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**1 - 4**of**4**### An Existential Locality Theorem

"... Abstract. We prove an existential version of Gaifman's locality theorem andshow how it can be applied algorithmically to evaluate existential first-order sentences in finite structures. 1 Introduction Gaifman's locality theorem [12] states that every first-order sentence is equivalent toa Boolean co ..."

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Abstract. We prove an existential version of Gaifman's locality theorem andshow how it can be applied algorithmically to evaluate existential first-order sentences in finite structures. 1 Introduction Gaifman's locality theorem [12] states that every first-order sentence is equivalent toa Boolean combination of sentences saying: There exist elements a 1; : : : ; ak that arefar apart from one another, and each ai satisfies some local condition described by afirst-order formula whose quantifiers only range over a fixed-size neighborhood of an

### Mathematical Knowledge Archives in Theorema

"... Archives are implemented as an extension of Theorema for representing large bodies of mathematics. They provide various constructs for organizing knowledge bases in a natural way: breaking formulae across cells, grouping them in a hierarchical structure, attaching labels to subhierarchies, disambigu ..."

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Archives are implemented as an extension of Theorema for representing large bodies of mathematics. They provide various constructs for organizing knowledge bases in a natural way: breaking formulae across cells, grouping them in a hierarchical structure, attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces, addressing the domains of categories and functors as namespaces with variable opera− tions. All constructs are logic–internal in the sense that they have a natural translation to higher–order logic so that �mathematical knowledge management � can be treated by the object logic itself. 1

### A Comparative study of Forward Secure Publickey Method Using HIBE and BTE

"... T h e threat of key exposure becoming more acute as cryptographic computations are performed more frequently on poorly protected devices (smart-cards, mobile phones, even PCs), new techniques are needed to deal with this concern. One promising approach which we focus on here is to construct forward ..."

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T h e threat of key exposure becoming more acute as cryptographic computations are performed more frequently on poorly protected devices (smart-cards, mobile phones, even PCs), new techniques are needed to deal with this concern. One promising approach which we focus on here is to construct forward secure cryptosystems. The existence of non-trivial, forwardsecure public-key encryption (PKE) schemes,however, has been open.Forward-secure PKE has the obvious practical advantage that a compromise of the system does not compromise the secrecy of previouslyencrypted information; it is thus appropriate for devices operating in insecure environments. Furthermore, using such a scheme enables some measure of security against adaptive adversaries who may choose which parties to corrupt based on information learned in the course of a given protocol. We presented in this paper variant of scheme with better complexity; in particular, the publickey size and the key-generation/key-update times are independent of N. We suggested a method to achieve chosen ciphertext security for HIBE schemes using the CHK transformation. The resulting schemes are selective-ID chosen-ciphertext secure without random oracles, based on the BTE.