Ethereum's Justin Drake: AI May Break Crypto Keys Before Quantum Era
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https://nile1.com/ethereums-justin-drake-ai-may-break-crypto-keys-before-quantum-era/
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#cryptocurrencyWallets #ecdsa #ellipticCurve #freshAddresses #justinDrake #openai #privateKeys #quantumComp
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https://nile1.com/ethereums-justin-drake-ai-may-break-crypto-keys-before-quantum-era/
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#cryptocurrencyWallets #ecdsa #ellipticCurve #freshAddresses #justinDrake #openai #privateKeys #quantumComp
October 8, 2026 at 12:15 AM
Ethereum's Justin Drake: AI May Break Crypto Keys Before Quantum Era
..................
https://nile1.com/ethereums-justin-drake-ai-may-break-crypto-keys-before-quantum-era/
..................
#cryptocurrencyWallets #ecdsa #ellipticCurve #freshAddresses #justinDrake #openai #privateKeys #quantumComp
..................
https://nile1.com/ethereums-justin-drake-ai-may-break-crypto-keys-before-quantum-era/
..................
#cryptocurrencyWallets #ecdsa #ellipticCurve #freshAddresses #justinDrake #openai #privateKeys #quantumComp
EllipticCurve.btc
每一笔比特币交易的安全，
都来自这条曲线。
y² = x³ + 7
没有椭圆曲线，就没有比特币。
数学即信任。
#Bitcoin #EllipticCurve #secp256k1
每一笔比特币交易的安全，
都来自这条曲线。
y² = x³ + 7
没有椭圆曲线，就没有比特币。
数学即信任。
#Bitcoin #EllipticCurve #secp256k1
June 2, 2026 at 9:50 AM
EllipticCurve.btc
每一笔比特币交易的安全，
都来自这条曲线。
y² = x³ + 7
没有椭圆曲线，就没有比特币。
数学即信任。
#Bitcoin #EllipticCurve #secp256k1
每一笔比特币交易的安全，
都来自这条曲线。
y² = x³ + 7
没有椭圆曲线，就没有比特币。
数学即信任。
#Bitcoin #EllipticCurve #secp256k1
📄 Skyscraper: Fast Hashing on Big Primes: doi.org/10.46586/tch...
Skyscraper: Fast Hashing on Big Primes | IACR Transactions on Cryptographic Hardware and Embedded Systems
Arithmetic hash functions defined over prime fields have been actively developed and used in verifiable computation (VC) protocols. Among those, ellipticcurve- based SNARKs require large (256-bit and…
doi.org
December 5, 2025 at 4:35 PM
📄 Skyscraper: Fast Hashing on Big Primes: doi.org/10.46586/tch...
4/ Affine Coordinates `(x,y)` is the standard, intuitive way to represent a point on a 2D plane. You have an x-value and a y-value. Addition and Doubling ops in ECC require modular inversion(clock math).
#math #cryptography #affine #ellipticcurve
#math #cryptography #affine #ellipticcurve
October 22, 2025 at 5:35 PM
4/ Affine Coordinates `(x,y)` is the standard, intuitive way to represent a point on a 2D plane. You have an x-value and a y-value. Addition and Doubling ops in ECC require modular inversion(clock math).
#math #cryptography #affine #ellipticcurve
#math #cryptography #affine #ellipticcurve
A Selmer‑inspired framework creates elliptic curves via a Las Vegas algorithm that retries until a curve passes cryptographic checks. The curves run constant‑time. Read more: https://getnews.me/selmer-inspired-method-produces-transparent-elliptic-curve-parameters/ #ellipticcurve #selmer
October 6, 2025 at 4:57 AM
A Selmer‑inspired framework creates elliptic curves via a Las Vegas algorithm that retries until a curve passes cryptographic checks. The curves run constant‑time. Read more: https://getnews.me/selmer-inspired-method-produces-transparent-elliptic-curve-parameters/ #ellipticcurve #selmer
The Cofactor can be directly computed from the curve:
E = EllipticCurve(GF(2^256-2^32-2^9-2^8-2^7-2^6-2^4-1), [0,7])
G=E.lift_x(55066263022277343669578718895168534326250603453777594175500187360389116729240)
n=E.cardinality()
order=G.order()
assert n == order
print(n, order)
E = EllipticCurve(GF(2^256-2^32-2^9-2^8-2^7-2^6-2^4-1), [0,7])
G=E.lift_x(55066263022277343669578718895168534326250603453777594175500187360389116729240)
n=E.cardinality()
order=G.order()
assert n == order
print(n, order)
July 26, 2025 at 10:51 PM
The Cofactor can be directly computed from the curve:
E = EllipticCurve(GF(2^256-2^32-2^9-2^8-2^7-2^6-2^4-1), [0,7])
G=E.lift_x(55066263022277343669578718895168534326250603453777594175500187360389116729240)
n=E.cardinality()
order=G.order()
assert n == order
print(n, order)
E = EllipticCurve(GF(2^256-2^32-2^9-2^8-2^7-2^6-2^4-1), [0,7])
G=E.lift_x(55066263022277343669578718895168534326250603453777594175500187360389116729240)
n=E.cardinality()
order=G.order()
assert n == order
print(n, order)
So EllipticCurve(GF(191),[4,128]) and E2=EllipticCurve(GF(137),[4,128]) have |E|=168 and |E2|=142. E3=EllipticCurve(Zmod(137*191),[4,128]). Counting using lift_x on E3 gives 168*142. One point is double counted, but I think we also leave out the O point so it works out.
