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12
Limitations of the Upward Separation Technique
, 1990
"... this paper was presented at the 16th International Colloquium on Automata, Languages, and Programming [3] ..."
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Cited by 16 (0 self)
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this paper was presented at the 16th International Colloquium on Automata, Languages, and Programming [3]
Structural properties of oneway hash functions
 Advances in cryptology  CRYPTO 90, Lecture Notes in Computer Science
, 1991
"... We study the following two kinds of oneway hash functions: universal oneway hash functions (UOHs) and collision intractable hash functions (CIHs). The main property of the former is that given an initialstring x, it is computationally difficult to find a different string y that collides with x. An ..."
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Cited by 14 (6 self)
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We study the following two kinds of oneway hash functions: universal oneway hash functions (UOHs) and collision intractable hash functions (CIHs). The main property of the former is that given an initialstring x, it is computationally difficult to find a different string y that collides with x. And the main property of the latter is that it is computationally difficult to find a pair x � = y of strings such that x collides with y. Our main results are as follows. First we prove that UOHs with respect to initialstrings chosen arbitrarily exist if and only if UOHs with respect to initialstrings chosen uniformly at random exist. Then, as an application of the result, we show that UOHs with respect to initialstrings chosen arbitrarily can be constructed under a weaker assumption, the existence of oneway quasiinjections. Finally, we investigate relationships among various versions of oneway hash functions. We prove that some versions of oneway hash functions are strictly included in others by explicitly constructing hash functions that are oneway in the sense of the former but not in the sense of the latter. 1
Oneway permutations and selfwitnessing languages
 Journal of Computer and System Sciences
, 2003
"... A desirable property of oneway functions is that they be total, onetoone, and onto—in other words, that they be permutations. We prove that oneway permutations exist exactly if PaUPcoUP: This provides the first characterization of the existence of oneway permutations based on a complexityclas ..."
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Cited by 9 (2 self)
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A desirable property of oneway functions is that they be total, onetoone, and onto—in other words, that they be permutations. We prove that oneway permutations exist exactly if PaUPcoUP: This provides the first characterization of the existence of oneway permutations based on a complexityclass separation and shows that their existence is equivalent to a number of previously studied complexitytheoretic hypotheses. We study permutations in the context of witness functions of nondeterministic Turing machines. A language is in PermUP if, relative to some unambiguous, nondeterministic, polynomialtime Turingmachine acceptingthe language, the function mappingeach stringto its unique witness is a permutation of the members of the language. We show that, under standard complexitytheoretic assumptions, PermUP is a strict subset of UP. We study SelfNP, the set of all languages such that, relative to some nondeterministic, polynomialtime Turing machine that accepts the language, the set of all witnesses of strings in the language is identical to the language itself. We show that SATASelfNP; and, under standard complexitytheoretic assumptions, SelfNPaNP:
WitnessIsomorphic Reductions and Local Search
 Complexity, Logic, and Recursion Theory
, 1997
"... We study witnessisomorphic reductions, a type of structurepreserving reduction between NP decision problems. We completely determine the relative power of the different models of witnessisomorphic reduction, and we show that witnessisomorphic reductions can be used in a uniform approach to the loc ..."
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Cited by 5 (2 self)
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We study witnessisomorphic reductions, a type of structurepreserving reduction between NP decision problems. We completely determine the relative power of the different models of witnessisomorphic reduction, and we show that witnessisomorphic reductions can be used in a uniform approach to the local search problem. 1 Introduction The "natural" NP complete decision problems are very much alike. They not only are of the same complexity, but also are in the same polynomialtime isomorphism degree [BH77], and the reductions/isomorphisms between many of these problems are parsimonious [Sim75]. One would expect that such a tight connection between NPcomplete problems "of interest" would lead to an integrated approach when dealing with the closely related optimization problems. This however is not common practice in operations research. Indeed, typically, for each individual NP optimization problem new techniques and heuristics are invented. It seems that though existing reductions show a ...
Connections among Several Versions of OneWay Hash Functions
 Proc. of IEICE of Japan E73
, 1990
"... We study the following two kinds of oneway hash functions: universal oneway hash functions (UOHs) and collision intractable hash functions (CIHs). The main property of the former is that given an initialstring x, it is computationally difficult to find a different string y that collides with x. An ..."
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Cited by 2 (1 self)
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We study the following two kinds of oneway hash functions: universal oneway hash functions (UOHs) and collision intractable hash functions (CIHs). The main property of the former is that given an initialstring x, it is computationally difficult to find a different string y that collides with x. And the main property of the latter is that it is computationally difficult to find a pair x 6= y of strings such that x collides with y. Our main results are as follows. First we prove that UOHs with respect to initialstrings chosen arbitrarily exist if and only if UOHs with respect to initialstrings chosen uniformly at random exist. Then, as an application of the result, we show that UOHs with respect to initialstrings chosen arbitrarily can be constructed under a weaker assumption, the existence of oneway quasiinjections. Finally, we investigate relationships among different versions of oneway hash functions. We prove that some versions of oneway hash functions are strictly included i...
Enforcing and defying associativity, commutativity, totality, and strong noninvertibility for oneway functions in complexity theory
 In ICTCS
, 2005
"... Rabi and Sherman [RS97,RS93] proved that the hardness of factoring is a sufficient condition for there to exist oneway functions (i.e., ptime computable, honest, ptime noninvertible functions) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve th ..."
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Rabi and Sherman [RS97,RS93] proved that the hardness of factoring is a sufficient condition for there to exist oneway functions (i.e., ptime computable, honest, ptime noninvertible functions) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve the sufficient condition to P = NP. More generally, in this paper we completely characterize which types of oneway functions stand or fall together with (plain) oneway functions—equivalently, stand or fall together with P = NP. We look at the four attributes used in Rabi and Sherman’s seminal work on algebraic properties of oneway functions (see [RS97,RS93]) and subsequent papers—strongness (of noninvertibility), totality, commutativity, and associativity—and for each attribute, we allow it to be required to hold, required to fail, or “don’t care. ” In this categorization there are 3 4 = 81 potential types of oneway functions. We prove that each of these 81 featureladen types stand or fall together with the existence of (plain) oneway functions. Key words: computational complexity, complexitytheoretic oneway functions, associativity, 1.1
Abstract
, 2005
"... We prove that Psel, the class of all Pselective sets, is EXPimmune, but is not EXP/1immune. That is, we prove that some infinite Pselective set has no infinite EXPtime subset, but we also prove that every infinite Pselective set has some infinite subset in EXP/1. Informally put, the immunity ..."
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We prove that Psel, the class of all Pselective sets, is EXPimmune, but is not EXP/1immune. That is, we prove that some infinite Pselective set has no infinite EXPtime subset, but we also prove that every infinite Pselective set has some infinite subset in EXP/1. Informally put, the immunity of Psel is so fragile that it is pierced by a single bit of information. The above claims follow from broader results that we obtain about the immunity of the Pselective sets. In particular, we prove that for every recursive function f, Psel is DTIME(f)immune. Yet we also prove that Psel is not Π p 2 /1immune. 1