Secure Multi-Party Computation of Probabilistic Threat Propagation

Transcription

1 Secure Multi-Party Computation of Probabilistic Threat Propagation Emily Shen Nabil Schear, Ellen Vitercik, Arkady Yerukhimovich Graph Exploitation Symposium 216 DISTRIBUTION STATEMENT A. Approved for public release: distribution unlimited. This material is based upon work supported by the Assistant Secretary of Defense for Research and Engineering under Air Force Contract No. FA C-2 and/or FA D-1. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Assistant Secretary of Defense for Research and Engineering. 216 Massachusetts Institute of Technology. Delivered to the US Government with Unlimited Rights, as defined in DFARS Part or 714 (Feb 214). Notwithstanding any copyright notice, U.S. Government rights in this work are defined by DFARS or DFARS as detailed above. Use of this work other than as specifically authorized by the U.S. Government may violate any copyrights that exist in this work.

2 Problem: Collaborative Cyber Defense Companies should share cyber threat information with each other and USG to prevent attacks Sector-Specific Sharing Centers Global cyber situational awareness benefits all However, cybersecurity information is sensitive Prior attacks may indicate weaknesses in defense Business information could be used by competitors Goal: Compute joint analytics without sharing sensitive cyber security information MPC PPT class -

3 Cloud Threat Sharing Tenant A Internet/ WAN Cloud Tenant B Cloud introduces provider and multiple tenants with varying trust MPC PPT class - 4

4 Cloud Threat Sharing Tenant A Internet/ WAN Cloud Tenant B Cloud introduces provider and multiple tenants with varying trust MPC PPT class - 5

5 Outline Motivation Probabilistic Threat Propagation (PTP) Secure Multi-Party Computation (MPC) Application of MPC to PTP MPC PPT class - 6

6 Probabilistic Threat Propagation (PTP) Tenant A Internet/ WAN Cloud Tenant B Goal: Use connectivity graph and known bad hosts to predict other compromised hosts MPC PPT class - 7 Kevin M. Carter, Nwokedi C. Idika, William W. Streilein: Probabilistic Threat Propagation for Network Security. IEEE Transactions on Information Forensics and Security 9(9): (214)

7 Probabilistic Threat Propagation (PTP) Tenant A Internet/ WAN Cloud Tenant B Tenants don t want to share compromised host info with each other or with provider MPC PPT class - 8 Kevin M. Carter, Nwokedi C. Idika, William W. Streilein: Probabilistic Threat Propagation for Network Security. IEEE Transactions on Information Forensics and Security 9(9): (214)

8 Outline Motivation Probabilistic Threat Propagation (PTP) Secure Multi-Party Computation (MPC) Application of MPC to PTP MPC PPT class - 9

9 Secure Multi-Party Computation (MPC) Ideal World Real World x 1 x 1 x 5 x 2 x 5 MPC Protocol x 2 x 4 x Output: (y 1,,y n ) = f(x 1,, x n ) x 4 x MPC emulates a trusted party, assuming no more than a threshold number of adversarial parties, guaranteeing: Correctness of computation Confidentiality of inputs and outputs MPC PPT class - 1

10 Secret Sharing Overview Party 7 Party 1 Party n s 1 s 7 s n Party 2 s 2 Party s Party 4 s 4 Each secret value can be split into pieces ( shares ) If enough people combine shares, they can reconstruct the secret Otherwise, no one learns any info Party 6 s 6 Party 5 s 5 Slide credit: Sasha Berkoff MPC PPT class - 11

11 MPC Based on Secret Sharing Party i To perform MPC, each party: Sends shares of its secret to each other party Computes on shares Addition: local computation Multiplication: requires interaction Interacts to combine manipulated shares to obtain final answer Slide credit: Sasha Berkoff MPC PPT class - 12

12 Secret Sharing Example To secret share for a threshold k: Give each party a point on a random degree-k polynomial Reconstruction: interpolate any >k points to recover degree-k polynomial Addition (s + t): f(i) + g(i) Multiplication (s t): f(i) g(i), then interactive degree reduction Share s + t s t Example: threshold k = 1 (f + g)(x) f(x) g(x) 1 2 Party Secret sharing can be used to compute any arithmetic function securely MPC PPT class - 1 BGW Ben-or, Goldwasser, Wigderson: Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation (Extended Abstract). STOC 1988

13 Outline Motivation Probabilistic Threat Propagation (PTP) Secure Multi-Party Computation (MPC) Application of MPC to PTP MPC PPT class - 14

14 Secure Multi-Party Computation of PTP Tenant A Internet/ WAN Cloud Tenant B Tenants secret-share compromised host info with other tenants, jointly compute PTP securely MPC PPT class - 15

15 Secure Multi-Party Computation of PTP Tenant A Internet/ WAN Cloud Tenant B Each party learns about compromised hosts in its own network and on the Internet MPC PPT class - 16

16 Secure Multi-Party Computation of PTP Probabilistic Threat Propagation Algorithm MPC Operations N 2 mult-by-const N 2 mult-by-const, adds N 2 adds N 2 mults N mults, N adds N mults, 2N adds, 1 comp Map high-level algorithm to mathematical operations Low overhead: add; multiply by constants High overhead: multiply, compare MPC PPT class - 17

17 MPC Optimization Techniques 1 Fixed Point Arithmetic 2 Oblivious Selection Sparse Matrices Efficiently compute on noninteger values using secure fixed point arithmetic Representation Addition Select/assign values to/from secret indices using secretshared indicator vector Reduce computation on sparse matrices by storing only nonzero entries Original Multiplication = ( a b) 2 Original shares Indicator vector New shares Sparse Nonzeros 5 Row indices Col indices All MPC computation done on integer values MPC hides selection/assignment indices MPC operations only needed on nonzero entries MPC PPT class - 18

18 Performance of Secure Multi-Party Computation of PTP Time for 5 iterations (seconds) hours 86 Seconds Baseline MPC Optimized MPC Number of nodes Optimizations result in >25 speedup over baseline MPC MPC PPT class - 19

19 Summary Graph analytics (e.g., probabilistic threat propagation) have important applications to cyber security Privacy concerns may restrict ability to perform joint analytics Secure multi-party computation enables privacy-preserving computation of analytics Designed and optimized MPC for PTP, achieving significant speedup over baseline MPC Future work: design and optimize secure computation other useful graph analytics MPC PPT class - 2