Verifying K Value in Sagemath | Bitcointalksearch.org

vjudeu

hero member

Activity: 667

Merit: 1529

Quote

So how did you find your G spot?

Nobody knows that. It seems someone used 0x48ce563f89a0ed9414f5aa28ad0d96d6795f9c62 as a magic number to start with, but nobody knows why: https://www.youtube.com/watch?v=NGLR2N4EK58

And there are more magic numbers outside Bitcoin, even with reward for explaining them: https://bitcointalksearch.org/topic/bounty-offered-to-crack-the-seeds-for-nist-curves-5469657

Quote

you can now learn by communicating with an artificial intelligence

AI is terrible at math, try asking about block hashes and transactions, in most cases it will be completely wrong, and it can give you for example an answer, where Bitcoin transaction format is mixed with Ethereum and other altcoins.

mamuu

member

Activity: 71

Merit: 19

Quote from: Bglhn on March 21, 2024, 07:48:53 PM

So how did you find your G spot? and p is your prime? I'm trying to learn, but I don't have enough knowledge.

You have to research and learn, I can't explain this situation, you can now learn by communicating with an artificial intelligence.

Bglhn

newbie

Activity: 30

Merit: 0

So how did you find your G spot? and p is your prime? I'm trying to learn, but I don't have enough knowledge.

mamuu

member

Activity: 71

Merit: 19

Quote from: mamuu on February 08, 2024, 05:35:52 PM

on sagemath
-------------------------------

sage:#prime [type:integer] but prime sage:P = 115792089237316195423570985008687907853269984665640564039457584007908834671663 sage:#Elliptic Curve y2=x3+7 for P [type:curve] sage:E = EllitpicCurve(GF(P),[0,7]) sage:#Elliptic Curve Order [type:integer] sage:N = E.order() sage:#Base Point G [type:point] sage:G= E(55066263022277343669578718895168534326250603453777594175500187360389116729240,32670510020758816978083085130507043184471273380659243275938904335757337482424) sage:# "public_key = secret*G" or "public_key = E(pubkey_x,pubkey_y)" [type:point], we know "pubkey_x,pubkey_y" sage:public_key = E(pubkey_x,pubkey_y) sage:# "K=random_number*G" [type:point] than "r = K[0]" [type:integer] , you known "r" sage:K = E.lift_x(r) sage:#K is_correct ? we don't know sage:r = your_value #[type:integer] sage:s = your_value #[type:integer] sage:z = your_value #[type:integer] sage:w = 1/s %N sage:u1 = z * w %N sage:u2 = r * w %N sage:#correct "K" point [type:point] sage:u2*public_key + u1*G #[type:point] sage:+K == u2*public_key + u1*G #(true or false) sage:-K == u2*public_key + u1*G #(true or false) sage r == Integer(+K[0]) #(true or false) [type:integer] sage r == Integer(-K[0]) #(true or false) [type:integer] sage:var("k x") sage:k*s == r*x+z #[type:variable] sage : K*s == r*public_key + z*G #[type:point] (true or false)

this line type: point
R = E.lift_x(r)

+K and -K are [points], and k is [integer].

in this case

K=(x/s)*PubKey + (z/s)*G

or
K = k*G

k=randint(1,N) #i.e. a random number, you can only try to find this number. it is very difficult in this process.

You can find "k" directly with the values r,s,z
With E.lift_x(R) you get either "+K" or "-K" and this is a "point". However, you cannot find the value "k", which is an integer.

Bglhn

newbie

Activity: 30

Merit: 0

Hello, what is your formula to find k? I've been looking for this too and couldn't find a solution.

krashfire

jr. member

Activity: 96

Merit: 6

Life aint interesting without any cuts and bruises

Quote from: whanau on February 23, 2024, 02:57:44 PM

# Compute the new signature point
P = k * G (k = your new k on test)

# Check if the x-coordinate of the signature point matches r
if P.x() == r:
print(f"Found k candidate: {k:x} ")
private_key = (s * k - z) * mod_inv(r, n) % n
print("Private Key : %02x " % private_key)

Thank You!!

whanau

member

Activity: 113

Merit: 28

Quote from: krashfire on February 09, 2024, 10:27:38 PM

Ok. Got it. Thank you so much! But I still need to verify the K value found. How do I do it correctly? Your method only shows whether K+ or K- is the correct one. But I still need to verify the K value by brute forcing. So how do I write the code to verify the K found?

# Compute the new signature point
P = k * G (k = your new k on test)

# Check if the x-coordinate of the signature point matches r
if P.x() == r:
print(f"Found k candidate: {k:x} ")
private_key = (s * k - z) * mod_inv(r, n) % n
print("Private Key : %02x " % private_key)

