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Old 2021-10-19, 15:51   #12
henryzz
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Originally Posted by Dobri View Post
More on the topic can be found here, https://eprint.iacr.org/2011/292.
This looks like an interesting paper that seems to generate some potentially useable non-linear polynomials for some small examples. Is there any code anyway that implements some of these ideas? I have been unable to replicate their examples in Maple.
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Old 2021-10-19, 17:57   #13
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This looks like an interesting paper that seems to generate some potentially useable non-linear polynomials for some small examples. Is there any code anyway that implements some of these ideas? I have been unable to replicate their examples in Maple.
There seems to be no source code provided by the authors.
Here is a link to the final version of the paper published in 2016, https://www.koreascience.or.kr/artic...050645801.page.
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Old 2021-10-20, 10:00   #14
henryzz
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Originally Posted by Dobri View Post
There seems to be no source code provided by the authors.
Here is a link to the final version of the paper published in 2016, https://www.koreascience.or.kr/artic...050645801.page.
Thanks for the updated link. This version made it clearer that while they have generalized Prest
and Zimmermann's extension to Montgomery's method, it isn't an improvement to the asymptotic complexity but just to flexibility. While useful finding good combinations of p and r is very difficult for larger composites.
This version mentioned that https://arxiv.org/abs/1109.6398 had continued their work.
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Old 2021-10-20, 13:41   #15
Dobri
 
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This version mentioned that https://arxiv.org/abs/1109.6398 had continued their work.
Indeed, there is one more paper published in 2015, https://daneshyari.com/en/article/4598897, https://hal.inria.fr/hal-01097069.

Here are also links to the preceding works on this topic by Prest and Zimmermann (2012), https://hal.inria.fr/inria-00540483, and Williams (2010), https://www.math.ttu.edu/~cmonico/re...nie_Thesis.pdf.
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