Random number generators discussion

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the math behind mother
Author:  Date: 2004-12-18 21:27
Well I have some good news and some bad news. First, I have finished my password generator and it is available here: www.unix.com/showthread.php?s=&threadid=16116 It can generate passwords according to a template. I asked for hexadecimal passwords 80 characters long. And I generated one million of them. The resulting data file passed diehard. At last, I have my password generator.

One of the generators you wanted, a 2^16 with three terms can be designed with my 64 bit tools. Here are some that I found:
61111 1234 4180 17,201,222,602,028,482,559 8,600,611,301,014,241,279
61111 1234 4465 17,201,222,602,047,160,319 8,600,611,301,023,580,159
61111 1234 5233 17,201,222,602,097,491,967 8,600,611,301,048,745,983
61111 1234 5290 17,201,222,602,101,227,519 8,600,611,301,050,613,759
61111 1234 5965 17,201,222,602,145,464,319 8,600,611,301,072,732,159
61111 1234 6025 17,201,222,602,149,396,479 8,600,611,301,074,698,239

The first 3 integers are the multipliers. The next integer is the connection integer. And finally the period.
Now for the bad news. A Multiply with Carry is strickly periodic, but a Recursion with Carry is eventually periodic. A sequence can have a leader before it becomes periodic. Marsaglia calls these rho sequences. I have found a rho sequence that leads to a period of one.

The carry is rather large....that is guaranteed to be the case. If the carry is less than the sum of the multipliers, it will stay there. So I now initialize the carry modulo the sum of the multipiers. And actually, that is what Marsaglia suggests. Once I figure something out, I always seem to be able to find it in Marsaglia's paper. But he certainly isn't as explicit as he could be.

Happy Holidays!

thread the math behind mother new - Perderabo - 2004-11-24
last replythread the math behind mother new - Agner - 2004-11-25
last replythread the math behind mother new - Perderabo - 2004-11-25
last replythread the math behind mother new - Agner - 2004-11-26
last reply the math behind mother - Perderabo - 2004-12-18