May 18, 2025 at 8:57 PM
So EllipticCurve(GF(191),[4,128]) and E2=EllipticCurve(GF(137),[4,128]) have |E|=168 and |E2|=142. E3=EllipticCurve(Zmod(137*191),[4,128]). Counting using lift_x on E3 gives 168*142. One point is double counted, but I think we also leave out the O point so it works out.
Because this is a _modular_ curve, its points correspond to (isomorphism classes of) elliptic curves with a bit of extra structure. The four non-cusp points correspond to the curves listed here:
https://www.lmfdb.org/EllipticCurve/Q/50/a/
They have short Weierstrass equations:
\\[ […]
https://www.lmfdb.org/EllipticCurve/Q/50/a/
They have short Weierstrass equations:
\\[ […]
Original post on mathstodon.xyz
mathstodon.xyz
January 13, 2025 at 5:23 AM
Because this is a _modular_ curve, its points correspond to (isomorphism classes of) elliptic curves with a bit of extra structure. The four non-cusp points correspond to the curves listed here:
https://www.lmfdb.org/EllipticCurve/Q/50/a/
They have short Weierstrass equations:
\\[ […]
https://www.lmfdb.org/EllipticCurve/Q/50/a/
They have short Weierstrass equations:
\\[ […]
Consider
E=EllipticCurve(Zmod(17*19),[3,7])
where this is true. One question I have, which I suspect is true, is that as long as your decomposition for your multiple doesn't ever involve 14, you won't ever compute a different point.
E=EllipticCurve(Zmod(17*19),[3,7])
where this is true. One question I have, which I suspect is true, is that as long as your decomposition for your multiple doesn't ever involve 14, you won't ever compute a different point.
December 17, 2024 at 7:25 AM
Consider
E=EllipticCurve(Zmod(17*19),[3,7])
where this is true. One question I have, which I suspect is true, is that as long as your decomposition for your multiple doesn't ever involve 14, you won't ever compute a different point.
E=EllipticCurve(Zmod(17*19),[3,7])
where this is true. One question I have, which I suspect is true, is that as long as your decomposition for your multiple doesn't ever involve 14, you won't ever compute a different point.
Alright; so technically this "works":
```
def elliptic_curve_factorization(N):
E = EllipticCurve(Zmod(N), [3,7])
p = random_point_on_curve(E)
acc = p
while True:
try:
acc += acc
except:
break
return gcd(N,acc[0]-p[0])
```
```
def elliptic_curve_factorization(N):
E = EllipticCurve(Zmod(N), [3,7])
p = random_point_on_curve(E)
acc = p
while True:
try:
acc += acc
except:
break
return gcd(N,acc[0]-p[0])
```
December 14, 2024 at 4:08 AM
Alright; so technically this "works":
```
def elliptic_curve_factorization(N):
E = EllipticCurve(Zmod(N), [3,7])
p = random_point_on_curve(E)
acc = p
while True:
try:
acc += acc
except:
break
return gcd(N,acc[0]-p[0])
```
```
def elliptic_curve_factorization(N):
E = EllipticCurve(Zmod(N), [3,7])
p = random_point_on_curve(E)
acc = p
while True:
try:
acc += acc
except:
break
return gcd(N,acc[0]-p[0])
```