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    • 8. 发明授权
    • Method for generating a random prime number within a predetermined interval
    • 用于在预定间隔内生成随机素数的方法
    • US07149763B2
    • 2006-12-12
    • US10236942
    • 2002-09-09
    • Marc JoyePascal Paillier
    • Marc JoyePascal Paillier
    • G06F7/58
    • G06F7/72G06F2207/7204
    • A random prime number is generated within a predetermined interval by precalculating and storing a single value that functions as a universal parameter for generating prime numbers of any desired size. The value, π, is chosen as a product of k prime numbers. A number a is also chosen such that is co-prime with π. Once the values for π and a have been determined they can be stored and used for all subsequent iterations of the prime number generating algorithm. To generate a prime number, a random number x is chosen with uniform distribution, and a candidate prime number within the predetermined interval is calculated on the basis of the random number. This candidate is tested for primality, and returned as the result if it is prime. If the candidate is not prime, the random number x is multiplied by a, and used to generate a new candidate. This procedure is repeated, until the candidate is prime. Since a single value, namely π, needs to be precalculated, economies of storage are achieved. In addition, the interval of interest is approximated with a higher degree of resolution. Moreover, it is possible to utilize the same value of π for a number of different intervals.
    • 通过预先计算和存储用作产生任意期望大小的素数的通用参数的单个值来在预定间隔内生成随机素数。 值pi被选为k个素数的乘积。 数字a也被选择为与pi共同配置。 一旦已经确定了pi和a的值,它们可被存储并用于素数生成算法的所有后续迭代。 为了生成素数,以均匀分布选择随机数x,并且基于随机数来计算预定间隔内的候选素数。 这个候选人被测试为原始性,如果它是素数,则作为结果返回。 如果候选者不是素数,则将随机数x乘以a,并用于生成新候选。 重复此过程,直到候选者为素数。 由于需要对单一值(即pi)进行预先计算,因此可以实现储存经济。 另外,感兴趣的间隔用更高的分辨率近似。 此外,可以使用与多个不同间隔相同的p i值。