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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第6期64卷 4179-4190页

作者： Komargodski, Ilan Naor, Moni Yogev, Eylon Cornell Tech New York NY 10044 USA Weizmann Inst Sci Dept Comp Sci & Appl Math IL-76100 Rehovot Israel

Secret sharing schemes allow a dealer to distribute a secret piece of information among several parties such that only qualified subsets of parties can reconstruct the secret. The collection of qualified subsets is called an access structure. The best known example is the k-threshold access structure, where the qualified subsets are those of size at least k. When k = 2 and there are n parties, there are schemes for sharing an l-bit secret in which the share size of each party is roughly max{l, log n} bits, and this is tight even for secrets of 1 b. In these schemes, the number of parties n must be given in advance to the dealer. In this paper, we consider the case where the set of parties is not known in advance and could potentially be infinite. Our goal is to give the tth party arriving the smallest possible share as a function of t. Our main result is such a scheme for the k-threshold access structure and 1-bit secrets where the share size of party t is (k-1).log t+poly(k).o(log t). For k = 2 we observe an equivalence to prefix codes and present matching upper and lower bounds of the form log t + log log t + log log log t + O(1). Finally, we show that for any access structure there exists such a secret sharing scheme with shares of size 2(t-1).

关键词： Secret sharing threshold evolving access structure prefix code

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How to Share a Secret, Infinitely 14th

How to Share a Secret, Infinitely

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14th International Theory of Cryptography Conference (TCC)

作者： Komargodski, Ilan Naor, Moni Yogev, Eylon Cornell Tech New York NY 10044 USA Weizmann Inst Sci Dept Comp Sci & Appl Math IL-76100 Rehovot Israel

ISBN: (纸本)9783662536438

关键词： Secret sharing threshold evolving access structure prefix code

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A Family of Data Compression codes with Multiple Delimiters 20

A Family of Data Compression Codes with Multiple Delimiters

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Prague Stringology Conference (PSC)

作者： Zavadskyi, Igor O. Anisimov, Anatoly V. Taras Shevchenko Natl Univ Kyiv 2d Glushkova ave Kiev Ukraine

ISBN: (纸本)9788001059968

A new family of perspective variable length self-synchronazable binary codes with multiple pattern delimiters is introduced. Each delimiter consists of a run of consecutive ones surrounded by zero brackets. These codes are complete and universal. A simple bijective correspondence between natural numbers and any multi-delimiter code set is established. A fast byte aligned decoding algorithm is constructed. Comparisons of text compression rate and decoding speed for different multi-delimiter codes, the Fibonacci code Fib3 and (s, c)-dense codes are also presented.

关键词： prefix code Fibonacci code data compression robustness completeness universality density multi-delimiter

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Synchronizing Strongly Connected Partial DFAs 38

Synchronizing Strongly Connected Partial DFAs

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38th International Symposium on Theoretical Aspects of Computer Science (STACS)

作者： Berlinkov, Mikhail, V Ferens, Robert Ryzhikov, Andrew Szykula, Marek Ural Fed Univ Inst Nat Sci & Math Ekaterinburg Russia Univ Wroclaw Inst Comp Sci Wroclaw Poland Univ Gustave Eiffel LIGM Marne La Vallee France

ISBN: (纸本)9783959771801

We study synchronizing partial DFAs, which extend the classical concept of synchronizing complete DFAs and are a special case of synchronizing unambiguous NFAs. A partial DFA is called synchronizing if it has a word (called a reset word) whose action brings a non-empty subset of states to a unique state and is undefined for all other states. While in the general case the problem of checking whether a partial DFA is synchronizing is PSPACE-complete, we show that in the strongly connected case this problem can be efficiently reduced to the same problem for a complete DFA. Using combinatorial, algebraic, and formal languages methods, we develop techniques that relate main synchronization problems for strongly connected partial DFAs with the same problems for complete DFAs. In particular, this includes the Cerny and the rank conjectures, the problem of finding a reset word, and upper bounds on the length of the shortest reset words of literal automata of finite prefix codes. We conclude that solving fundamental synchronization problems is equally hard in both models, as an essential improvement of the results for one model implies an improvement for the other.

关键词： Cerny conjecture literal automaton partial automaton prefix code rank conjecture reset threshold reset word synchronizing automaton synchronizing word

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It's Been 1,000,000 Years Since Huffman

It's Been 1,000,000 Years Since Huffman

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Data Compression Conference (DCC)

作者： Moffat, Alistair Univ Melbourne Melbourne Vic 3010 Australia

ISBN: (纸本)9781479984305

Summary form only given. Huffman codes are legendary in the computing disciplines, and are embedded in a wide range of critically important communications and storage codecs. With 2015 marking the 64th anniversary of their development -- 1,000,000 years in binary -- it is timely to review Huffman and related codes, and the many mechanisms that have been developed for computing and deploying them.

