but we are not talking about +-N 
we are talking about weakness .
do you know secq256k1? (not secp256k1) and their parameters? check it out and think...
Secp256k1 group order == Secq256k1 base field order: True
Secp256k1 base field order == Secq256k1 group order: True
run in on https://sagecell.sagemath.org/
I checked that out and thought about it for a few minutes, I found it not interesting, other coins copy pasted bitcoin's curve with a bit of modification, what is special about it?we are talking about weakness .
do you know secq256k1? (not secp256k1) and their parameters?
check it out and think...Secp256k1 group order == Secq256k1 base field order: True
Secp256k1 base field order == Secq256k1 group order: True
run in on https://sagecell.sagemath.org/
Code:
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
q = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
# Secp256k1
P = GF(p)
aP = P(0x0000000000000000000000000000000000000000000000000000000000000000)
bP = P(0x0000000000000000000000000000000000000000000000000000000000000007)
Secp256k1 = EllipticCurve(P, (aP, bP))
Secp256k1.set_order(q)
# Secq256k1
Q = GF(q)
aQ = P(0x0000000000000000000000000000000000000000000000000000000000000000)
bQ = P(0x0000000000000000000000000000000000000000000000000000000000000007)
Secq256k1 = EllipticCurve(Q, (aQ, bQ))
Secq256k1.set_order(p)
print(
"Secp256k1 group order == Secq256k1 base field order:",
Secp256k1.order() == Secq256k1.base_field().cardinality()
)
print(
"Secp256k1 base field order == Secq256k1 group order:",
Secp256k1.base_field().cardinality() == Secq256k1.order()
)
q = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
# Secp256k1
P = GF(p)
aP = P(0x0000000000000000000000000000000000000000000000000000000000000000)
bP = P(0x0000000000000000000000000000000000000000000000000000000000000007)
Secp256k1 = EllipticCurve(P, (aP, bP))
Secp256k1.set_order(q)
# Secq256k1
Q = GF(q)
aQ = P(0x0000000000000000000000000000000000000000000000000000000000000000)
bQ = P(0x0000000000000000000000000000000000000000000000000000000000000007)
Secq256k1 = EllipticCurve(Q, (aQ, bQ))
Secq256k1.set_order(p)
print(
"Secp256k1 group order == Secq256k1 base field order:",
Secp256k1.order() == Secq256k1.base_field().cardinality()
)
print(
"Secp256k1 base field order == Secq256k1 group order:",
Secp256k1.base_field().cardinality() == Secq256k1.order()
)
As I said earlier, the one and only "weakness" of secp256k1 is the old known DLP, it's been there ever since the big bang! If you or anyone else like to worry for no reason, then good luck with it.
Imagine you have selected 1 atom inside of a planet in a galaxy billions of years apart from earth and deposited your bitcoins on it, and now you are worried someone might go there and grab that 1 atom! I'd better fire up my antimatter fueled spaceship to go after it.😂