Category: ECC

🔁 What is an endomorphism in general?

In mathematics, an endomorphism is a function from a space to itself that preserves the structure of that space.

• For a group, it’s a group homomorphism \(f: G \rightarrow G\)
• For a vector space, it’s a linear map \(f: V \rightarrow V\)
• For

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problem:

compute multiple scalar multiplication of ECC

\(S=k_i\cdot P_i\)

step 1:

decompose each scalar

step 2:

gather the decomposed scalars that has the same base together

step 3:

compute the gathered scalars addition using bucket method.

A very good explanation of the algorithm here

more readings here

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🔧 What is Lazy Field Arithmetic?

Lazy field arithmetic delays reductions modulo \(p\) to avoid expensive operations after every add/mul. Instead of immediately reducing results, the library tracks a conservative magnitude, which represents how many times larger than \(p\) a value might be.

📐 What is magnitude?

Magnitude …

Definition: Elliptic Curve, Group, Field

The elliptic curve is defined by an equation, but when it comes to practices, it is discrete and finite, i.e, we cannot work on elliptic curves that are defined on \(\mathbb{R}\), instead, we defined it on a field \(\mathbb{F}_p\) .

The points on the curve …