R.P. Brent, "Parallel algorithms for integer factorization", London Mathematical Society Lecture Note Series vol. 154, Number Theory and Cryptography, J.H. Loxton (ed.), pp. 26-37, Cambridge University Press, 1990. Home/Search Document Not in Database Summary Related Articles Check |
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Square-Root Algorithms For The Discrete Logarithm Problem (a Survey) - Teske (2001) (3 citations) (Correct)
....On each processor we use the same iterating function, initialize a sequence (y k ) by computing a random power of g and then proceed as in the serial rho method. However, we look for a match not among the terms of that single sequence (which would give only a speed up of a factor of p m [Bre90]) but among all terms computed on all m processors. This is done using the distinguished point method which works as follows: One de nes a set D 2 hgi that consists of all group elements that satisfy a certain distinguishing property. The elements in D are called distinguished point. A popular ....
R. P. Brent. Parallel algorithms for integer factorization. In J. H. Loxton, editor, Number theory and cryptography, volume 154 of London Mathematical Society Lecture Note Series, pages 26-37. Cambridge University Press, 1990.
Optimal Multipliers For LCGs With Prime Moduli: Parallel.. - Brunner, Uhl (Correct)
....less than 0:1 ) it is executed sequentially. Nevertheless, for very large moduli this share might increase and reduce the efficiency of the parallel execution on massively parallel architectures according to Amdahl s Law (see e.g. 17, p. 57] and [3, p. 16] In such a case parallel factorization [6] may be employed to resolve this problem. As already explained before we use a completely different parallelization approach for both algorithms as compared to earlier work [7] since the current implementations are not dominated by the primitive root test. For very large moduli (much larger as ....
....case the use of a different quality measure (see e.g. the results of the spectral test) may help to decide which parameter to use. Prime modulus m Multiplier K P q i=1 a i P [1] 29 18 2 8 P [2] 541 331 3 15 P [3] 7919 3325 2 20 P [4] 104729 43955 2 26 P [5] 1299709 818870 2 32 P [6] = 15485863 6507610 2 37 P [7] 179424673 104026441 3 43 P [8] 2038074743 1289818712 2 48 P [9] 22801763489 9450445177 2 53 P [10] 252097800623 95844202539 2 58 P [11] 2760727302517 1706241728712 2 63 Table 4.1: Some optimal multipliers 4.2 Efficiency of the parallelization. We ....
R.P. Brent. Parallel algorithms for integer factorization. In J.H. Loxton, editor, Number Theory and Cryptography, volume 154 of London Mathematical Society Lecture Note Series, pages 26--37. Cambridge University Press, Cambridge, 1990. 16 D. BRUNNER AND A. UHL
Parallel Collision Search with Cryptanalytic Applications - van Oorschot, Wiener (1996) (51 citations) (Correct)
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R.P. Brent, "Parallel algorithms for integer factorization", London Mathematical Society Lecture Note Series vol. 154, Number Theory and Cryptography, J.H. Loxton (ed.), pp. 26-37, Cambridge University Press, 1990.
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