Can someone explain the jump function in Xoshiro256**?

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liweij...@gmail.com

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Jul 21, 2020, 10:54:48 PM7/21/20
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Hi, 

I”ve read “Efficient Jump Ahead for F2-Linear Random Number Generators “and “Scrambled Linear Pseudorandom Number Generators“, and I downloaded the source code in it.unimi.dsi.util. But I still can’t understand the input and logic of the function jump(long[] jump).   Can someone be nice enough to explain the details?

Thank you!

Felicity



Sebastiano Vigna

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Jul 22, 2020, 3:04:06 AM7/22/20
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> On 22 Jul 2020, at 04:54, liweij...@gmail.com wrote:
>
> Hi,
>
> I”ve read “Efficient Jump Ahead for F2-Linear Random Number Generators “and “Scrambled Linear Pseudorandom Number Generators“, and I downloaded the source code in it.unimi.dsi.util. But I still can’t understand the input and logic of the function jump(long[] jump). Can someone be nice enough to explain the details?

Try to have a look at Section 8 of https://arxiv.org/pdf/1402.6246.pdf

Ciao,

seba

Felicity Li

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Jul 22, 2020, 4:01:18 AM7/22/20
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Thank you a lot! 
Now I think I’ve got the idea of the jump function. The input 4 longs are the 256 coefficients of the polynomial of the generative matrix M. And you mentioned in the paper that these coefficients can be carried out using standard techniques “Quadratures to find x^(2^k) mod P(x),etc” Could you please provide more info on these methods so that I can look at?

Again. many thanks!

Sebastiano Vigna

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Jul 22, 2020, 4:59:22 AM7/22/20
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The polynomial is just x^j mod p(x), where p(x) is the characteristic polynomial of the transition matrix. You can do that with any algebra package.
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Sent from my Android device with K-9 Mail. Please excuse my brevity.
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