krashfire

jr. member

Activity: 96

Merit: 6

Life aint interesting without any cuts and bruises

Quote from: mamuu on February 08, 2024, 05:35:52 PM

on sagemath
-------------------------------

sage:#prime [type:integer] but prime sage:P = 115792089237316195423570985008687907853269984665640564039457584007908834671663 sage:#Elliptic Curve y2=x3+7 for P [type:curve] sage:E = EllitpicCurve(GF(P),[0,7]) sage:#Elliptic Curve Order [type:integer] sage:N = E.order() sage:#Base Point G [type:point] sage:G= E(55066263022277343669578718895168534326250603453777594175500187360389116729240,32670510020758816978083085130507043184471273380659243275938904335757337482424) sage:# "public_key = secret*G" or "public_key = E(pubkey_x,pubkey_y)" [type:point], we know "pubkey_x,pubkey_y" sage:public_key = E(pubkey_x,pubkey_y) sage:# "K=random_number*G" [type:point] than "r = K[0]" [type:integer] , you known "r" sage:K = E.lift_x(r) sage:#K is_correct ? we don't know sage:r = your_value #[type:integer] sage:s = your_value #[type:integer] sage:z = your_value #[type:integer] sage:w = 1/s %N sage:u1 = z * w %N sage:u2 = r * w %N sage:#correct "K" point [type:point] sage:u2*public_key + u1*G #[type:point] sage:+K == u2*public_key + u1*G #(true or false) sage:-K == u2*public_key + u1*G #(true or false) sage r == Integer(+K[0]) #(true or false) [type:integer] sage r == Integer(-K[0]) #(true or false) [type:integer] sage:var("k x") sage:k*s == r*x+z #[type:variable] sage : K*s == r*public_key + z*G #[type:point] (true or false)

this line type: point
R = E.lift_x(r)

Ok. Got it. Thank you so much! But I still need to verify the K value found. How do I do it correctly? Your method only shows whether K+ or K- is the correct one. But I still need to verify the K value by brute forcing. So how do I write the code to verify the K found?

mamuu

member

Activity: 71

Merit: 19

on sagemath
-------------------------------

sage:#prime [type:integer] but prime sage:P = 115792089237316195423570985008687907853269984665640564039457584007908834671663 sage:#Elliptic Curve y2=x3+7 for P [type:curve] sage:E = EllitpicCurve(GF(P),[0,7]) sage:#Elliptic Curve Order [type:integer] sage:N = E.order() sage:#Base Point G [type:point] sage:G= E(55066263022277343669578718895168534326250603453777594175500187360389116729240,32670510020758816978083085130507043184471273380659243275938904335757337482424) sage:# "public_key = secret*G" or "public_key = E(pubkey_x,pubkey_y)" [type:point], we know "pubkey_x,pubkey_y" sage:public_key = E(pubkey_x,pubkey_y) sage:# "K=random_number*G" [type:point] than "r = K[0]" [type:integer] , you known "r" sage:K = E.lift_x(r) sage:#K is_correct ? we don't know sage:r = your_value #[type:integer] sage:s = your_value #[type:integer] sage:z = your_value #[type:integer] sage:w = 1/s %N sage:u1 = z * w %N sage:u2 = r * w %N sage:#correct "K" point [type:point] sage:u2*public_key + u1*G #[type:point] sage:+K == u2*public_key + u1*G #(true or false) sage:-K == u2*public_key + u1*G #(true or false) sage r == Integer(+K[0]) #(true or false) [type:integer] sage r == Integer(-K[0]) #(true or false) [type:integer] sage:var("k x") sage:k*s == r*x+z #[type:variable] sage : K*s == r*public_key + z*G #[type:point] (true or false)

this line type: point
R = E.lift_x(r)

krashfire

jr. member

Activity: 96

Merit: 6

Life aint interesting without any cuts and bruises

Quote from: mamuu on February 07, 2024, 04:44:58 PM

Hello there

"R = E.lift_x(r)"
there are 2 possibilities in this line for point R
"R" or "-R"

If "public_key" is not a string but a "point" object(like G) with "E" element (Ellipric Curve)

"R= u2*public_key + u1*G"

it's the right thing to do.

Thank you.

So you are saying i should instead write it like this?

Code:

def verify(r, s, z, public_key, k):
# Compute modular inverse of s
w = modinv(s, n)

# Compute u1 and u2
u1 = z * w % n
u2 = r * w % n

# Compute R using the provided x-coordinate r
R = E.lift_x(r)

# Compute the candidate public key using the provided k value
candidate_public_key = u1 * public_key + u2 * G

# Check if the x-coordinate of the computed R matches that of the candidate public key
if R[0] == candidate_public_key[0]:
print("Signature matches")
return True
else:
print("Invalid signature")
return False

mamuu

member

Activity: 71

Merit: 19

Hello there

"R = E.lift_x(r)"
there are 2 possibilities in this line for point R
"R" or "-R"

If "public_key" is not a string but a "point" object(like G) with "E" element (Ellipric Curve)

"R= u2*public_key + u1*G"

it's the right thing to do.

Thank you.

krashfire

jr. member

Activity: 96

Merit: 6

Life aint interesting without any cuts and bruises

How do i verify if the found K value is the correct value given for an R signature and a public key?

i really need help for someone to check my code.

Code:

def verify(r, s, z, public_key, k):
w = modinv(s, n)
u1 = z * w % n
u2 = r * w % n
R = E.lift_x(r)
# Compute the candidate public key using the known k value
candidate_public_key = u1 * G + u2 * R
if public_key == candidate_public_key:
print("Signature matches")
return True
else:
print("Invalid signature")
return False

def find_k_bruteforce(r, s, z, pub):
i = 1
max_iterations = 1000 # Add a maximum iteration limit
while i <= max_iterations:
k = (r * i + z) * modinv(s, n) % n
print("i=", i, "k==", hex(k))
# Verify the signature using the candidate k
if verify(r, s, z, pub, k):
print("Found k:", hex(k))
return k
else:
print(f"Attempt {i}: Incorrect k value {hex(k)}")
i += 1 # Increment i for the next iteration
raise Exception("Failed to find a valid k value within the maximum iterations")

how do i verify the k value found? my calculations are wrong. it verifies the wrong k value.

Topic: Verifying K Value in Sagemath (Read 232 times)