On the lattice structure of certain linear congruential sequences related to AWC/SWB generators
نویسندگان
چکیده
منابع مشابه
On lattice profile of the elliptic curve linear congruential generators
Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (abbr. EC-LCG) under this new la...
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We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ` = 8, 9, . . . , 64, 127, 128, we take as a modulus m the largest prime smaller than 2`, and provide a list of multipliers a such that the MLCG with modulus m and multiplier a has a good lattice structure in dimensions 2 to 32. W...
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This sequence was first considered as a pseudorandom number generator by D. H. Lehmer. For the power generator we are given integers e, n > 1 and a seed u = u0 > 1, and we compute the sequence ui+1 = u e i (mod n) so that ui = u ei (mod n). A popular case is e = 2, which is called the Blum–Blum–Shub (BBS) generator. Both of these generators are periodic sequences, and it is of interest to compu...
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Linear congruential generators (LCGs) remain the most popular method of pseudorandom number generation on digital computers. Ease of implementation has favored implementing LCGs with power-of-two moduli. However, prime modulus LCGs are superior in quality to power-of-two modulus LCGs, and the use of a Mersenne prime minimizes the computational cost of generation. When implemented for parallel c...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1994
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1994-1220826-x