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Fig. 11.3 De-centralized data mining with horizontal and vertical partitioning. In the for-
mer, all parties share the same attributes but have different instances. In the latter, parties
have different attributes of the same instances.
Methods addressing these important scenarios are mainly based on the use of
cryptographic techniques (see Yang et al. (2006)) for a discussion of the computa-
tional performance of these kinds of methods). The main idea is to encrypt each
party's data, and share the encrypted data with other parties so that a dedicated al-
gorithm working on encrypted data can produce a result that can then be made
available to all the parties (or, in some cases, to just one selected party). The key
idea in these approaches is the concept of homomorphic encryption of the data
(Paillier 1999) 1 . It will be best explained with the use of a very simple example.
Suppose that we have two parties, A and B , each having a data vector a 1 ,…a n and
b 1 ,…b n , respectively. They cannot show their vector to each other, but they want to
1 Another approach is the use of the Secure Multiparty Computation (SMC) framework.
SMC offers algorithms in which parties compute function results on arguments each of
them owns, through the use of especially designed circuitry, without sharing the argument
values with each other (see e.g. Lindell, Y. and B. Pinkas (2009). "Secure Multiparty
Computation for Privacy-Preserving Data Mining." Journal of Privacy and Confidentiality
1 (1): 59-98. for a thorough presentation of privacy-oriented computation in a distributed
environment we consider here). While theoretically elegant and secure, this approach has
not yet produced computationally acceptable implementations.
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