Читать книгу Handbook of Intelligent Computing and Optimization for Sustainable Development - Группа авторов - Страница 106

The “elliptic curve” in a finite field known as E(GF) is a curve in cubic-form derived from the Weierstrass equation: y² + β₁xy + β₃y = x³ + β₂x² + β₄x + β₆ in GF. In this case, β_i ∈ GF and GF is a finite field [4].

The curve E(GF(p)) has the form: y² = x³ + ax + b in which p is a prime greater than 3, a, b ∈ GF(p) and 4a³ + 27b² ≠ 0. (β₁ = β₂ = β₃ = 0; β₄ = a and β₆ = b on the Weierstrass equation) [4].