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Asymmetric encryption uses two keys: a public key and a private key Whatever is encrypted with one key can be decrypted only with the other key In this scenario, I give my public key out to the world so anyone can retrieve it Then I keep my private key secure When someone wants to send me an encrypted message that person encrypts it with my public key Once it is encrypted with my public key it can be decrypted only with my private key This solves both the key exchange problem and the non-repudiation problem Asymmetric encryption, though, is very slow The important thing to remember with asymmetric encryption is that the key does not have to be sent over a secure channel, but it does have to be sent over a trusted channel A secure channel is one on which no one can read any information in transit.

Note: The results of this subsection are partly given in Magnus & Neudecker (1988, 9, Sec. 9 and 13) and partly follow from their results by straightforward application of the rules for the trace and matrix derivatives, notably the chain rule and the product rules of Section 10.5.

thesis, School of Computer Science, Carleton University, January 2001 38 H O Tan and I Korpeoglu Power ef cient data gathering and aggregation in wireless sensor networks ACM SIGMOD Record, 32(4):66 71, December 2003 39 M Khan, G Pandurangan, and B Bhargava Energy-Ef cient Routing Schemes for Sensor Networks, Technical Report CSD TR 03-013, Purdue University, July 2003..

The COOP and the P2P distributed database environments are two new DDBE alternatives. Both of them support dynamic content-provider deployment and participation (registration and deregistration) as the primary goal. Because they both share some common architectural subsystems (namely, the GIS and the LDS), they both allow multiple versions of global constructs and multiple deployment plans for the same global construct to coexist within the environment at the same time. These environments work best for read operations, because they provide no architectural mechanism for enforcing data synchronization of of ine content (content deployed at LDBEs that are unregistered at the time of modi cation). Although they do not prohibit CRUD operations, the implementation of non-read operations is more complex than read-only operations. The COOP environment uses separate components and/or subsystems for the major functions used in implementing a distributed query: the parsing, disambiguation, and processing of the smaller parts of the query based on deployment details. The P2P uses a single component or subsystem for all query processing steps (parsing, disambiguation, and processing of parts). Both environments use a separate client subsystem, a separate GIS subsystem, and separate LDS subsystem. Clients connect to the DQSP component or subsystem in the COOP environment or the QSP component or subsystem in the P2P environment. Both environments rely on the Directory Services (especially the Registration Service) provided by the underlying DDBE Platform. The dynamic registration and lack of total synchronization are the primary differences between these environments and traditional DDBEs. These are also the primary differences between these environments and other DDBE alternatives. However, the COOP and P2P environments both share some characteristics in common with federated DDBEs. There are also other DDBE alternatives that use a similar (but not identical) approach for query plan creation and optimization.

A trusted channel is one on which you can read information, but you are assured that the information comes from a trusted source and therefore has not been modified in transit Asymmetric encryption requires a trusted channel because anyone can generate a key pair and spoof someone s public key To minimize or reduce the chance of spoofing you have to have some level of confidence that the key came from the expected recipient How does asymmetric encryption solve the non-repudiation problem Remember that with asymmetric encryption, anything encrypted with one key can be decrypted only with the second key If I want to prove that I sent something I would encrypt it with my private key By doing this, although anyone could read the message, only I could have sent it because the public key will work only on a message encrypted with my private key.

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