Scalar Multiplication & the ECDLP

Scalar multiplication is the core EC operation: compute k×P by repeatedly applying the group law. The ECDLP — finding k given k×P — is the hard problem securing all elliptic-curve cryptography.

k×P = P + P + ... + P (k times). For k=4: 4P = P+P = 2P; 2P+2P = 4P. For k=2^256, direct iteration is infeasible. We need an efficient algorithm.