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Threshold public key encryption is a cryptographic primitive where a secret key of an organization is distributed among special members called decryption servers (insiders) and a certain threshold number of insiders must cooperate to decrypt any ciphertext. Threshold public key encryption with an additional randomized algorithmTsplitis called resplittable threshold public key encryption (RTPKE). Cryptographic primitiveRTPKEwas introduced by Hanaokaet al.[Generic construction of chosen ciphertext secure proxy re-encryption, inCT-RSA, San Francisco, CA, USA, LNCS, O. Dunkelman, ed., Springer-Verlag, Heidelberg, 2012, pp. 349–364] in a generic construction of chosen ciphertext attack secure proxy re-encryption scheme. InMIST2013 conference Singhet al.[Lattice based efficient threshold public key encryption scheme, J. Wirel. Mob. Netw. Ubiquitous Comput. Dependable Appl. (JoWUA) 4(4) (2013), pp. 93–107] presented lattice-basedRTPKEscheme based on Regev's LWE [On lattices, learning with errors, random linear codes, and cryptography, inSTOC, Baltimore, MD, USA, H.N. Gabow and R. Fagin, eds., ACM, University of Wales, Cardiff, 2005, pp. 84–93] assumption. In this paper, we propose lattice-basedRTPKEscheme in the identity-based setting. [ABSTRACT FROM AUTHOR]

This paper proposes an encryption scheme secure against chosen cipher text attack, built on the Niederreiter encryption scheme. The security of the scheme is based on the hardness of the Syndrome Decoding problem and the Goppa Code Distinguishability problem. The scheme uses the techniques provided by Peikert and Waters using the lossy trapdoor functions. Compared to the existing IND-CCA2 secure variants in standard model due to Dowsley et.al. and Freeman et. al. (using the κ repetition paradigm initiated by Rosen and Segev), this scheme is more efficient as it avoids κ repetitions. [ABSTRACT FROM AUTHOR]

For a fixed integer r ≥ 2, the K[sub r]-packing problem is to find the maximum number of pairwise vertex-disjoint K[sub r]'s (complete graphs on r vertices) in a given graph. The K[sub r]-factor problem asks for the existence of a partition of the vertex set of a graph into K[sub r]'s. The K[sub r]-packing problem is a natural generalization of the classical matching problem, but turns out to be much harder for r ≥ 3 — it is known that for r ≥ 3 the K[sub r]-factor problem is NP-complete for graphs with clique number r [16]. This paper considers the complexity of the K[sub r]-packing problem on restricted classes of graphs. [ABSTRACT FROM AUTHOR]

In 1998, at Eurocrypt, a novel primitive, called Proxy Re-Encryption (PRE) was introduced by Blaze, Bleumer and Strauss [1]. In the given concept, a delegator computes re-encryption key and gives it to the semi trusted proxy. Then proxy can convert a message, enciphered with Alice's public key into a message, enciphered with Bob's public key without knowing the message. Upto best our knowledge, we have proposed the first unidirectional PRE scheme, which is noninteractive and based on lattice based identity based cryptosystem. In this scheme a trapdoor function is used for lattices, which is proposed by Micciancio and Peikert [2]. It is simple, efficient, strong and easy to implement compared to [3]. In 2013, Wang et al.[4, 5] introduced a new primitive: PRE + , which is similar to the conventional PRE except that, in PRE + scheme encryptor computes re-encryption keys. Here encryptor is the delegator. We have also constructed a lattice identity based unidirectional PRE + scheme. [ABSTRACT FROM AUTHOR]

In Peer-to-Peer (P2P) network systems, content (object) delivery between nodes is often required. One way to study such a distributed system is by defining games, which involve selfish nodes that make strategic choices on replicating content in their local limited memory (cache) or accessing content from other nodes for a cost. These Selfish Replication games have been introduced in Chun et al. (2004) for nodes that do not have any capacity limits, leaving the capacitated problem, i.e. Capacitated Selfish Replication (CSR) games, open. In this work, we first form the model of the CSR games, for which we perform a Nash equilibria analysis. In particular, we focus on hierarchical networks, given their extensive use to model communication costs of content delivery in P2P systems. We present an exact polynomial-time algorithm for any hierarchical network, under two constraints on the utility functions: 1) "Nearer is better", i.e. the closest the content is to the node the less its access cost is, and 2) "Independence of irrelevant alternatives", i.e. aggregation of individual node preferences. This generalization represents a vast class of utilities and more interestingly allows each of the nodes to have simultaneously completely different functional forms of utility functions. In this general framework, we present CSR games results on arbitrary networks and outline the boundary between intractability and effective computability in terms of the network structure, object preferences, and the total number of objects. Moreover, we prove that the problem of equilibria existence becomes NP-hard for general CSR games. By adding some constraints in the number of objects and their preferences, we show that the equilibrium can be found in polynomial time. Finally, we introduce the fractional version of CSR games (F-CSR) to represent content distribution. We prove that equilibrium exists for every F-CSR game, but it is PPAD-complete. [ABSTRACT FROM AUTHOR]