E. Teske. New algorithms for finite abelian groups. PhD thesis, Technische Universit at Darmstadt, 1998. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Speeding up Pollard's Rho Method for Computing Discrete Logarithms - Teske (1998) (20 citations) Self-citation (Teske) (Correct)
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E. Teske. New algorithms for finite abelian groups. PhD thesis, Technische Universit at Darmstadt, 1998.
The Pohlig-Hellman Method Generalized for Group Structure.. - Teske Self-citation (Teske) (Correct)
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E. Teske, New algorithms for finite abelian groups, Ph.D. thesis, Technische Universitat Darmstadt, Germany, 1998.
On Random Walks For Pollard's Rho Method - Teske (2000) (3 citations) Self-citation (Teske) (Correct)
.... is similar to the spread of the corresponding Weibull distribution; this agrees with the experimental evidence that when an iterating function yields a mean value of ( p jGj close to the random case, then the variance is close to the variance of the random case, which is 2 Gamma =2 (see [Tes98a]) Hence, we have to choose the size of the sample space very carefully. We can derive from [Kec93] that, for example, if we work with a sample space of size N = 30 and we get an average ON RANDOM WALKS FOR POLLARD S RHO METHOD 5 value of ( p jGj = 1:26, we can only have a 20 confidence ....
E. Teske, New algorithms for finite abelian groups, Ph.D. thesis, TechnischeUniversitat Darmstadt, Germany, 1998, Shaker Verlag, Aachen.
Speeding Up Pollard's Rho Method For Computing Discrete Logarithms - Teske (1998) (20 citations) Self-citation (Teske) (Correct)
....value y 0 ; but this case is very rare for large group orders jGj = p. Remark 2.1. Under the assumption that f is a random mapping and that jGj is large enough such that a continuous approximation is valid, the expected value of the right hand side of (2.1) is approximately 1:229 p jGj=2 . See [16] for details. 3. The Iterating Functions We next define some new iterating functions. For r 2 N, let T 1 ; T r be a partition of G into r pairwise disjoint and roughly equally large sets. The set f1; 2; jGjg is denoted by [j1; jGj[j. To indicate that an element m is randomly ....
E. Teske. New algorithms for finite abelian groups. PhD thesis, Technische Universitat Darmstadt, 1998.
The Pohlig-Hellman Method Generalized for Group Structure.. - Teske (1998) Self-citation (Teske) (Correct)
....is necessary for the uniqueness of the representation. In the context of group structure computation this does not mean a restriction. This is because even if the initially given generators do not form a direct product, they can be transformed accordingly in the course of the computation (see [7] for details) In this paper we give an algorithm to solve the EDLP. This algorithm has the nice property that x and y are computed simultaneously , which implies that the lack of any a priori knowledge about y does not increase the run time. We show that, if combined with the baby step ....
E. Teske, New algorithms for finite abelian groups, Ph.D. thesis, Technische Universitat Darmstadt, Germany, 1998.
Speeding up Pollard's Rho Method for Computing Discrete Logarithms - Teske (1998) (20 citations) Self-citation (Teske) (Correct)
....value y 0 ; but this case is very rare for large group orders jGj = p. Remark 1. Under the assumption that f is a random mapping and that jGj is large enough such that a continuous approximation is valid, the expected value of the right hand side of (1) is approximately 1:229 p jGj=2 . See [16] for details. 3 The Iterating Functions We next define some new iterating functions. For r 2 IN, let T 1 ; T r be a partition of G into r pairwise disjoint and roughly equally large sets. The set f1; 2; jGjg is denoted by [j1; jGj[j. To indicate that an element m is randomly ....
E. Teske. New algorithms for finite abelian groups. PhD thesis, Technische Universit at Darmstadt, 1998.
Better Random Walks For Pollard's Rho Method - Teske (1998) (1 citation) Self-citation (Teske) (Correct)
.... to assume 6 EDLYN TESKE that ( p jGj is similarly distributed; this is partially confirmed by experiments showing that when our iterating function yields a mean value close to the random case, then the variance is close to the variance of the random case, which is 2 Gamma =2 (see [Tes98a]) Hence, we have to choose the size of the sample space very carefully. We can derive from [Kec93] that, for example, if we work with a sample space of size N = 30 and we get an average value of ( p jGj = 1:26, we can only have a 20 confidence that the correct mean value lies between ....
E. Teske, New algorithms for finite abelian groups, Ph.D. thesis, Technische Universit at Darmstadt, Germany, 1998, Shaker Verlag, Aachen.
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