# Haowen chan  cmu Outline  The Secure Aggregation Problem  Algorithm Description  Algorithm Analysis Proof (sketch) of correctness Proof (sketch) of.

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haowen chan  cmu Outline  The Secure Aggregation Problem  Algorithm Description  Algorithm Analysis Proof (sketch) of correctness Proof (sketch) of overhead bound

haowen chan  cmu In-Network Data Aggregation (( )) Q “What is the sum of all the sensor readings?” 2 4 1 3 0 3 2 0 + 4 + 6 + 9 9 + 15 Answer: Sensor readings

haowen chan  cmu Attacker Model  Unsecured deployment area  Sensor nodes not tamper-resistant  Adversary may undetectably take control of sensor nodes or base station

haowen chan  cmu Correct Data Aggregation (( )) Q 2 4 1 3 0 3 2 0 4 6 9 9 15 3 0 4 2

haowen chan  cmu Sensor Reading Falsification (( )) Q 2 4 1 3 0 3 2 0 4 6 15 21 3 0 10 2 Malicious node reports false sensor reading (within legal bounds)

haowen chan  cmu Sensor Reading Falsification  General aggregation problem: Assume no application-specific information  Attacker’s data indistinguishable from true data Sensor reading falsification is always possible in any general secure aggregation algorithm  Attacker’s ability limited by how many nodes compromised

haowen chan  cmu Aggregation Result Falsification (( )) Q 2 4 1 3 0 3 2 0 4 6 100 106 3 0 4 2 Malicious node reports false aggregation result

haowen chan  cmu Aggregation Result Falsification  Single malicious node may cause unbounded deviation in query result  Secure aggregation problem: Can we restrict the attacker’s ability to falsify aggregation results?  Tightest possible restriction without application knowledge: Attacker can only perform sensor reading falsification attacks or equivalent

haowen chan  cmu Prior Related Work  Either probabilistic detection or only for special cases  Single malicious node L. Hu and D. Evans [2003] P. Jadia and A. Mathuria [2004]  Flat aggregator topology B. Przydatek, A. Perrig, D. Song [2003] W. Du, J. Deng, Y. Han, P.K. Varshney [2003]  Probabilistic Detection B. Przydatek, A. Perrig, D. Song [2003] Y. Yang, X. Wang, S. Zhu, G. Cao [2006]

haowen chan  cmu Our Algorithm  General hierarchical (tree-based) aggregation topologies  Multiple (unbounded) number of compromised nodes  Achieves tightest possible bound on adversary ability to change aggregation result  Low communication overhead edge-congestion O ( l og 2 n )

haowen chan  cmu Outline  The Secure Aggregation Problem  Algorithm Description  Algorithm Analysis Proof (sketch) of correctness Proof (sketch) of overhead bound

haowen chan  cmu Preventing SUM Result Deflation  Consider only the SUM aggregate Straightforward reductions from COUNT, AVG, MEDIAN to SUM  Adversary only wishes to reduce the aggregate result  Sensor readings are nonnegative: in [0, m]  Let the sum of reported sensor readings of all legitimate nodes be S. If adversary reports any S’ < S then we detect its presence.  Adversary gains no additional benefit from aggregation result falsification vs. sensor reading falsification

haowen chan  cmu Generating Commitments  Require nodes to cryptographically commit to a single version of the aggregation process  Any aggregation result falsification cause in an inconsistency in some position in the commitment structure Verification process can discover inconsistency

haowen chan  cmu Commitment Tree  Aggregation Tree  Commitment Tree F E D C B A M A M A M AB M B M AB M C M C … M AB = h ( M A jj M B ) ; v A + v B M D M ABCD M ABCD } v AB M ABCD = h ( M AB jj M D jj M C ) ; v AB + v D + v C … M E M E M F M A = A ; v A M B = B ; v B M R

haowen chan  cmu Main Idea  Commitment structure is probed to verify aggregation correctness  Prior work: Querier performs probing Cannot probe every node Too much congestion near base station  New idea: Distribute the verification process to the sensor nodes  Every sensor node checks that its sensor reading was included in the aggregate

haowen chan  cmu Self-verification  Querier disseminates commitment tree root M R using authenticated broadcast E.g. [Perrig et al. ’01]  Node A verifies its own contribution: Node A receives commitment tree root M R Node A requests all off-path vertices for M A Verify that the inputs to each aggregation step are non-negative Verify that the correct M R can be recomputed ¹ TESLA

haowen chan  cmu Self-Verification of Node C M A M B M AB M C M D M ABCD M E M F R eques t o ® -pa t h ver t i ces f or M C C h ec k t h a t v AB ; v D ; v E ; v F area ll non-nega t i ve M R R ecompu t e M ABCD ; M R

haowen chan  cmu Aggregating Verification Results  Each node shares a secret key with querier  Node A ’s “OK” bit phrase for query k :  OK bit phrases are aggregated using XOR on the way to the querier  Querier verifies that received aggregate bitphrase is XOR of all bit phrases If any node does not respond with OK, this test will fail: aggregation result rejected. MAC K A ( Q uery k ver i ¯ e d OK b yno d e A )

