1. Ioannis Ioannidis, Ananth Grama and Ioannis Ioannidis
A Secure Protocol for Computing Dot-products in Clustered and Distributed Environments
Ioannis Ioannidis, Ananth Grama and Ioannis Ioannidis

2. The Problem Dot-products are the basis of many important applications
Scientific computations
Data mining
Transaction processing
Biometrics
Use of distributed environments creates security issues
Data too valuable to expose
Untrusted links or hosts
Spoofing is very easy

3. A Solution Use conventional cryptography
Secure tunneling can protect the links
More complex protocols offer protection against untrusted hosts
Unfortunately, public-key crypto has a high complexity
Modular exponentiation computations can have a crippling effect on the overall performance

4. Security Vs. Efficiency
Ideally, no information should leak about the participating vectors during a secure dot-product protocol
However, in a clustered environment, security need not be so tight
Rarely an attack will be powerful enough to demand the highest level of protection
Some leakage may be acceptable, since the same dot-product will not be computed multiple times
Small compromises in security can lead to large gains in efficiency

5. An Efficient Alternative
Use linear algebra properties to achieve a sufficient level of security
Hide a vector inside a matrix
Scramble the matrix
Multiply the matrix by the other vector
Retrieve the dot-product
A large part of the computations can be reused
Both parties must share a secret – a number – before the protocol

6. An Efficient Alternative
Security is not perfect
A small number of equations will leak
Statistics can give something away
But is sufficient for a real-world setting
If you don’t need to execute the same instance many times, leaking a few equations is not such big problem
Statistical attacks demand larges amounts of information
Not so easy to gather them in clustered environments

7. Overhead Considerations
Two types of overhead
Time overhead
How much more computation needs to be performed
Public-key cryptography adds an unacceptable amount of overhead
But it is the only solution if perfect secrecy is the goal
Communication overhead
Network latency prevails in larger networks
Bit count is the decisive factor in tight networks

8. Stability Considerations
Algebraic manipulations of the data can introduce numerical errors in scientific computation data
Any protocol applied to real-valued vectors must be numerically stable to be of practical importance

9. Experimental Results
The protocol was executed on two PIII/450Mhz machines coupled with a Gigabit Ethernet network
Data were randomly generated vectors of length 10⁶
We measured the total overhead (computation and communication)
Communication overhead was expected to be a factor of 4

10. Experimental Results
Measured overhead showed a factor of 4.69 overhead
Communication overhead is the dominating factor, even on a fast network
Average numerical error was measured to 4.5•10ˉ⁹

11. Conclusions and Ongoing Research
It is possible to execute multiparty, real-valued dot-product computations efficiently and with satisfactory security
Binary dot-products pose a different problem due to the sparsity of the vectors
Number theoretic techniques introduce large time and communication overheads