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The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Open Problems in Number Theoretic Complexity, II
"... this paper contains a list of 36 open problems in numbertheoretic complexity. We expect that none of these problems are easy; we are sure that many of them are hard. This list of problems reflects our own interests and should not be viewed as definitive. As the field changes and becomes deeper, new ..."
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this paper contains a list of 36 open problems in numbertheoretic complexity. We expect that none of these problems are easy; we are sure that many of them are hard. This list of problems reflects our own interests and should not be viewed as definitive. As the field changes and becomes deeper, new problems will emerge and old problems will lose favor. Ideally there will be other `open problems' papers in future ANTS proceedings to help guide the field. It is likely that some of the problems presented here will remain open for the forseeable future. However, it is possible in some cases to make progress by solving subproblems, or by establishing reductions between problems, or by settling problems under the assumption of one or more well known hypotheses (e.g. the various extended Riemann hypotheses, NP 6= P; NP 6= coNP). For the sake of clarity we have often chosen to state a specific version of a problem rather than a general one. For example, questions about the integers modulo a prime often have natural generalizations to arbitrary finite fields, to arbitrary cyclic groups, or to problems with a composite modulus. Questions about the integers often have natural generalizations to the ring of integers in an algebraic number field, and questions about elliptic curves often generalize to arbitrary curves or abelian varieties. The problems presented here arose from many different places and times. To those whose research has generated these problems or has contributed to our present understanding of them but to whom inadequate acknowledgement is given here, we apologize. Our list of open problems is derived from an earlier `open problems' paper we wrote in 1986 [AM86]. When we wrote the first version of this paper, we feared that the problems presented were so difficult...
Improving Privacy in Cryptographic Elections
, 1986
"... This report describes two simple extensions to the paper A Robust and Verifiable Cryptographically Secure Election Scheme presented in the 1985 Symposium on the Foundations of Computer Science. The first extension allows the "government" to be divided into an arbitrary number of "tellers". With ..."
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This report describes two simple extensions to the paper A Robust and Verifiable Cryptographically Secure Election Scheme presented in the 1985 Symposium on the Foundations of Computer Science. The first extension allows the "government" to be divided into an arbitrary number of "tellers". With this extension, trust in any one teller is sufficient to assure privacy, even if the remaining tellers conspire in an attempt to breach privacy. The second extension allows a government to reveal (and convince voters of) the winner in an election without releasing the actual tally. Combining these two extensions in a uniform manner remains an open problem. 1 Introduction and Background In [CoFi85], a protocol was presented which gives a method of holding a mutually verifiable secretballot election. The participants are the voters, a government, a trusted "beacon" which generates publically readable random bits, and a trusted global clock. The protocol has four basic phases. In phas...
More Efficient Cryptosystems From k th Power Residues ⋆
"... Abstract. At Eurocrypt 2013, Joye and Libert proposed a method for constructing public key cryptosystems (PKCs) and lossy trapdoor functions (LTDFs) from (2 α) thpower residue symbols. Their work can be viewed as nontrivial extensions of the wellknown PKC scheme due to Goldwasser and Micali, and ..."
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Abstract. At Eurocrypt 2013, Joye and Libert proposed a method for constructing public key cryptosystems (PKCs) and lossy trapdoor functions (LTDFs) from (2 α) thpower residue symbols. Their work can be viewed as nontrivial extensions of the wellknown PKC scheme due to Goldwasser and Micali, and the LTDF scheme due to Freeman et al., respectively. In this paper, we will demonstrate that this kind of work can be extended more generally: all related constructions can work for any k th residues if k only contains small prime factors, instead of (2 α) thpower residues only. The resultant PKCs and LTDFs are more efficient than that from JoyeLibert method in terms of decryption speed with the same message length.
Cryptographic Applications of thResiduosity Problem with an Odd Integer
"... Abstract Let and n be positive integers. An integer z with gcd(z;n) = 1 is called a thresidue modn if there exists an integer x such that z x (mod n), or a thnonresidue modn if there doesn't exist such anx. Denote by Z n the set of integers relatively prime to n between 0 and n. The problem of de ..."
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Abstract Let and n be positive integers. An integer z with gcd(z;n) = 1 is called a thresidue modn if there exists an integer x such that z x (mod n), or a thnonresidue modn if there doesn't exist such anx. Denote by Z n the set of integers relatively prime to n between 0 and n. The problem of determining whether or not a randomly selected element z 2 Z n is a thresidue modn is called the thResiduosity Problem ( thRP), and appears to be intractable when n is a composite integer whose factorization is unknown. In this paper, we explore some important properties of thRP for the case where is an odd integer greater than 2, and discuss its applications to cryptography. Based on the di culty of thRP, we generalize the GoldwasserMicali bitbybit probabilistic encryption to a blockbyblock probabilistic one, and propose a direct protocol for the dice casting problem over a network. This problem is a general one which includes the wellstudied coin ipping problem. 1