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How to find a element in elliptic curve ?(code added)

asked 2020-08-19 20:20:52 -0600

Duglas gravatar image

updated 2021-01-05 20:14:19 -0600

dan_fulea gravatar image

$Q=G*x$

$Q_2=G_2*y$

$G_2 = Q[n]=G[t]$

$Q=Q2$

$Q$, $G$, $G_2$ are points on elliptic curve.

$x$, $y$ are big integers.

$Q$, $Q_2$, $G$, $G_2$, $y$ are known.

How to find x ?

P.s. help me please. I'm very need help.


Pastebin code copy(more usefull) https://pastebin.com/C2vgKCJ0


CODE:

p = 2 * * 256 - 2 * * 32 - 2 * * 9 - 2^8 - 2^7 - 2^6 - 2^4 - 1

a = 0x0000000000000000000000000000000000000000000000000000000000000000

b = 0x0000000000000000000000000000000000000000000000000000000000000007

F = GF(p)
eccurve = EllipticCurve(F,[a, b])
curve = eccurve
ord = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141

Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798

Gy = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8

G = curve(Gx,Gy,1)
# This is a setion with data about Q !!! 
# We are not calculating Q and we need find  x and calculate Qz=x*G=Q. 
# We are know Q,G but don't know x !!! 

Q = curve(0x8b05b0603abd75b0c57489e451f811e1afe54a8715045cdf4888333f3ebc6e8b,
        0x1d10f88145db40fb889e2ddce81bda7c27f5b615acd6179dbb30f4fe7f40fb39)

print(Q)

R = Zmod(ord)

####end of section
# this section calculated G2,y and Q = G2*y
x0 = R(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
y = 1/x0

G2 = ZZ( y ) * Q

Q2 = ZZ(x0) * G2

# End of section

# This section after x was find. Find  x and paste to this code:

# x = ....

# Qresult=ZZ (x) * G
# print("Q==Qresult'", Q == Qresult)
# # end of section

print("Q==Q2'", Q2 == Q)

print("Q",Q)

print("Q2",Q2)

print("y",y)

print("G",G)

print("G2",G2)

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Comments

Could you please provide the code to construct Q, G, G_2, y ?

tmonteil gravatar imagetmonteil ( 2020-08-20 03:56:22 -0600 )edit

I will provide code for construct Q, G, G_2, y shortly. Thank you for your answer Tmonteil !!!Tmonteil I hope for your future help. Br !

Duglas gravatar imageDuglas ( 2020-08-20 07:19:19 -0600 )edit

HELP ME PLLEEEEASE FIND X ???? PLEEEASSSEE

Duglas gravatar imageDuglas ( 2020-08-20 17:08:01 -0600 )edit

HELP ME PLEASE ???

Duglas gravatar imageDuglas ( 2020-08-21 10:28:05 -0600 )edit

Please format sage / python code as code. For this, just indent all the code in some editor with 4 spaces or copy+paste it here, mark it, and while having it marked hit that button with the 101 and 010 on it. As it is, the question is not readable. It would be also a good idea to describe the objects you have first, then the "needed $x$" with given properties. Could you please edit the question to have a readable text?

dan_fulea gravatar imagedan_fulea ( 2020-08-24 18:00:38 -0600 )edit

1 answer

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answered 2021-01-05 23:16:58 -0600

tmonteil gravatar image

updated 2021-01-05 23:17:24 -0600

What you are looking for is the discrete logarithm:

sage: x = G.discrete_log(Q) ; x
1155

sage: Q == G * x
True
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Asked: 2020-08-19 20:20:52 -0600

Seen: 180 times

Last updated: Jan 05