What is Secp256k1?

Secp256k1 is the name of the elliptic curve used by Bitcoin to implement its public key cryptography. When a user wishes to generate a public key using their private key, they multiply their private key, a large number, by the Generator Point, a defined point on the secp256k1 curve.

Is ECC better than RSA?

How does ECC compare to RSA? As you can see in the chart above, ECC is able to provide the same cryptographic strength as an RSA-based system with much smaller key sizes. For example, a 256 bit ECC key is equivalent to RSA 3072 bit keys (which are 50% longer than the 2048 bit keys commonly used today).

What is the formula for Weierstrass’s elliptic function?

℘ ( z ; τ ) = ℘ ( z ; 1 , τ ) = 1 z 2 + ∑ n 2 + m 2 ≠ 0 { 1 ( z + m + n τ ) 2 − 1 ( m + n τ ) 2 } . {\\displaystyle \\wp (z; au )=\\wp (z;1, au )= {\\frac {1} {z^ {2}}}+\\sum _ {n^ {2}+m^ {2} eq 0}\\left\\ { {1 \\over (z+m+n au )^ {2}}- {1 \\over (m+n au )^ {2}}ight\\}.}

Which is the simplest solution of a Weierstrass equation?

Genus one solutions of differential equations can be written in terms of Weierstrass elliptic functions. Notably, the simplest periodic solutions of the Korteweg–de Vries equation are often written in terms of Weierstrass p-functions. | f ( z ) | = | f ( x + i y ) | = 1 . {\\displaystyle \\left|f (z)ight|=\\left|f (x+iy)ight|=1\\;.}

Is the Weierstrass function a function of a complex variable?

for any pair of generators of the lattice defines the Weierstrass function as a function of a complex variable and a lattice. ℘ ( z ; τ ) = ℘ ( z ; 1 , τ ) = 1 z 2 + ∑ n 2 + m 2 ≠ 0 { 1 ( z + m + n τ ) 2 − 1 ( m + n τ ) 2 } .

What’s the difference between a long and short Weierstrass equation?

In some texts I see a “long” Weierstrass equation and in some I see a “short” Weierstrass equation, what is the difference between the two? Are they equivalent? Also since I am considering finite fields should a, b ∈ F q?