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Abstract. We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions that are powers of primes is(More)
We introduce a scalable searching protocol for locating and retrieving content in random networks with Power-Law (PL) and heavy-tailed degree distributions. The proposed algorithm is capable of finding any content in the network with probability one in time O(log N), with a total traffic that provably scales sub-linearly with the network size, N. Moreover,(More)
Widespread Internet use has led to the emergence of several kinds of large-scale social networks in cyberspace, most notably e-mail networks. Unfortunately, the tremendous convenience that e-mail affords comes at a high price: Although the network's underlying connectivity is hidden, making it almost impossible to build a comprehensive directory of every(More)
Summingbird is an open-source domain-specific language implemented in Scala and designed to integrate online and batch MapReduce computations in a single framework. Sum-mingbird programs are written using dataflow abstractions such as sources, sinks, and stores, and can run on different execution platforms: Hadoop for batch processing (via(More)
We introduce a scalable searching algorithm for finding nodes and contents in random networks with Power-Law (PL) and heavy-tailed degree distributions. The network is searched using a prob-abilistic broadcast algorithm, where a query message is relayed on each edge with probability just above the bond percolation threshold of the network. We show that if(More)
We prove the security of quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages in a way that their security is(More)
We characterize the complete set of protocols that may be used to securely encrypt n quantum bits using secret and random classical bits. In addition to the application of such quantum encryption protocols to quantum data security, our framework allows for generalizations of many classical cryptographic protocols to quantum data. We show that the encrypted(More)
In this paper we introduce Social VPNs, a novel system architecture which leverages existing social networking infrastructures to enable ad-hoc VPNs which are self-configuring, self-managing, yet maintain security against untrusted parties. The key principles in our approach are: (1) self-configuring virtual network overlays enable seamless bi-directional(More)