The problem that finding k according to P, Q and the elliptic curve E is called the Elliptic Curve Discrete Logarithm Problem (ECDLP) over the finite field GF(p).

Since P = dG, it is equivalent to solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) that the attacker tends to solve d using P, which is difficult on computation.

According to the proof process of Theorem 1, the attacker can compute kG = sG + (r + s)P, but it is equivalent to solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) that solving the random number k on this basis, which is difficult on computation.