Special form of finite fields (FFs), called vector FFs (VFFs), is defined in the vector spaces over the ground finite field GF (p) using particular types of the multiplication operation over vectors. Implementation of the cryptographic algorisms based on elliptic curves (ECs) over VFFs provides significantly higher performance than the implementation of the EC-based algorithms, in which the ECs are defined over the ground fields and extension finite fields of polynomials.