Why this happend ? order of result point smaler then nultiplyes point and b ?

[COBRAS]

Hello, in code

# Note that these encrypt and decrypt functions are
# dummy stub functions to illustrate the main
# points.

def encrypt(symmkey, message):
    return symmkey

def key_does_decrypt(symmkey, cipherText):
    return (symmkey == cipherText)

b = 0x23fbd850a237fe4d283e4ca287aa6f8339f2f6dd134db1f6bb4861f6965749eb

p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
E = EllipticCurve(GF(p), [0,2])
Grp = E.abelian_group()
g = Grp.gens()[0]
numElements = g.order()
print( "{0} = {1}".format(numElements, factor(numElements)) )

n1 = 3
n2 = 13*13
n3 = 3319
n4 = 22639
n5 = 1013176677300131846900870239606035638738100997248092069256697437031

x = crt([0,0,1,0,0], [n1,n2,n3,n4,n5])
print(x)
P = x*g
print(P)
print('order of P = {0}'.format(P.order()))

Q = b * P

cipherText = encrypt(Q, "Hello")

y = 0
for i in range(1, 3319):
  if key_does_decrypt(i*P, cipherText):
      y = i

print('b mod 3319 = {0}'.format(y))

why if  P= x * G = 0x527abe0041d1ab698ab55cbcebd134f08bc75a6b734c62375c96f7abef9e4b18 * G

and


Q = b * P = 0x23fbd850a237fe4d283e4ca287aa6f8339f2f6dd134db1f6bb4861f6965749eb * P

cipherText = encrypt(Q, "Hello")

then privkey fron point ciphrrText = only 3036 in dec ?

How it posible downgrade orders of point and privkeys so mach ?

Why then use secp256k1 order of a point P always = infinity, but on curves with b = 2,3,4,5,6 not = infinity ?  

[COBRAS]

How it posible downgrade orders of point and privkeys so mach ?

The point and private key do not have an order. The order is defined for the group, which is the number of elements in that group.

Why then use secp256k1 order of a point P always = infinity, but on curves with b = 2,3,4,5,6 not = infinity ?  

Order of the curve is equal to N not infinity. We are working over a finite field after all.

You thant say ehat  print('order of P = {0}'.format(P.order())) is not order of a point ?


thrn multiple VERY BIG x to G : P = x*G we get publick key with  BiG privkey. And after multiply this Big pubkey too enothrer BIG b = Q, afer publikey Q multiply to text2hex we RESULT  = ONLY 1036.

How to implement this to curve b=7 secp256k1 ? Ofcause with order N - 1


ps order of a point = infinity then N / scalar of pubkey = infinity


 

[pooya87]

You thant say ehat  print('order of P = {0}'.format(P.order())) is not order of a point ?

Sorry, forget what I said before, the order of a point on elliptic curve is defined as smallest integer m so that mP = O
I don't understand your question to answer it though.

[COBRAS]

You thant say ehat  print('order of P = {0}'.format(P.order())) is not order of a point ?

Sorry, forget what I said before, the order of a point on elliptic curve is defined as smallest integer m so that mP = O
I don't understand your question to answer it though.

How to change code for get smale order of point on 256k1 with d = 7

[n0nce]

Hey COBRAS, I'll look at your code later, but in general, I notice that you're reducing your chances of getting good answers by putting very little effort in your questions.
You jot down whatever is on your mind, without structure, without grammar-checking it before posting.
Also by not introducing your goal, what you tried and what the results were, this burden is completely put on the reader, which again decreases your chances of someone putting in that time.

Instead, put in that time yourself, as you're the one seeking an answer.
StackOverflow's classic 'How do I ask a good question?' is a very good starting point, in my opinion, which can also be applied to this forum.

[COBRAS]

Hey COBRAS, I'll look at your code later, but in general, I notice that you're reducing your chances of getting good answers by putting very little effort in your questions.
You jot down whatever is on your mind, without structure, without grammar-checking it before posting.
Also by not introducing your goal, what you tried and what the results were, this burden is completely put on the reader, which again decreases your chances of someone putting in that time.

Instead, put in that time yourself, as you're the one seeking an answer.
StackOverflow's classic 'How do I ask a good question?' is a very good starting point, in my opinion, which can also be applied to this forum.

Hello. I thant convert point from order 2^255 bit, to order 3652 bit., and after bruteforce point for find privkey.

I wal already modify order of curve in enother scrypt , then multiply point to -1 and result was not more then new N(order of curve). But, then I multiply point of privkey > new order of curve point go to unknown region(not simple 0 and not simple "not more then order of curve ")