Buggy transliteration of https://github.com/warner/python-ecdsa/blob/master/ecdsa/ellipticcurve.py

eliptical.ijs

cocurrent 'CurveFp'
  Help=: 'Elliptic Curve over the field of integers modulo a prime.'
  create=:3 :0
    NB. The curve of points satisfying y^2 = x^3 + a*x + b (mod p).
    'P A B'=: x:&> y
    poly=: B,A,0,1
  )

  p=:3 :'P'
  a=:3 :'A'
  b=:3 :'B'

  containsPoint=:4 :0
    0 = P|(0 0 1 p. y) - poly p. x
  )

cocurrent 'Point'
  Help=:'A point on an elliptic curve'
  create=:3 :0
    This=: coname''
    'Curve X Y Order'=: args=. 4{.y,<'' assert. (#y) e. 3 4
    ORDERED=: -. '' -: 3 {:: args
    if.#Curve do.
NB.       assert. X containsPoint__Curve Y
    end.
    if. ORDERED do.
      assert. infinite mul__This Order
    end.
  )

  infinite=:3 :0
    (''-:Curve__y)*.(''-:X__y)*.''-:Y__y
  )

  invmod=: 4 : 0
    NB. inverse of y mod x (x|y)
    NB. uc vc ud vd d c  where d c init as x y
    NB. q =. d<.@%c -- (4&{ <.@%~ {:)
    a=. imw^:_ ] 1x,0x,0x,1x,x,y
    if. 1~: 4{a do. 0 return. end.
    if.0< 2{ a do. 2{ a else. x+2{a end.
  )

  imw =: ((2&{ - {. * 4&{ <.@% {:),(3&{ - 1&{ * 4&{ <.@% {:), 2&{., ({: | 4&{) ,~{:)^:(0 ~: {:)

  eq=:3 :0
    if. #cy=. Curve__y do.
      if.-.#Curve do. 0 return. end.
      if. A__Curve ~: A__cy do. 0 return. end.
      if. B__Curve ~: B__cy do. 0 return. end.
      if. P__Curve ~: P__cy do. 0 return. end.
    else. if. #Curve do. 0 return. end.
    end.
    (xy'')-: xy__y''
  )

  add=:3 :0
    NB. add another point to this point
    if. infinite y do. This return. end. NB. infinity is the new zero
    if. infinite This do. y return. end.
    assert. Curve -: Curve__y NB. can only add points on same curve
    p=. p__Curve'' NB. add
    if. X = X__y do.
      if. 0 = p | Y + Y__y do.
        INFINITY return.
      else.
        double'' return.
      end.
    end.
    l=.  p | (Y__y - Y) * p invmod X__y-X
    x3=. p | (0 0 1 p. l) - X+X__y
    y3=. p | (l * (X - x3)) - Y
    (Curve; x3; y3) conew 'Point' return.
  )


  leftmostBit=: </\&.#:
  bitAnd=: *./@,:&.|.&.#:
  mul=: 3 :0
    e=. y
    if. ORDERED do. e=. Order|e end.
    if. 0 = e do. INFINITY return. end.
    if. infinite This do. INFINITY return. end.
    assert. e > 0
    e3=. e*3
    negativeSelf=. (Curve;X;(-Y);Order) conew 'Point'
    i =. leftmostBit e3
    result=. This
    while. 1 < i=. <. -: i do.
      result=. double__result''
      if. (0 ~: e3 bitAnd i) *. (0 = e bitAnd i) do. result=. add__This result end.
      if. (0 = e3 bitAnd i) *. (0 ~: e bitAnd i) do. result=. add__negativeSelf result end.
    end.
  )

  str=:3 :0
    if. infinite This do. 'infinity' return. end.
    '(',(":X),',',(":Y),')'
  )

  double=:3 :0
    NB. Return a new point that is twice this one
    if. infinite This do. INFINITY return. end.
    p=. p__Curve''
    a=. a__Curve''
    l=. p | ((a,0,3) p. X) * p invmod 2*Y
    x3=. p | (l*l) - 2*X
    y3=. p | (l*(X-x3)) - Y
    (Curve; x3; y3) conew 'Point'
  )

  x0=: 3 :'X'
  y0=: 3 :'Y'
  xy=: 3 :'X,Y'
  curve=: 3 :'Curve'
  order=: 3 :'Order'

