1. DStress: Efficient Differentially Private Computations on Distributed Data
Antonis Papadimitriou, Arjun Narayan, Andreas Haeberlen
University of Pennsylvania

2. Motivation: Systemic risk
Bank A
Bank C
Bank B
If house prices fall
If house prices fall
Bank A
Bank B
Bank C
debt=200
debt=200
payout = 20
Capital =
100 80
Capital =
100
102
120
Capital =
200
218 20 20 18
Banks reduce risk by buying “insurance” contracts
This means they rely on others to meet obligations
B and A will have problems if C goes bankrupt
Systemic risk: The risk of snowball bankruptcies in the financial graph
Measuring it could provide early warning (2008 crisis!)

3. I knew C was going to kill us all!
Challenge: Privacy
All 3 banks fail!
Bank A
Bank B
Bank C
debt=200
debt=200
I knew C was going to kill us all!
Capital = 80
Capital =
102
Capital =
218
Why can’t we collect data and measure the systemic risk?
Economists have algorithms, e.g., [EN, EGJ]
We know how to execute graph algorithms
Privacy concern 1: Graph values and edges are very sensitive
Privacy concern 2: Even the output of the computation can leak information

4. Approach All 3 banks fail! 80 102 218
Bank A
debt=200
Bank B
Bank C
All 3 banks fail!
debt=200
Capital = 80
Capital =
102
Capital =
218
Banks keep data and take part in distributed computation
Goal: Privacy and efficiency
Output privacy
Value privacy
Edge privacy
Efficiency
Result: Private distributed graph computations (not only systemic risk!)
Differential privacy
Existing
Secure multiparty computation (MPC)
Secure message transfer protocol
New
Formulation as vertex programs

5. Outline Systemic risk Privacy concerns Approach
Distributed computation
Protecting values
Protecting edges
Protecting output
Evaluation

6. How do systemic risk algorithms work?40
27/
135/ 40
Bank A
Bank B
Bank C
200 20
Capital = 80
Capital =
102
Capital = 20
prorate: 162*(200/240) = 135
In-payments = = 60
Capital = = 162
Shortfall = = 78
Systemic risk = total shortfall
[EN01] computes the systemic risk by simulating payment between banks
Economists formulate this as a matrix computation
Step:
Aggregation:
But matrix operations are expensive in secure multiparty computation (MPC)
Computing systemic risk for entire US graph would take > 200 years!
𝐹𝐹 𝑝 ′ 𝑝 =Λ 𝑝 ′ Π Τ Λ 𝑝 ′ 𝑝+ 𝐼−Λ 𝑝 ′ 𝑝 +𝑒 +(𝐼−Λ( 𝑝 ′ ))( 𝑝 )
( 𝑝 −𝑝)

7. Systemic risk as a vertex program40
27/
135/ 40
Bank A
Bank B
Bank C
200 20
Capital = 80
Capital =
102
Capital = 20
Idea: Run algorithm as a distributed simulation
The simulation of payments can be expressed as a vertex program
Advantage: Vertex programs are faster in MPC
No matrix ops, no need to read entire matrix

8. Privately running vertex programs
We had to overcome several challenges
Protecting values
Secret sharing
Secure MPC
Protecting edges
Re-sharing
Variant of ElGamal encryption
Re-randomizable encryption keys
Homomorphic mixing
Protecting output
Differential privacy
Sensitivity and utility analysis
Read our paper for details!

9. Privately running vertex programs: Value privacy
B’s Committee
C’s Committee 20
-37 78
-12 52 54
Bank A
Bank B
Bank C
20/200
135/200
Capital = 80
102 20 17
-13
+35
-29 10
Challenge: Hide intermediate values of the computation
Solution: Committee of k banks
Secret sharing and MPC
Result: No committee member can observe intermediate state!

10. Privately running vertex programs: Edge privacy
B’s Committee
C’s Committee
Bank A
Bank B
Bank C 17 17 17
-13
-13
-13
Aha! Contract
(C,B) exists
I have to use blue key – so (C,B) exists
+35
+35
+35
-29
-29
-29 10 10 10
Challenge 1: Direct communication can leak edge
Solution 1: Route shares via C and B
They already know about edge (C,B)
Challenge 2: Encryption keys can leak edge
Solution 2: Use re-randomizable encryption keys
Please look at paper for other challenges!

11. Privately running vertex programs: Output privacy
$100±𝜀
$2000±𝜀 VS
Problem: Output can leak information
Solution: Differential privacy
Add noise to result
Mask contribution of any individual contract
Systemic risk with noise
OK, because we’re looking for devastating effects
For details look at our paper!

12. Outline Systemic risk Privacy concerns Approach
Distributed computation
Protecting values
Protecting edges
Protecting output
Evaluation

13. Implementation and experimental setup
Evaluation questions:
What is the computational cost of vertex programs in MPC?
What is the communication cost of vertex programs in MPC?
How does the size of MPC blocks affect the cost of vertex computations?
What is the cost of message transfers?
What is the end-to-end cost of DStress?
How does DStress compare to monolithic MPC?
Can DStress scale to the size of the entire US financial network?
Evaluation questions:
What is the computational cost of vertex programs in MPC?
What is the communication cost of vertex programs in MPC?
How does the size of MPC blocks affect the cost of vertex computations?
What is the cost of message transfers?
What is the end-to-end cost of DStress?
How does DStress compare to monolithic MPC?
Can DStress scale to the size of the entire US financial network?

14. What is the cost of vertex program steps in MPC?
Vertex update
Message transfer
Aggregate …
Iterations
Vertex update
Message transfer
Aggregate …
Iterations
12 members
16 members
8 members
20 members
[EN01]
EGJ[14]
Aggregation
We evaluated the cost of MPC steps
Eisenberg-Noe, “Systemic Risk in Financial Systems”, Management Science, 2001
Elliott-Golub-Jackson. "Financial networks and contagion." American Economic Review, 2014
Tradeoff between performance and privacy (committee sizes)
Completion time is reasonable even for committees of 20 banks
The largest inter-bank collusion observed involved 16 banks

15. Can DStress scale to the US financial network?
# US banks
We show DStress performance for large networks
This is an extrapolation from smaller scale experiments
DStress would take less than 5 hours for the US financial system!
Compare that with 200+ years for naïve application of MPC

16. Conclusion
Motivation: Computing the systemic risk could serve as an early warning system for the financial network
Solution: DStress can execute distributed vertex programs with privacy guarantees
Challenges: Many subtle ways sensitive information can leak
Differential privacy to protect output
Secret sharing and MPC to hide intermediate values
Secure message transfer protocol to hide edges
Evaluation: DStress could be used for graphs the size of the US financial system
Thank you!