Static vs AdaptiveStatic UC Security
Assumptions SA-OT and PuzzleNECESS. And SUFF.
Rounds O(1)-rounds
What can we compute?
Any PPT computation
Conclusion
• Characterize when Adaptive UC is achievable• Next… Reduce complexity assumptions
– trapdoor simulatable PKE are suff. for NCE [CDMW09]– improve round complexity
• [Recent] UC-Adaptive Security in O(d)-rounds [V14]
• Angel Based UC-Security [PS04,CLP10,…]– reasonable model without any setup– implies SPS– linear-blowup in rounds with black-box tech. [GS12]
How can we achieve semi-honest2-party computation?
O(1)-rnd adaptive
^
… still open
THANKS