ISO/IEC 15946 specifies public-key cryptographic techniques based on elliptic curves. These include the establishment of keys for secret-key systems, and digital signature mechanisms. This part of ISO/IEC 15946 describes the mathematical background and general techniques necessary for implementing any of the mechanisms described in other parts of ISO/IEC 15946 and other ISO/IEC standards. The scope of this part of ISO/IEC 15946 is restricted to cryptographic techniques based on elliptic curves defined over finite fields of prime power order (including the special cases of prime order and characteristic two). The representation of elements of the underlying finite field when the field is not of prime order (i.e. which basis is used) is outside the scope of this part of ISO/IEC 15946. ISO/IEC 15946 does not specify the implementation of the techniques it defines. Interoperability of products complying with this part of ISO/IEC 15946 will not be guaranteed.