haowen chan  cmu Aggregating with XOR 0010 0011 0110 1111 0101 1010 1000

haowen chan  cmu Outline  The Secure Aggregation Problem  Algorithm Description  Algorithm Analysis Proof (sketch) of correctness Proof (sketch) of overhead bound

haowen chan  cmu Motivating Observations  Correctness: Self-verification is cumulative Net result of all nodes performing independent self-verification is equivalent to having a central querier verify every node  Efficiency: Standard metric: congestion – maximum communication load on any single edge Self-verification incurs low congestion Even if every node performs self-verification

haowen chan  cmu Correctness  Lemma: If two legitimate nodes A and B both pass their verifications, then the SUM aggregate has value at least v A + v B M A M AX M AXYZ v AX ¸ v A M X v X ¸ 0 M YZ v YZ ¸ 0 Observation: Intermediate sums are non-decreasing. v AXYZ ¸ v A

haowen chan  cmu Correctness M C M A M B M R M X M Y v Y ¸ v B v X ¸ v A v C ¸ v A + v B v R ¸ v A + v B s i nce h i sco ll i s i on-res i s t an t M X an d M Y are d i s t i nc t M C : LCA o f M A an d M B

haowen chan  cmu Correctness  Corollary: If all legitimate nodes pass their verifications, then the final aggregation result is at least  Lower bound: Adversary cannot report result less than sum of legitimate sensor readings.  Upper bound? S = X i l eg i t v i

haowen chan  cmu Upper Bound  Reduce upper bound problem to lower bound  Compute simultaneously the complement sum aggregate (recall that )  Querier checks:  Adversary: to increase, must decrease. But neither nor can be decreased below contribution of legitimate nodes. S = n X i = 1 v i S = n X i = 1 ( m ¡ v i ) v i 2 [ 0 ; m ] S S S SS S = nm ¡ S

haowen chan  cmu Efficiency  Suppose aggregation tree is balanced  When node A self-verifies, it receives all off-path vertices in the commitment tree  Maximum congestion: leaf edge messages A O ( l ogn ) O ( l ogn )

haowen chan  cmu Efficiency  Self-verification of other nodes (e.g. node B) does not increase communication load on any edge of the path between node A and the root A B C Y X M X M Y M Y M X M Y M X

haowen chan  cmu Efficiency  Edge congestion in balanced aggregation trees:  For arbitrary unbalanced aggregation topology: Define a balanced logical aggregation overlay over the physical topology (details in paper) Incurs multiplicative factor  Edge congestion for general aggregation trees: O ( l ogn ) l ogn O ( l og 2 n )

haowen chan  cmu Naive Commitment Tree  Aggregation Tree  Commitment Tree F E D C B A M A M A M AB M B M AB M C M C M D M ABCD M ABCD M E M E M F M ABCDEF Topology of commitment tree is identical to aggregation tree (with addition of pendant vertices to all internal nodes)

haowen chan  cmu Balancing the Commitment Tree  Aggregation Tree unbalanced Naïve Commitment Tree unbalanced  Long paths in commitment tree High communication overhead  Idea: Instead of one commitment tree, keep a forest of complete commitment trees  Construct this using delayed aggregation )) O ( l ogn )

haowen chan  cmu Delayed Aggregation  Only perform aggregation on subtrees of equal height M A M A D C B A M AB M B M AB M C M AB ; M C M D M CD M ABCD M ABC M ABC

haowen chan  cmu Delayed Aggregation  All trees in commitment forest are complete and have distinct heights  Tallest tree has height at most  At most trees  Each sensor node receives (and transmits) commitment subtree root values  edge congestion (proof in paper) l ogn O ( l ogn ) l ogn O ( l og 2 n )

haowen chan  cmu Congestion Bound  Commitment tree overlay network of the aggregation tree  Each commitment tree vertex resides at the sensor node that created it  For A to self-probe, Send all off-path vertices to its leaf vertex.  congestion at leaf edge of MAMA O ( l ogn ) O ( l ogn ) ! M A M A

haowen chan  cmu Congestion Bound  In aggregation tree, each sensor node reports roots of subtrees to its parent  Responsible for receiving traffic for parent edges incident to these vertices in the commitment forest  edge-congestion in commitment forest edge congestion in aggregation tree. O ( l ogn ) O ( l ogn ) O ( l ogn ) ) O ( l og 2 n )

haowen chan  cmu Conclusion  Secure data aggregation algorithm Suitable for general tree-based aggregation topologies Resilient vs multiple malicious nodes Tightest possible guarantees on adversary detection (without assuming application knowledge) Low edge congestion Limitation: need to know the set of responding nodes  Future Work: Secure versions of more sophisticated aggregation functions Defences vs sensor reading falsification O ( l og 2 n )

haowen chan  cmu Secure Hierarchical In-network Data Aggregation for Sensor Networks Haowen Chan Adrian Perrig and Dawn Song Carnegie Mellon University

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