Topic: Bitcoin has a mathematical loophole (Read 156 times)
Very interesting calculations, I never thought about something like that. I partially have a solution to this problem, at the university when I was taking mathematics, I liked the site https://plainmath.net/post-secondary/calculus-and-analysis/integral-calculus that by calculating integrals, just what I need It was. Take a closer look on the website, there are a lot of similar questions about calculations, I am sure that you will find the answers you need.
Elliptic Curve Vulnerability
Elliptic curve function
y^2 = x^3 +7 This function is visible
y^2 = x^3 +7 mod p is imaginary and invisible, because it is different from ordinary functions
Added a mod operation. The disadvantages are poor confidentiality, and the advantages are integers.
#If p=q, k=(3x2+a)/2y1modp
#If P≠Q, then k=(y2-y1)/(x2-x1)modp
Both point addition and point multiplication are available, and Euclid expands modular arithmetic
extended_gcd (denominator, modulus)
Please note that not all numbers have Euclidean extended modulus arithmetic
For example 1/2 mod 4 fails
Only when gcd(a,p)==1, can there be Euclidean extended modulus operation
1/3 mod 7 success
The denominator is the value of the y coordinate, it can be any number, and the loophole comes out
Since p is a prime number, gcd(a,p)==1 Note: The greatest common divisor of gcd
How simple is it really, wrong
When gcd(7,7)!=1 this is an important point and
When gcd(21,7)!= 1.
How to calculate the coordinates of this vulnerability?
There are theoretically, I guess, my mathematics level is limited
Elliptic curve function
y^2 = x^3 +7 This function is visible
y^2 = x^3 +7 mod p is imaginary and invisible, because it is different from ordinary functions
Added a mod operation. The disadvantages are poor confidentiality, and the advantages are integers.
#If p=q, k=(3x2+a)/2y1modp
#If P≠Q, then k=(y2-y1)/(x2-x1)modp
Both point addition and point multiplication are available, and Euclid expands modular arithmetic
extended_gcd (denominator, modulus)
Please note that not all numbers have Euclidean extended modulus arithmetic
For example 1/2 mod 4 fails
Only when gcd(a,p)==1, can there be Euclidean extended modulus operation
1/3 mod 7 success
The denominator is the value of the y coordinate, it can be any number, and the loophole comes out
Since p is a prime number, gcd(a,p)==1 Note: The greatest common divisor of gcd
How simple is it really, wrong
When gcd(7,7)!=1 this is an important point and
When gcd(21,7)!= 1.
How to calculate the coordinates of this vulnerability?
There are theoretically, I guess, my mathematics level is limited
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