Dates

ECC is the first variant of the asymmetric encryption method RSA algorithm. Like the RSA algorithm, the ECC technology is based on a mathematical problem: the calculation of discrete logarithms (DL) in suitable amounts.

The group of observed elements corresponds to the group of points determined by a mathematical equation (i.e. the equation of the elliptic curve). Just like with the multiplication of numbers, association rules can be defined based on such points. Consecutive execution of such association rules results in exponentiation-like operations. All cryptographic protocols provided for such a case can be used accordingly without any problems.

The decisive advantage of this method is that none of the currently known algorithms for the solution of the DL problem for finite fields (such as those of the DSA algorithm) can be applied. Since only very general methods are available for the DL problem of sample point groups, keys and parameters can be noticeably shorter without running the risk of affecting the security of such keys and parameters. The effect of shorter keys can be decisive for memory or processing time critical applications such as in Smart Cards and other small devices.

The advantages of this type of method have lead to the integration of the method class into all major standardization efforts. Corresponding algorithms have been integrated into IEEE, ANSI, ISO/IEC, DIN standard drafts, and the German Signature Act of 1997, which stipulates the possible applications of electronically generated manual signature equivalents.

In contrast to current asymmetric methods, ECC technology is based on a mathematical model with a much higher complexity. Elemental knowledge in the area of modular arithmetic is sufficient for RSA (or DSA) algorithm applications. However, the know how required for ECC-based cryptography is considerably higher, especially with regard to the definition of suitable system parameters.