  INFINITY=: ('';'';'') conew 'Point'


cocurrent 'test'

  test_add=: 3 :0
    'c x1 y1 x2 y2 x3 y3'=: y
    p1=. (c;x1;y1) conew 'Point'
    p2=. (c;x2;y2) conew 'Point'
    p3=. add__p1 p2
    prefix=. (str__p1''),' + ',(str__p2''),' = ',(str__p3''),' '
    if. (x3 ~: x0__p3'') +. (y3 ~: y0__p3'') do.
      smoutput prefix,'Failure: should give (',(":x3),',',(":y3),')'
    else.
      smoutput prefix,' Good.'
    end.
  )

  test_double=: 3 :0
    NB. We expect that on curve c, 2*(x1,y1) = (x3, y3).
    'c x1 y1 x3 y3'=: y
    p1=. (c;x1;y1) conew 'Point'
    p3=. double__p1''
    prefix=. (str__p1''),' doubled = ',(str__p3''),' '
    if. (x3 ~: x0__p3'') +. y3 ~: y0__p3'' do.
      smoutput prefix,'Failure: should give (',(":x3),',',(":y3),').'
    else.
      smoutput prefix,' Good.'
    end.
  )

  test_double_infinity=: 3 :0
    NB. We expect that on curve c, 2*INFINITY = INFINITY.
    p1=. INFINITY_Point_
    p3=. double__p1''
    prefix=: (str__p1''),' doubled = ',(str__p3''),' '
    if. -. (xy__p1'') -: xy__p3'' do.
      smoutput prefix,'Failure: should give (',(":x0__p1''),',',(":y0__p1''),').'
    else.
      smoutput prefix,' Good.'
    end.
  )

  test_multiply=: 3 :0
    'c x1 y1 m x3 y3'=: y
    p1=. (c;x1;y1) conew 'Point'
    p3=. mul__p1 m
    prefix=. (str__p1''),' * ',(":m),' = ',(str__p3''),' '
    if. (x3 ~: x0__p3'') +. (y3 ~: y0__p3'') do.
      smoutput prefix,'Failure: should give (',(":x3),',',(":y3),')'
    else.
      smoutput prefix,' Good.'
    end.
  )


main=:3 :0
  c=. (23;1;1) conew 'CurveFp'
  test_add c;3;10;9;7;17;20
  test_double c;3;10;7;12
  test_add c;3;10;3;10;7;12
  test_multiply c;3;10;2;7;12

  test_double_infinity c

  g=. (c;13;7;7) conew 'Point'
  check=. INFINITY_Point_
  for_i. i. 7+1 do.
    p=. mul__g 7 | i
    prefix=. (str__g''),' * ',(":i),' = ',(str__p''),', expected ',(str__check''),' . . . '
    if. eq__p check do.
      smoutput prefix,' Good.'
    else.
      smoutput prefix,'Bad.'
    end.
    check=. add__check g
  end.

  p=. 6277101735386680763835789423207666416083908700390324961279x
  r=. 6277101735386680763835789423176059013767194773182842284081x
  dfhx=. 16x #. 16 | '0123456789ABCDEF0123456789abcdef' i. ]
  c=. dfhx '3099d2bbbfcb2538542dcd5fb078b6ef5f3d6fe2c745de65'
  b=. dfhx '3099d2bbbfcb2538542dcd5fb078b6ef5f3d6fe2c745de65'
  Gx=. dfhx '188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012'
  Gy=. dfhx '07192b95ffc8da78631011ed6b24cdd573f977a11e794811'
  
  c192=. (p;_3;b) conew 'CurveFp'
  p192=. (c192;Gx;Gy;r) conew 'Point'

  d=. 651056770906015076056810763456358567190100156695615665659x
  Q=. mul__p192 d
  if. (x0__Q'') ~: dfhx '62B12D60690CDCF330BABAB6E69763B471F994DD702D16A5' do.
    smoutput 'p192 * d came out wrong.'
  else.
    smoutput 'p192 * d came out right.'
  end.

  k=. 6140507067065001063065065565667405560006161556565665656654x
  R=. k * x0__p192''
  if. (xy__R'') ~: dfhx&> '885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD';'9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835' do.
    smoutput 'k * p192 came out wrong.'
  else.
    smoutput 'k * p192 came out right.'
  end.

  u1=. 2563697409189434185194736134579731015366492496392189760599x
  u2=. 6266643813348617967186477710235785849136406323338782220568x
  temp=. mul__p192 u1
  temp=. add_temp_ mul__Q u2
  if. (xy_temp_'') ~: dfhx&> '885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD';'9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835' do.
    smoutput '(u1 * p192)  + (u2 * Q) came out wrong.'
  else.
    smoutput '(u1 * p192)  + (u2 * Q) came out right.'
  end.
)

main''