elliptic-shiho / ecpy Goto Github PK

from ecpy import *

F, E, G, n = EllipticCurveRepository('secp224k1')

print G * n

Sun Mar 26 21:27:57 JST 2017 ~/prog/lab/mathematics/ecpy/scripts 93%
> python issue_3.py 
Point (2662552069424839940829238116501617128533613759701004695707473099760 : 15996838278203546540884017352821306960302774013401163842202920884487 : 1) on Elliptic Curve y^2 = x^3 + 5 over FiniteField(26959946667150639794667015087019630673637144422540572481099315275117)

must be n * G == Inifinity

Reference: http://www.secg.org/sec2-v2.pdf

• secp192k1
• secp192r1
• secp224k1
• secp224r1
• secp256k1
• secp256r1
• secp384r1
• secp521r1

Parameter

In the file "https://github.com/elliptic-shiho/ecpy/blob/master/examples/boneh_lynn_shacham_short_signature.py", I would like to know why you have all those parameters please?

In your "https://github.com/elliptic-shiho/ecpy/blob/master/ecpy/elliptic_curve/EllipticCurveRepository.py" nor https://safecurves.cr.yp.to has that specific number (p, l, etc.). I even did not found them on Google.

MapToPoint

I tried to replace all those parameter with yours (for example: (F, E, G, n) = EllipticCurveRepository("secp521r1")).

In addition, I tried to replace FiniteField with ExtendedFiniteField + both possible functions.

None of those works with MapToPoint.

Case FiniteField:

MapToPoint(E, E.field(12313))
Traceback (most recent call last):
File "", line 1, in
File "/usr/local/lib/python2.7/site-packages/ecpy/elliptic_curve/pairing.py", line 116, in MapToPoint
x = cubic_root(y**2 - 1)
File "/usr/local/lib/python2.7/site-packages/ecpy/utils/root.py", line 183, in cubic_root
rho = F(random.randint(1, p - 1), random.randint(1, p - 1))
File "/usr/local/lib/python2.7/site-packages/ecpy/rings/Ring.py", line 12, in call
return s.element_class(s, *x)
TypeError: init() takes exactly 3 arguments (4 given)

Case ExtendedFiniteField:

MapToPoint(E, E.field(hash_ID))
Traceback (most recent call last):
File "", line 1, in
File "/usr/local/lib/python3.7/site-packages/ecpy/elliptic_curve/pairing.py", line 117, in MapToPoint
Q = E(x, y)
File "/usr/local/lib/python3.7/site-packages/ecpy/elliptic_curve/EllipticCurve.py", line 78, in call
return s.element_class(s, *x)
File "/usr/local/lib/python3.7/site-packages/ecpy/elliptic_curve/EllipticCurve.py", line 354, in init
raise ArithmeticError("Invalid Point: (%s, %s, %s)" % (s.x, s.y, s.z))
ArithmeticError: Invalid Point: (mpz(37625453826780433377388048957201879362379477227012885069949001701454994121997751017162539005563127226988793675695228), mpz(12847647103851729428361901244548237337583883889892318731641379765076369134081500062657316972842886439414859445286270), 1)

• Implement l-torsion subgroup
• Implement Schoof algorithm
• Pass a test

Hi there,

Trying to get a random point on the elliptic curve raises an OverflowError in fields/FractionField for a 1536 bit p.
At lines 17-18 division must be done with // resulting in an int, that fixes the problem in my case.
I am using python 3.8 and reading your comment here #11 (comment) I guess ecpy was designed for python 2 at start but should work with python 3 too.

p = int(1641994227143377578153959399792871920054683918885673627721570851196750119415869674552942116832787561034894051277808905393148828520318225610178038512107187213731502506665338175685440485362224276062335386653431331251385091624504002080671595682282775620734083404790580129809073016308980466457936622480862655461693371423143228641053476783371900991044809670840439812478238543038118782100267663731306103046856471371034228707099062234903458075497898386216130191035140731)

F = FiniteField(p)
E = EllipticCurve(F, 0, 1)
P_pr = E.random_point()

Hope it helps.

Is it possible to make compatible with python3?

I keep running into errors due to the hashing and message printing.

• support F_2, F_{2^k} fields
  • elliptic curve support
• support F_3, F_{3^k} fields
  • elliptic curve support