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PAPER Special Section on Cryptography and Information Security The Computational Difficulty of Solving Cryptographic Primitive Problems Related to the Discrete Logarithm Problem
, 2005
"... SUMMARY To the authors ’ knowledge, there are not many cryptosystems proven to be as difficult as or more difficult than the discrete logarithm problem. Concerning problems related to the discrete logarithm problem, there are problems called the double discrete logarithm problem and the eth root of ..."
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of the discrete logarithm problem. These two problems are likely to be difficult and they have been utilized in cryptographic protocols such as verifiable secret sharing scheme and group signature scheme. However, their exact complexity has not been clarified, yet. Related to the eth root of the discrete
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 572 (5 self)
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the modern (complexity theoretic) formulation of the Church–Turing thesis. We show the existence of a problem, relative to an oracle, that can be solved in polynomial time on a quantum Turing machine, but requires superpolynomial time on a boundederror probabilistic Turing machine, and thus not in the class
On Cryptographic Schemes Based on Discrete Logarithms and Factoring
"... Abstract. At CRYPTO 2003, Rubin and Silverberg introduced the concept of torusbased cryptography over a finite field. We extend their setting to the ring of integers modulo N. We so obtain compact representations for cryptographic systems that base their security on the discrete logarithm proble ..."
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Abstract. At CRYPTO 2003, Rubin and Silverberg introduced the concept of torusbased cryptography over a finite field. We extend their setting to the ring of integers modulo N. We so obtain compact representations for cryptographic systems that base their security on the discrete logarithm
Discrete Logarithms in Finite Fields and Their Cryptographic Significance
, 1984
"... Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u GF(q) is that integer k, 1 k q  1, for which u = g k . The wellknown problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its appl ..."
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Cited by 104 (7 self)
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Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u GF(q) is that integer k, 1 k q  1, for which u = g k . The wellknown problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its
Theoretical Background on Cryptographic Primitives
"... This material intends to be a brief introduction to symmetric and asymmetric cryptographic primitives, pointing out some relevant design principles and security properties. Nonetheless, we call attention to the correct practical use and current standards. This material is intended in part to serve a ..."
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This material intends to be a brief introduction to symmetric and asymmetric cryptographic primitives, pointing out some relevant design principles and security properties. Nonetheless, we call attention to the correct practical use and current standards. This material is intended in part to serve
Cryptographic Primitives Based on Hard Learning Problems
, 1994
"... this paper, we give results in the reverse direction by showing how to construct several cryptographic primitives based on certain assumptions on the difficulty of learning. In doing so, we develop further a line of thought introduced by Impagliazzo and Levin [6]. As we describe, standard definition ..."
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Cited by 105 (4 self)
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this paper, we give results in the reverse direction by showing how to construct several cryptographic primitives based on certain assumptions on the difficulty of learning. In doing so, we develop further a line of thought introduced by Impagliazzo and Levin [6]. As we describe, standard
Discrete Logarithms in Finite Fields
, 1996
"... Given a finite field F q of order q, and g a primitive element of F q , the discrete logarithm base g of an arbitrary, nonzero y 2 F q is that integer x, 0 x q \Gamma 2, such that g x = y in F q . The security of many realworld cryptographic schemes depends on the difficulty of computing discr ..."
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Cited by 1 (0 self)
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Given a finite field F q of order q, and g a primitive element of F q , the discrete logarithm base g of an arbitrary, nonzero y 2 F q is that integer x, 0 x q \Gamma 2, such that g x = y in F q . The security of many realworld cryptographic schemes depends on the difficulty of computing
Results 1  10
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393,703