Journal•ISSN: 0097-5397

# SIAM Journal on Computing

About: SIAM Journal on Computing is an academic journal. The journal publishes majorly in the area(s): Time complexity & Approximation algorithm. It has an ISSN identifier of 0097-5397. Over the lifetime, 3514 publication(s) have been published receiving 307619 citation(s). The journal is also known as: SIAM J. Comput & SIAM J. Comput..

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Topics: Time complexity, Approximation algorithm, Upper and lower bounds ...read more

##### Papers

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Abstract: A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

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7,427 citations

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TL;DR: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples of an improved version of an algorithm for finding the strongly connected components of a directed graph.

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Abstract: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected componen...

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5,156 citations

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TL;DR: This work proposes a fully functional identity-based encryption (IBE) scheme based on bilinear maps between groups and gives precise definitions for secure IBE schemes and gives several applications for such systems.

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Abstract: We propose a fully functional identity-based encryption (IBE) scheme. The scheme has chosen ciphertext security in the random oracle model assuming a variant of the computational Diffie--Hellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure IBE schemes and give several applications for such systems.

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5,046 citations

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TL;DR: An algorithm is presented which finds all occurrences of one given string within another, in running time proportional to the sum of the lengths of the strings, showing that the set of concatenations of even palindromes, i.e., the language $\{\alpha \alpha ^R\}^*$, can be recognized in linear time.

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Abstract: An algorithm is presented which finds all occurrences of one given string within another, in running time proportional to the sum of the lengths of the strings. The constant of proportionality is low enough to make this algorithm of practical use, and the procedure can also be extended to deal with some more general pattern-matching problems. A theoretical application of the algorithm shows that the set of concatenations of even palindromes, i.e., the language $\{\alpha \alpha ^R\}^*$, can be recognized in linear time. Other algorithms which run even faster on the average are also considered.

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3,023 citations

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TL;DR: A digital signature scheme based on the computational difficulty of integer factorization possesses the novel property of being robust against an adaptive chosen-message attack: an adversary who receives signatures for messages of his choice cannot later forge the signature of even a single additional message.

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Abstract: We present a digital signature scheme based on the computational difficulty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosen-message attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a way that depends on the signatures of previously chosen messages) cannot later forge the signature of even a single additional message. This may be somewhat surprising, since in the folklore the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosen-message attack were considered to be contradictory. More generally, we show how to construct a signature scheme with such properties based on the existence of a "claw-free" pair of permutations--a potentially weaker assumption than the intractibility of integer factorization. The new scheme is potentially practical: signing and verifying signatures are reasonably fast, and signatures are compact.

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2,994 citations