Oh, doh, yes. I should have looked at my implementation of mul before posting.
Thanks, -- Raul On Thu, Jan 30, 2014 at 1:02 PM, Pascal Jasmin <godspiral2...@yahoo.ca> wrote: > Cliff Reiter's code uses a different algorithm than the python code (uses > jacobian coordinate transformation to avoid inverse mod calculation). His > code can be found here (but his first link is a good intro): > http://webbox.lafayette.edu/~reiterc/j/vector/factor_ecj.html > > For the python implementation, you want to look at __mul__ . __rmul__ I > believe just overloads the * operator perhaps for the right argument to *. > > The general overview of elyptic curve multiplication is that it involves > repeated doublings and additions. > > http://repl.it/languages/Python is a useful resource for figuring out python > code. But here is the only part I had trouble understanding: > > leftmostbit =: 2&#.@:({. , 0 $~ 2 -~ #)@:(2&#. inv) NB. for some reason > divides msb by 2. > > > > ________________________________ > From: Raul Miller <rauldmil...@gmail.com> > To: Programming forum <programm...@jsoftware.com> > Sent: Thursday, January 30, 2014 12:32:59 PM > Subject: Re: [Jprogramming] math requests > > > I have been looking at this, and I did a straightforward conversion of > the python code to J (not quite complete). And I have a couple issues > I would like to talk through before proceeding (I've also not yet > studied Cliff Reiter's code). > > First, I would like to quibble with what I assume is the underlying > standards document. The value INFINITY behaves like a zero in the > context of addition. That strikes me as a bit odd. > > Second, though, I would like to understand python's rules a bit better > - what happens when one multiples a Point with integer? > > Specifically, consider this excerpt from > https://github.com/warner/python-ecdsa/blob/master/ecdsa/ellipticcurve.py > : > > p192 = Point( c192, Gx, Gy, r ) > > # Checking against some sample computations presented > # in X9.62: > > d = 651056770906015076056810763456358567190100156695615665659 > Q = d * p192 > > The definitions of p192 and d are trivial for me to translate: > > p192=. (c192;Gx;Gy;r) conew 'Point' > > d=. 651056770906015076056810763456358567190100156695615665659x > > But how do I translate Q? > > In the definition of Point, I saw the following bit of python: > > def __rmul__( self, other ): > """Multiply a point by an integer.""" > > return self * other > > But if that is the relevant code, all it is telling me is that > multiplication is defined in terms of multiplication - as far as I can > see, there is no other definition for multiplying a Point and an > integer, nor have I seen any constructor for constructing a Point from > an integer. > > Before I spend too much time chasing down rabbit holes (I really > should be working on some other issues), can someone explain to me > what is supposed to happen here? > > Thanks, > > -- > Raul > > > On Wed, Jan 29, 2014 at 11:35 AM, Pascal Jasmin <godspiral2...@yahoo.ca> > wrote: >> >> >> With all of the mathematicians on this list, these functions have likely >> been implemented before in J. >> >> elyptic curve point add, multiplication and double >> a python reference implementation: >> https://github.com/warner/python-ecdsa/blob/master/ecdsa/ellipticcurve.py >> >> the functions are: __add__ __mul__ and double >> >> if I may suggest J explicit signatures for the first 2 functions as: >> >> F =: 4 : 0 >> 'yx yy yo' =. y >> 'xx xy xo' =. x >> ) >> >> Some other methods than the python reference could be considered here: >> >> http://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication >> >> >> also appreciated if you have in implementation of inverse_mod >> for reference function of same nate at: >> https://github.com/warner/python-ecdsa/blob/master/ecdsa/numbertheory.py >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
