1. Resilient Aggregation in Sensor Networks
David Wagner

2. An abstract model
Consider only a single base station and n associated sensor nodes.
Ignore the inner workings of the specific aggregation and communication protocol.
Ignore the structure of the multi-hop network.

3. Threat model
Each sensor node has a secure channel back to the base station.
Secure channels are independent.
The adversary can inject arbitrarily chosen malicious data readings at a few sensors.
The adversary’s capabilities are not unlimited.
Base stations remain trustworthy and unassailable.

4. Central question for secure aggregation
Which aggregation functionalities can be securely and meaningfully computed, in the presence of a few compromised nodes?
Any aggregate that is resilient against malicious attack will also be resilient against random failure.

5. Attacks on existing aggregation functions
The average is insecure.
The sum is insecure.
The minimum is insecure.
The maximum is insecure.
A single node can exert control over the whole function.
The count can be secured!

6. Estimation theory Root mean square error:
Given a sequence of observations X1,…,Xn from a known parameterized distribution p(X|θ) , where θ is a hidden parameter, the goal is to estimate θ as accurately as possible.
Root mean square error:

7. Suppose attack is specified by function A, the inaccuracy is measured by
An aggregation function is (k, α) resilient if f satisfies the following equation.

8. Informal result:
Let f be an unbiased estimator, let σ denote the standard deviation of f(X1,…,Xn) in the absence of compromised nodes. If f is (k,α) resilient, then it can be computed at a base station with bias on the order of ±ασ or less. Conversely, if f is not (k,α) resilient, then no matter how f is computed, the adversary can skew the result by more than ±ασ at least some of the time.

9. Satisfactory and unsatisfactory aggregation functions
Data model:
For continuous data, assume that each sensor reading follows the Gaussian distribution.
For 0/1-valued data, assume that each sensor reading follows the Bernoulli distribution.

10. 2. The minimum and maximum They are not (1,α) resilient The count
The average and sum
They are not (1,α) resilient.
2. The minimum and maximum
They are not (1,α) resilient
The count
It is (k, α) resilient.
The median

11. Tools for achieving resilient aggregation:
Truncation
Trimming
Open problem:
Consider in-network aggregation in the future.
Consider more complex aggregation functions.