关键词： Huffman code minimum-redundancy code prefix code Huffman codes

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Lossless Coding with Generalized Criteria

Lossless Coding with Generalized Criteria

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IEEE International Symposium on Information Theory (ISIT)

作者： Charalambous, Themistoklis Charalambous, Charalambos D. Rezaei, Farzad Univ Cyprus Dept Elect & Comp Engn Nicosia Cyprus

ISBN: (纸本)9781457705953

This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length, or, a convex combination of the average of an exponential function of the codeword length and the average codeword length. This framework encompasses as a special case several criteria previously investigated in the literature, while relations to universal coding is discussed. The coding algorithm derived is parametric resulting in re-adjusting the initial source probabilities via a weighted probability vector according to a merging rule. An algorithm is presented to compute the weighting vector.

关键词： Encoding Entropy Merging Minimization Probability distribution Redundancy average codeword length convex combination convex programming encoding exponential function generalized criteria initial source probability lossless coding maximum codeword length prefix code probability universal coding vectors weighted probability vector

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VARIABLE-LENGTH code BASED ON AN ORDER COMPLEXITY

VARIABLE-LENGTH CODE BASED ON AN ORDER COMPLEXITY

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Picture Coding Symposium 2009

作者： Hong, Soongi Eom, Minyoung Choe, Yoonsik Yonsei Univ Seoul 120749 South Korea

ISBN: (纸本)9781424445936

In this paper, we introduce new codeword sets based on order complexity (OC) which measures uncertainty of the order having each permutation string. The proposed codeword sets are generated by two procedures: Indexing and B-transform. Indexing is that a smaller positive integer is mapped to a permutation string whose OC is lower. B-transform plays role of generating a binary string from the permutation string on reflecting the OC, that is, low OC is represented by short binary strings and high OC is represented by long binary strings. The sets of these binary strings are our proposed codeword sets (B-codes). The B-codes are the uniquely decipherable complete variable length codeword sets and have shorter codeword length than most other variable length codes for values of 4 or more for the finite integers.

关键词： Variable-Length Coding Order Complexity Completeness prefix code Bubble Sort

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Bstj 50: 3. March 1971: Self-Synchronizing Sequential Coding with Low Redundancy. (Neumann, Peter G.)

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2016年

Bstj 50: 3. March 1971: Self-Synchronizing Sequential Coding with Low Redundancy. (Neumann, Peter G.) by published by

关键词： (neumann, bell system code code text code word codes coding encoding lag march peter prefix prefix code prefix codes redundancy. sequences sequential sequential code sequential codes sequential prefix synchronization synchronizing synchronizing sequences system technical

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Palindrome words and reverse closed languages

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2000年第4期75卷 389-402页

作者： Yu, SS Natl Chung Hsing Univ Dept Appl Math Taichung 40227 Taiwan

A word which is equal to its mirror image is called a palindrome word. Any language consisting of palindrome words is called a palindrome language. In this paper we investigate properties of palindrome words and languages. We show that there is no dense regular language consisting of palindrome words. A language contains all the mirror images of its elements is called a reverse closed language. Clearly, every palindrome language is reverse closed. We show that whether a given regular or context-free language is reverse closed is decidable. We study certain properties concerning reverse closed finite maximal prefix codes in this paper. Properties of languages that commute with reverse closed languages are investigated too.

关键词： palindrome primitive word 2-code regular language prefix code

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A class by principal congruence of a syntactically embedded language

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2007年第6期E90D卷 975-978页

作者： Moriya, Tetsuo Kokushikan Univ Fac Engn Dept Elect Engn Tokyo 1548515 Japan

In this paper, we introduce a syntactically embedded (s-embedded) language, and consider its principal congruence. The following three results are proved, where P-L is the principal congruence of a language L, and W(L) is the residual of L. (1) For a language K, s-embedded in M, K is equal to a I'm class. (2) For a language K, s-embedded in an infix language M, K is equal to a P-w(m) class. (3) For a nonempty s-embedded language L, if L is double-unitary, then L is equal to a Pw(m) class. From the above results, we can obtain those for principal congruence of some codes. For example, L-n is equal to a P-L(n-1) class for an inter code L of index n.

关键词： prefix code suffix code infix code conuna-free code inter code principal congruence

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