We establish the following, quite unexpected, result: replication of data for the computational Private Information Retrieval problem is not necessary. More specifically, based on the quadratic residuosity assumption, we present a single database, computationally-private information-retrieval scheme with O(n ffl ) communication complexity for any ffl ? 0.

A new public key encryption scheme, along with several variants, is proposed and analyzed. The scheme and its variants are quite practical, and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions. These appear to be the first public-key encryption schemes in the literature that are simultaneously practical and provably secure.

We describe and analyze a new digital signature scheme. The new scheme is quite efficient, does not require the the signer to maintain any state, and can be proven secure against adaptive chosen message attack under a reasonable intractability assumption, the so-called Strong RSA Assumption. Moreover, a hash function can be incorporated into the scheme in such a way that it is also secure in the random oracle model under the standard RSA Assumption.

Glover and Punnen (1997) asked whether there exists a polynomial time algorithm that always produces a tour which is not worse than at least n!=p(n) tours for some polynomial p(n) for every TSP instance on n cities. They conjectured that, unless P=NP, the answer to this question is negative. We prove that the answer to this question is, in fact, positive. A generalization of the TSP, the quadratic assignment problem, is also considered with respect to the analogous question. Probabilistic, graph-theoretical, group-theoretical and number-theoretical methods and results are used. Key words: Traveling salesman problem, quadratic assignment problem, approximation algorithm. 1 Introduction The domination number, dom(A;n), of an approximation algorithm for the traveling salesman problem (TSP) is the maximum integer k = k(n) such that, for every instance I of the TSP on n cities, A produces a tour T which is not worse than at least k tours in I including T itself. F. Glover and A.P. Punnen...

We introduce the notion of multi-trapdoor commitments which is a stronger form of trapdoor commitment schemes. We then construct two very e#cient instantiations of multi-trapdoor commitment schemes, based on the Strong RSA Assumption and the recently introduced Strong Di#e-Hellman Assumption.

We provide an overview of an emerging area of domination analysis (DA) of combinatorial optimization algorithms and problems. We consider DA theory and its relevance to computational practice. 1

The modular exponentiation problem is, given integers x; a; m with m ? 0, compute x a mod m. Let n denote the sum of the lengths of x, a, and m in binary. We present a parallel algorithm for this problem that takes O(n= log log n) time on the common CRCW PRAM using O(n 2+ffl ) processors. This algorithm is based on Bernstein's Explicit Chinese Remainder Theorem combined with a fast method for parallel prefix summation. We also present a linear time algorithm for the EREW PRAM. 1 Introduction. In this paper we present a new parallel algorithm for the modular exponentiation problem. This problem is, given integers x; a and a positive integer m, compute x a mod m. Applications for this problem are quite numerous, and include primality testing, integer factoring, the discrete logarithm problem, and cryptographic protocols based on these problems such as RSA. It is not an overstatement to say that modular exponentiation is a fundamentally important problem, and fast algorithms for t...

This document describes the Advanced Cryptographic Engine (ACE). It specifies a public key encryption scheme as well as a digital signature scheme with enough detail to ensure interoperability between different implementations. These schemes are almost as efficient as commercially used schemes, yet unlike such schemes, can be proven secure under reasonable and well-defined intractability assumptions. A concrete security analysis of both schemes is presented.

In this paper we analyze a slight modification of Jebelean’s version of the k-ary GCD algorithm. Jebelean had shown that on n-bit inputs, the algorithm runs in O(n²) time. In this paper, we show that the average running time of our modified algorithm is O(n²/ log n). This analysis involves exploring the behavior of spurious factors introduced during the main loop of the algorithm. We also introduce a Jebeleanstyle left-shift k-ary GCD algorithm with a similar complexity that performs well in practice.

Glover and Punnen (1997) asked whether there exists a polynomial time algorithm that always produces a tour which is not worse than at least n!=p(n) tours for some polynomial p(n) for every TSP instance on n cities. They conjectured that, unless P=NP, the answer to this question is negative. We prove that the answer to this question is, in fact, positive. A generalization of the TSP, the quadratic assignment problem, is also considered with respect to the analogous question. Probabilistic, graph-theoretical, group-theoretical and number-theoretical methods and results are used. Key words: the traveling salesman problem, the quadratic assignment problem, domination analysis, meta-heuristics. 1 Introduction The domination number, dom(A; n), of an approximation algorithm for the traveling salesman problem (TSP) is the maximum integer k = k(n) such that, for every instance I of the TSP on n cities, A produces a tour T which is not worse than at least k tours in I including T itself. Glov...