These MIT lecture notes for 18.783 cover the foundations of elliptic curves, from projective curves and the group law to isogenies, point counting, and the discrete logarithm problem. The notes pair each result with the algorithms that compute it and their complexity.

Key Topics

• Smooth plane cubics
• Finite field arithmetic
• Edwards curve models
• Division polynomials
• Pohlig–Hellman method

Author: Andrew V. Sutherland