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1. 发明申请

US20100030829A1 Method of generating random numbers 失效
标题翻译：产生随机数的方法
公开(公告)号：US20100030829A1
公开(公告)日：2010-02-04
申请号：US12379964
申请日：2009-03-05
申请人： Hiroshi Nakazawa , Naoya Nakazawa
发明人： Hiroshi Nakazawa , Naoya Nakazawa
IPC分类号： G06F7/58
CPC分类号： G06F7/586
摘要： A method of obtaining uniform and independent random numbers is given (a) comprising two distinct odd primes p1, p2 that give mutually coprime integers q1=(p1−1)/2 and q2=(p2−1)/2 with different parity to form the modulus d=p1p2; (b) comprising primitive roots z1, z2 of primes p1, p2, respectively, giving congruence relations z≡zj mod (pj) for j=1, 2 that determine the multiplier z; and (c) comprising the initial value n coprime with d=p1p2. The method generates the coset sequence n ={r1=n, r2, r3, . . . } of period T=2q1q2 recursively by rj+1=zrj mod (d) for j=1, 2, . . . in the reduced residue class group Z*d, giving {v1=r1/d, v2=r2/d, . . . } for output.
摘要翻译：给出了一种获得均匀和独立随机数的方法（a），其包括两个不同奇数素数p1，p2，它们给出相互互补的整数q1 =（p1-1）/ 2和q2 =（p2-1）/ 2，具有不同的奇偶校验形成模量d = p1p2; （b）分别包括素数p1，p2的原始根z1，z2，给出确定乘数z的j = 1,2的一致关系z≡zjmod（pj）和（c）包括具有d = p1p2的初始值n互质。该方法产生陪集序列n z = {r 1 = n，r 2，r 3，...，。。对于j = 1,2，递归地由rj + 1 = zrj mod（d）递归地计算周期T = 2q1q2。。。在减少残留类Z * d中，给出{v1 = r1 / d，v2 = r2 / d，。。 }输出。

2. 发明授权

US08443021B2 Method of generating random numbers 失效
标题翻译：产生随机数的方法
公开(公告)号：US08443021B2
公开(公告)日：2013-05-14
申请号：US12379964
申请日：2009-03-05
申请人： Hiroshi Nakazawa , Naoya Nakazawa
发明人： Hiroshi Nakazawa , Naoya Nakazawa
IPC分类号： G06F1/02 , G06F7/58
CPC分类号： G06F7/586
摘要： A method of obtaining uniform and independent random numbers is given (a) comprising two distinct odd primes p1, p2 that give mutually coprime integers q1=(p1−1)/2 and q2=(p2−1)/2 with different parity to form the modulus d=p1p2; (b) comprising primitive roots z1, z2 of primes p1, p2, respectively, giving congruence relations z≡zj mod(pj) for j=1, 2 that determine the multiplier z; and (c) comprising the initial value n coprime with d=p1p2. The method generates the coset sequence n ={r1=n, r2, r3, . . . } of period T=2q1q2 recursively by rj+1=zrj mod(d) for j=1, 2, . . . in the reduced residue class group Z*d, giving {v1=r1/d, v2=r2/d, . . . } for output.
摘要翻译：给出了一种获得均匀和独立随机数的方法（a），其包括两个不同奇数素数p1，p2，它们给出相互互补的整数q1 =（p1-1）/ 2和q2 =（p2-1）/ 2，具有不同的奇偶校验形成模量d = p1p2; （b）分别包括素数p1，p2的原始根z1，z2，给出确定乘数z的j = 1,2的一致关系z = zj mod（pj）和（c）包括具有d = p1p2的初始值n互质。该方法产生陪集序列n z = {r 1 = n，r 2，r 3，...，。。对于j = 1,2，递归地由rj + 1 = zrj mod（d）递归地计算周期T = 2q1q2。。。在减少残留类Z * d中，给出{v1 = r1 / d，v2 = r2 / d，。。 }输出。

3. 发明授权

US09778913B2 Method of generating uniform and independent random numbers 有权
公开(公告)号：US09778913B2
公开(公告)日：2017-10-03
申请号：US15065549
申请日：2016-03-09
申请人： Hiroshi Nakazawa , Naoya Nakazawa
发明人： Hiroshi Nakazawa , Naoya Nakazawa
IPC分类号： G06G7/58 , G06F7/58
CPC分类号： G06F7/586
摘要： For any multiplicative congruential generator (d, z) with an odd modulus d and a multiplier z coprime to d, a computationally innovative method is presented as specialized forms of 2nd degree spectral tests of (d, z^i) with 2≦i≦6, at the least. Providing with sharp and powerful sieving tools, the method enables the excavation of the integer set (d, z) as a generator of uniform and independent random numbers of excellent statistics with sufficiently long periods for simulations, and furnishes the selected generator with ways of clear, unambiguous and quantitative specifications of its performance.

4. 发明申请

US20120290632A1 METHOD OF GENERATING RANDOM NUMBERS II 审中-公开
标题翻译：产生随机数的方法II
公开(公告)号：US20120290632A1
公开(公告)日：2012-11-15
申请号：US13105351
申请日：2011-05-11
申请人： Hiroshi Nakazawa , Naoya Nakazawa
发明人： Hiroshi Nakazawa , Naoya Nakazawa
IPC分类号： G06F7/58
CPC分类号： G06F7/586
摘要： A method of obtaining uniform and independent random numbers is given 1. by taking two distinct odd primes p1,p2 that give mutually coprime integers, an odd q1=(p1−1)/2 and an even q2=(p2−1)/2, to form the modulus d=p1p2, 2. by taking primitive roots z1,z2 of primes p1,p2, respectively, and giving congruence relations z≡−z1 mod (p1) and z≡z2 mod (p2) that determine the multiplier z uniquely modulo d, and 3. by taking an initial value n coprime with d=p1p2. The method generates the sequence of integers {rj|1≦j≦T=2q1q2} recursively by congruence relations r1≡n mod(d), rj+1≡zrj mod (d), 0
摘要翻译：给出一种获得均匀和独立的随机数的方法1.通过获得相互互质整数的两个不同的奇素数p1，p2，奇数q1 =（p1-1）/ 2和偶数q2 =（p2-1）/ 通过分别取出素数p1，p2的原始根z1，z2，并给出确定一致性的一致关系z≡-z1 mod（p1）和z≡z2mod（p2）以形成模数d = p1p2,2。乘法器z唯一地模D，并且通过用d = p1p2取初始值n coprime。该方法通过一致关系r1≡nmod（d），rj +1≡zrjmod（d），0

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