[sage-devel] Re: Sage Enhancement Proposal: Edwards Curves Library
Yes, I too had pedagogy in mind. When I was reading about the Edwards model I thought it would have been nice if Sage had a library on it. In addition there are also some algorithms and tools which might be better used or only used with Edwards curves. For example, I have also implemented Dan Bernstein's Elligator encoding scheme. Also, as mentioned earlier, I am working on implementing the analogues of Velu's formulae for Edwards curves as described by Dustin Moody and Daniel Shumow which are more efficient than the original Velu's formulas for the Weierstrass model. I think we can also hope that, when applicable, Edwards curves will give more efficient implementations of algorithms already available for the Weierstrass model. Therefore, a library on the Edwards model might significantly expand Sage's capabilities. Adarsh. P.S. -- I have only begun learning about Elliptic curves and Sage in the past year. I would appreciate if anyone points out any inaccuracies in what I say. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: Sage Enhancement Proposal: Edwards Curves Library
I'm a bit ignorant about Edwards models. I understood its main usefulness was because it was faster than the usual models, requiring less arithmetic operations. Given that this was the primary usefulness, wouldn't it make sense to compare your library with some other fast libraries to show that it is actually faster. For example, why not use Dan Bernstein's highly optimised code. On the other hand, if there are theoretically interesting problems that can be studied only with the Edwards model, then there would be a reason to include it no matter what the practical performance is. Bill. On Saturday, 21 February 2015 06:13:31 UTC+1, Adarsh Saraf wrote: Hi Martin, Basically the module that I have written implements the Edwards model as an 'EdwardsCurve' class with an accompanying EdwardsCurvePoint class. For the methods that I have implemented, I have tried to mimic those in the Elliptic Curves library already in Sage. But I do not have different classes for the different types of base fields for it was not necessary for my work. Once I have added a patch and people feel that it would be better to have these classes, then we can easily do that too. Plus, I am also thinking of adding the documentation mimicking that for Elliptic Curves. The main functions that I have implemented as of now are: 1. Point addition 2. Scalar multiplication 3. Additive order of the points 4. Returning random points on the curve 5. Returning the n-torsion subgroup given n 6. Returning all the points on the curve in the finite field setting 7. Returning the isomorphic Weierstrass model as an 'EllipticCurve' object These are my further plans: 1. Have a method to obtain an 'EdwardsCurve' given a Weierstrass curve, after the base field extension if necessary 2. Implement the analogues of Velu's formulae for computing an isogeny given the kernel generators Adarsh. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Sage Enhancement Proposal: Edwards Curves Library
2015-02-23 15:54 UTC+01:00, Bill Hart goodwillh...@googlemail.com: On the other hand, if there are theoretically interesting problems [...] Pedagogical purpose can be fine as well. But in that case, the documentation has to be irreproachable. Vincent -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: Sage Enhancement Proposal: Edwards Curves Library
I think this would be for pedagogical purposes. There would be no point (that I can see) in duplicating all the functionality now available for Weierstrass models. Obvioulsy Bernstein's optimised formulas should be used, otherwise there is really little point. But don't artificially restrict to finite fields. John On 23 February 2015 at 15:04, Vincent Delecroix 20100.delecr...@gmail.com wrote: 2015-02-23 15:54 UTC+01:00, Bill Hart goodwillh...@googlemail.com: On the other hand, if there are theoretically interesting problems [...] Pedagogical purpose can be fine as well. But in that case, the documentation has to be irreproachable. Vincent -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: Sage Enhancement Proposal: Edwards Curves Library
cc:ing sage-nt 2015-02-20 10:04:37 UTC+1, Adarsh Saraf: Hello everybody, As part of my Masters thesis, I have developed a module related to the Edwards model for Elliptic Curves. I was of the opinion that it would be helpful for many if it can be integrated into Sage. Would like to know if you also feel the same and if I should open a ticket on the trac server? Also the functions were written to suit my needs and are therefore not as well written as they ought to be for Sage. I would work on it if it seems useful to add the module to Sage. Awaiting your comments, Adarsh Saraf -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: Sage Enhancement Proposal: Edwards Curves Library
Hi Martin, Basically the module that I have written implements the Edwards model as an 'EdwardsCurve' class with an accompanying EdwardsCurvePoint class. For the methods that I have implemented, I have tried to mimic those in the Elliptic Curves library already in Sage. But I do not have different classes for the different types of base fields for it was not necessary for my work. Once I have added a patch and people feel that it would be better to have these classes, then we can easily do that too. Plus, I am also thinking of adding the documentation mimicking that for Elliptic Curves. The main functions that I have implemented as of now are: 1. Point addition 2. Scalar multiplication 3. Additive order of the points 4. Returning random points on the curve 5. Returning the n-torsion subgroup given n 6. Returning all the points on the curve in the finite field setting 7. Returning the isomorphic Weierstrass model as an 'EllipticCurve' object These are my further plans: 1. Have a method to obtain an 'EdwardsCurve' given a Weierstrass curve, after the base field extension if necessary 2. Implement the analogues of Velu's formulae for computing an isogeny given the kernel generators Adarsh. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
