Theoretical and practical estimate of cryptographic operations on elliptic and hyperelliptic curves complexity with taking into account realization on modern hardware is carried out. Generalization of metric for comparing performance crypto transformations on different genus curves over GF(2m ) to prime finite field case is carried out. The availability of using of hyperelliptic curves arithmetic in asymmetric cryptography protocols is confirmed by experiments. The foreground tasks for future research in this area are determined.
cryptosystem, open key cryptography, complexity, resistance, finite field, elliptic curve, hyperelliptic curve, divisor, 64-bit hardware