point add was not commutative in the python implementation either.
Consider:
y3 = ( l * ( self.__x - x3 ) - self.__y ) % p
Thanks,
--
Raul
On Thu, Jan 30, 2014 at 10:41 PM, Pascal Jasmin <godspiral2...@yahoo.ca> wrote:
> Hi Cliff,
> I don't understand how to go from xyz back to xy coordinates.
>
>
> At any rate, here is the affine (python) implementation. (I posted invmod
> earlier):
>
>
> Pointadd =: 1 : 0 NB. n is curve p a b
> :
> p =. {. m NB.'p a b' =. n
> if. y -: p,0 do. x return. end.
> if. x -: p,0 do. y return. end.
> if. x -: y do. m Pointdouble y return. end.
> 'xx xy' =. x
> 'yx yy' =. y
> if. (xx = yy) *. 0=p|xy+yy do. p,0 return. end.
> l =. p | (p invmod yx - xx ) * yy - xy
> (p| (l*xx -x3 ) - xy ) ,~ x3=. p | yx -~ xx -~ l * l
> )
> Pointdouble =: 4 : 0
> 'p a'=. 2{. x
> if. y -: p,0 do. y return. end.
> 'xx xy' =. y
> l =. p | (p invmod xy * 2 ) * a + 3 * *: xx
> (p| (l*xx -x3 ) - xy ) ,~ x3=. p | (+: xx) -~ l * l
> )
> Pointmul =: 1 : 0 NB. sum of binary mask of repeated squares
> :
> m Pointadd/^:(1<#) |. bin # |. m Pointdouble^:(i. # bin =. 2 #. inv x) y
> )
>
> It passes the python tests, but it worries me that addition is not
> commutative. I also don't know how to code the point at infinity (I put 0,p
> but that is never reached).
>
> 3 10 (23 Pointadd) 9 7
> 17 20
>
> (23 1 Pointadd) each /\ 18 # <3 10
> ┌────┬────┬────┬────┬────┬────┬────┬─────┬───┬─────┬───┬─────┬────┬─────┬────┬─────┬────┬────┐
> │3 10│7 12│19 5│17 3│9 16│12 4│11 3│13 16│0 1│20 13│6 3│22 19│16 2│12 15│12
> 8│16 21│22 4│6 20│
> └────┴────┴────┴────┴────┴────┴────┴─────┴───┴─────┴───┴─────┴────┴─────┴────┴─────┴────┴────┘
>
> ,. (2+ i.16) (23 1 Pointmul)"0 1 ] 3 10
> 7 12
> 19 5
> 17 3
> 9 16
> 12 4
> 11 3
> 13 16
> 0 1
> 6 4
> 18 20
> 16 20
> 5 15
> 13 21
> 2 21
> 5 19
> 18 3
>
> These lists diverge after the item 0 1 is reached, which is the origin and a
> good candidate for infinity? I don't seem to understand what order is.
>
>
>
>
>
> ----- Original Message -----
> From: Cliff Reiter <reit...@lafayette.edu>
> To: programm...@jsoftware.com
> Cc:
> Sent: Wednesday, January 29, 2014 3:32:21 PM
> Subject: Re: [Jprogramming] math requests
>
> Some elliptic curve stuff; I think there is a +1 error that Roger Hui
> noticed in the factorization method.
>
> http://archive.vector.org.uk/art10007270
> http://archive.vector.org.uk/art10007280
>
> Best, Cliff
>
>
> On 1/29/2014 11:35 AM, Pascal Jasmin 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
>>
>
> --
> Clifford A. Reiter
> Lafayette College, Easton, PA 18042
> http://webbox.lafayette.edu/~reiterc/
>
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