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On Using Fast Exponentiation Algorithm in PDAs (or: How Secure is the Discrete Logarithm Problem Assumption in PDAs?) (Extended Abstract)
"... Personal Digital Assistants (PDAs) are the miniature of normal size PCs, with a very limited computational power. In this paper, we investigate the security of PDAs when they are used to perform some cryptographic applications. In our context, we investigate the computation y = g x (mod p), for a pr ..."
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prime p, which is believed to be secure in the sense of the Discrete Logarithm Problem (DLP) assumption. To be more precise, knowing only p, g and y, it is hard to derive x. We note that this computation is the most important operation in most cryptographic algorithms. However, due to the limited
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factol: It is not clear whether this is still true when quantum mechanics is taken into consider ..."
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Cited by 1111 (5 self)
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into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... 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. ..."
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Cited by 1277 (4 self)
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. 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
Lower Bounds for Discrete Logarithms and Related Problems
, 1997
"... . This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element is ..."
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Cited by 288 (11 self)
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. This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element
Practical Verifiable Encryption and Decryption of Discrete Logarithms
, 2003
"... This paper addresses the problem of designing practical protocols for proving properties about encrypted data. To this end, it presents a variant of the new public key encryption of Cramer and Shoup based on Paillier’s decision composite residuosity assumption, along with efficient protocols for ve ..."
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Cited by 169 (24 self)
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This paper addresses the problem of designing practical protocols for proving properties about encrypted data. To this end, it presents a variant of the new public key encryption of Cramer and Shoup based on Paillier’s decision composite residuosity assumption, along with efficient protocols
The Power of Convex Relaxation: NearOptimal Matrix Completion
, 2009
"... This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering. In ..."
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Cited by 359 (7 self)
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This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering
Assumptions Related to Discrete Logarithms: Why Subtleties Make a Real Difference
 Advances in CryptologyEurocrypt 2001, LNCS 2045
, 2002
"... The security of many cryptographic constructions relies on assumptions related to Discrete Logarithms (DL), e.g., the Di#eHellman, Square Exponent, Inverse Exponent or Representation Problem assumptions. In the concrete formalizations of these assumptions one has some degrees of freedom o#ered ..."
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Cited by 22 (2 self)
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The security of many cryptographic constructions relies on assumptions related to Discrete Logarithms (DL), e.g., the Di#eHellman, Square Exponent, Inverse Exponent or Representation Problem assumptions. In the concrete formalizations of these assumptions one has some degrees of freedom o
The Discrete Logarithm Problem On Elliptic Curves Of Trace One
 JOURNAL OF CRYPTOLOGY
, 1999
"... In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves who ..."
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Cited by 117 (2 self)
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In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves
An Efficient Group Signature Based on the Discrete Logarithm Problem
"... Group signature schemes permit a group member signing on messages anonymously and unlinkably on behalf of a group. The anonymity can be revoked when arguments occurred. This paper proposes an efficient group signature scheme based on the discrete logarithm problem, which means no trapdoor functions ..."
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Group signature schemes permit a group member signing on messages anonymously and unlinkably on behalf of a group. The anonymity can be revoked when arguments occurred. This paper proposes an efficient group signature scheme based on the discrete logarithm problem, which means no trapdoor functions
The Discrete Logarithm Problem
"... For large prime numbers p, computing discrete logarithms of elements of the multiplicative group (Z/pZ) ∗ is at present a very difficult problem. The security of certain cryptosystems is based on the difficulty of this computation. In this expository paper we discuss several generalizations of the d ..."
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For large prime numbers p, computing discrete logarithms of elements of the multiplicative group (Z/pZ) ∗ is at present a very difficult problem. The security of certain cryptosystems is based on the difficulty of this computation. In this expository paper we discuss several generalizations
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