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Discrete Log Problem
"... i.e., the discrete log) is hard to compute. 2 Shor's Quantum Algorithm Before diving into the details of Shor's algorithm, we'll begin with a few comments. First, a preliminary observation: Fact 1 Suppose that we know the order k of the generator g 2 Z p . Then, if g r j x (mod ..."
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i.e., the discrete log) is hard to compute. 2 Shor's Quantum Algorithm Before diving into the details of Shor's algorithm, we'll begin with a few comments. First, a preliminary observation: Fact 1 Suppose that we know the order k of the generator g 2 Z p . Then, if g r j x
DiscreteLog with Compressible Exponents
 Advances in Cryptology — CRYPTO ’90, LNCS
, 1998
"... Introduction Many key distribution systems are based on the assumption that the DiscreteLog (DL) problem is hard. The implementations could be more efficient if a significantly smaller exponent could be used, without lowering the complexity of the DL problem. When the exponent is known to reside ..."
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Cited by 4 (0 self)
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Introduction Many key distribution systems are based on the assumption that the DiscreteLog (DL) problem is hard. The implementations could be more efficient if a significantly smaller exponent could be used, without lowering the complexity of the DL problem. When the exponent is known to reside
Discretelogbased signatures may not be equivalent to discrete log
 ASIACRYPT 2005, LNCS 3788
, 2005
"... Abstract. We provide evidence that the unforgeability of several discretelog based signatures like Schnorr signatures cannot be equivalent to the discrete log problem in the standard model. This contradicts in nature wellknown proofs standing in weakened proof methodologies, in particular proofs e ..."
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Cited by 28 (2 self)
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Abstract. We provide evidence that the unforgeability of several discretelog based signatures like Schnorr signatures cannot be equivalent to the discrete log problem in the standard model. This contradicts in nature wellknown proofs standing in weakened proof methodologies, in particular proofs
Secure Distributed Key Generation for DiscreteLog Based Cryptosystems
, 1999
"... Abstract. Distributed key generation is a main component of threshold cryptosystems and distributed cryptographic computing in general. Solutions to the distributed generation of private keys for discretelog based cryptosystems have been known for several years and used in a variety of protocols an ..."
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Cited by 168 (4 self)
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Abstract. Distributed key generation is a main component of threshold cryptosystems and distributed cryptographic computing in general. Solutions to the distributed generation of private keys for discretelog based cryptosystems have been known for several years and used in a variety of protocols
Speeding Up the Discrete Log Computation on Curves With Automorphisms
, 1999
"... We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on ABC elliptic curves. This includes the first known attack on CM (hyper)elliptic curves, as well as most of the hyperelliptic curves described in the literature. ..."
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Cited by 39 (2 self)
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We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on ABC elliptic curves. This includes the first known attack on CM (hyper)elliptic curves, as well as most of the hyperelliptic curves described in the literature.
A.: The Discrete Log is Very Discreet
 In: STOC
, 1990
"... In this paper we consider the oneway function fg,N(X) = gX (modN), where N is a Blum integer. We prove that under the commonly assumed intractability of factoring Blum integers, almost all its bits are individually hard, and half of them are simultaneously hard. As a result, fg,N can be used in ef ..."
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Cited by 15 (0 self)
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In this paper we consider the oneway function fg,N(X) = gX (modN), where N is a Blum integer. We prove that under the commonly assumed intractability of factoring Blum integers, almost all its bits are individually hard, and half of them are simultaneously hard. As a result, fg,N can be used in efficient pseudorandom bit generators and multibit commitment schemes, where messages can be drawn according to arbitrary probability distributions. 1
On the Computation of the Discrete LogPolar Transform
, 2007
"... This paper reports an algorithm for computing the logpolar transform (LPT) of a digital image using optimal parameters for use in an active vision system. In the past, only cursory attention has been given to the selection of transform parameters. This is likely because the exact values of the para ..."
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Cited by 1 (0 self)
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This paper reports an algorithm for computing the logpolar transform (LPT) of a digital image using optimal parameters for use in an active vision system. In the past, only cursory attention has been given to the selection of transform parameters. This is likely because the exact values
An algorithm for solving the discrete log problem on hyperelliptic curves
, 2000
"... Abstract. We present an indexcalculus algorithm for the computation of discrete logarithms in the Jacobian of hyperelliptic curves defined over finite fields. The complexity predicts that it is faster than the Rho method for genus greater than 4. To demonstrate the efficiency of our approach, we de ..."
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Cited by 96 (9 self)
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Abstract. We present an indexcalculus algorithm for the computation of discrete logarithms in the Jacobian of hyperelliptic curves defined over finite fields. The complexity predicts that it is faster than the Rho method for genus greater than 4. To demonstrate the efficiency of our approach, we
Designing and detecting trapdoors for discrete log cryptosystems
 ADVANCES IN CRYPTOLOGY CRYPTO '92
, 1993
"... Using a number field sieve, discrete logarithms modulo primes of special forms can be found faster than standard primes. This has raised concerns about trapdoors in discrete log cryptosystems, such as the Digital Signature Standard. This paper discusses the practical impact of these trapdoors, and ..."
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Cited by 16 (0 self)
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Using a number field sieve, discrete logarithms modulo primes of special forms can be found faster than standard primes. This has raised concerns about trapdoors in discrete log cryptosystems, such as the Digital Signature Standard. This paper discusses the practical impact of these trapdoors
An Efficient Discrete Log Pseudo Random Generator
 Crypto ’98, LNCS No. 1462
, 1998
"... Abstract. The exponentiation function in a finite field of order p (a prime number) is believed to be a oneway function. It is well known that O(log log p) bits are simultaneously hard for this function. We consider a special case of this problem, the discrete logarithm with short exponents, which ..."
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Cited by 29 (1 self)
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Abstract. The exponentiation function in a finite field of order p (a prime number) is believed to be a oneway function. It is well known that O(log log p) bits are simultaneously hard for this function. We consider a special case of this problem, the discrete logarithm with short exponents, which
Results 1  10
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