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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
Limits on the Provable Consequences of Oneway Permutations
, 1989
"... We present strong evidence that the implication, "if oneway permutations exist, then secure secret key agreement is possible" is not provable by standard techniques. Since both sides of this implication are widely believed true in real life, to show that the implication is false requires a new m ..."
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We present strong evidence that the implication, "if oneway permutations exist, then secure secret key agreement is possible" is not provable by standard techniques. Since both sides of this implication are widely believed true in real life, to show that the implication is false requires a new model. We consider a world where dl parties have access to a black box or a randomly selected permutation. Being totally random, this permutation will be strongly oneway in provable, informationthevretic way. We show that, if P = NP, no protocol for secret key agreement is secure in such setting. Thus, to prove that a secret key greement protocol which uses a oneway permutation as a black box is secure is as hrd as proving F NP. We also obtain, as corollary, that there is an oracle relative to which the implication is false, i.e., there is a oneway permutation, yet secretexchange is impossible. Thus, no technique which relativizes can prove that secret exchange can be based on any oneway permutation. Our results present a general framework for proving statements of the form, "Cryptographic application X is not likely possible based solely on complexity assumption Y." 1
Limits on the Provable Consequences of Oneway Functions
, 1989
"... This technical point will prevent the reader from suspecting any measuretheoretic fallacy. ..."
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This technical point will prevent the reader from suspecting any measuretheoretic fallacy.
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"... The literature of cryptography has a curious history. Secrecy, of course, has always played a central role, but until the First World War, important developments appeared in print in a more or less timely fashion and the field moved forward in much the same way as other specialized disciplines. As l ..."
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The literature of cryptography has a curious history. Secrecy, of course, has always played a central role, but until the First World War, important developments appeared in print in a more or less timely fashion and the field moved forward in much the same way as other specialized disciplines. As late as 1918, one of the most influential cryptanalytic papers of the twentieth century, William F. Friedman’s monograph The Index of Coincidence and Its Applications in Cryptography, appeared as a research report of the private Riverbank Laboratories [577]. And this, despite the fact that the work had been done as part of the war effort. In the same year Edward H. Hebern of Oakland, California filed the first patent for a rotor machine [710], the device destined to be a mainstay of military cryptography for nearly 50 years. After the First World War, however, things began to change. U.S. Army and Navy organizations, working entirely in secret, began to make fundamental advances in cryptography. During the thirties and forties a few basic papers did appear in the open literature and several treatises on the subject were published, but the latter were farther and farther behind the state of the art. By the end of the war the transition was complete. With one notable exception, the public literature had died. That exception was Claude Shannon’s paper “The Communication Theory of Secrecy Systems, ” which