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The Security of all RSA and Discrete Log Bits
, 2003
"... We study the security of individual bits in an RSA encrypted message EN (x). We show that given EN (x), predicting any single bit in x with only a nonnegligible advantage over the trivial guessing strategy, is (through a polynomial time reduction) as hard as breaking RSA. Moreover, we prove that bl ..."
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Cited by 14 (0 self)
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that blocks of O(log log N) bitsofxare computationally indistinguishable from random bits. The results carry over to the Rabin encryption scheme. Considering the discrete exponentiation function gx modulo p, with probability 1 − o(1) over random choices of the prime p, the analog results are demonstrated
Security of almost all discrete log bits
 Electronic Colloq. on Comp. Compl., Univ. of Trier
, 1998
"... Let G be a finite cyclic group with generator α and with an encoding so that multiplication is computable in polynomial time. We study the security of bits of the discrete log x when given exp α(x), assuming that the exponentiation function exp α(x) = α x is oneway. We reduce he general problem to ..."
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Cited by 9 (0 self)
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Let G be a finite cyclic group with generator α and with an encoding so that multiplication is computable in polynomial time. We study the security of bits of the discrete log x when given exp α(x), assuming that the exponentiation function exp α(x) = α x is oneway. We reduce he general problem
The Security of all RSA and Discrete Log Bits
"... Abstract We study the security of individual bits in an RSA encrypted message EN (x). We show that given EN(x), predicting any single bit in x with only a nonnegligible advantage over the trivial guessing strategy, is (through a polynomial time reduction) as hard as breaking RSA. Moreover, we prove ..."
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prove that blocks of O(log log N) bits of x are computationally indistinguishable from random bits. The results carry over to the Rabin encryption scheme. Considering the discrete exponentiation function gx modulo p, with probability 1 o(1) over random choices of the prime p, the analog results
The Security of all RSA and Discrete Log Bits
"... Abstract We study the security of individual bits in an RSA encrypted message EN (x). We show that given EN(x), predicting any single bit in x with only a nonnegligible advantage over the trivial guessing strategy, is (through a polynomial time reduction) as hard as breaking RSA. Moreover, we prove ..."
Abstract
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prove that blocks of O(log log N) bits of x are computationally indistinguishable from random bits. The results carry over to the Rabin encryption scheme. Considering the discrete exponentiation function gx modulo p, with probability 1 o(1) over random choices of the prime p, the analog results
Iterative decoding of binary block and convolutional codes
 IEEE TRANS. INFORM. THEORY
, 1996
"... Iterative decoding of twodimensional systematic convolutional codes has been termed “turbo” (de)coding. Using loglikelihood algebra, we show that any decoder can he used which accepts soft inputsincluding a priori valuesand delivers soft outputs that can he split into three terms: the soft chann ..."
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Cited by 610 (43 self)
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Iterative decoding of twodimensional systematic convolutional codes has been termed “turbo” (de)coding. Using loglikelihood algebra, we show that any decoder can he used which accepts soft inputsincluding a priori valuesand delivers soft outputs that can he split into three terms: the soft
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 961 (11 self)
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polynomials feZ[X] into irreducible factors in Z[X]. Here we call f ~ Z[X] primitive if the greatest common divisor of its coefficients (the content of f) is 1. Our algorithm performs well in practice, cf. [8]. Its running time, measured in bit operations, is O(nl2+n9(log[fD3). Here f~Tl[X] is the polynomial
Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
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Cited by 574 (5 self)
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to be specified. We prove that O(log T) bits of precision suffice to support a T step computation. This justifies the claim that the quantum Turing machine model should be regarded as a discrete model of computation and not an analog one. We give the first formal evidence that quantum Turing machines violate
A distributed algorithm for minimumweight spanning trees
, 1983
"... A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange ..."
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Cited by 435 (3 self)
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and exchange messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log2N + 2E, and a message contains at most one edge weight plus log28N bits. The algorithm can be initiated spontaneously at any node or at any subset
Electronic Colloquium on Computational Complexity, Report No. 37 (1999) The Security of all RSA and Discrete Log Bits
"... We study the security of individual bits in an RSA encrypted message EN (x). We show that given EN(x), predicting any single bit in x with only a nonnegligible advantage over the trivial guessing strategy, is (through a polynomial time reduction) as hard as breaking RSA. Moreover, we prove that blo ..."
Abstract
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that blocks of O(log log N) bits of x are computationally indistinguishable from random bits. The results carry over to the Rabin encryption scheme. Considering the discrete exponentiation function g x modulo p, with probability 1−o(1) over random choices of the prime p, the analog results are demonstrated
How to Use Expert Advice
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1997
"... We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worstcase situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the ..."
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Cited by 377 (79 self)
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We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worstcase situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance
Results 1  10
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