Elliptic Curve Digital Signature Algorithm

ECDSA (Elliptic Curve Digital Signature Algorithm) is a public key algorithm for creating a digital signature, similar in structure to DSA, but defined, unlike it, not over a finite numerical field, but in a group of points on an elliptic curve.

Peculiarities

The strength of the encryption algorithm is based on the problem of the discrete logarithm in a group of points on an elliptic curve. Unlike the simple discrete logarithm problem and the integer factorization problem, there is no subexponential algorithm for the discrete logarithm problem on the group of points of an elliptic curve. For this reason, the "power per key bit" is significantly higher in an algorithm that uses elliptic curves.

D. Brown (Daniel R. L. Brown) proved that the ECDSA algorithm is not more secure than DSA. He formulated a security constraint for ECDSA which led to the following conclusion:

“If an elliptic curve group can be modeled by the main group and its hash function satisfies a certain educated guess, then ECDSA is resistant to a matched-plaintext attack with forgery in place.

The ECDSA algorithm was adopted as an ANSI standard in 1999, and as an IEEE and NIST standard in 2000. Also in 1998, the algorithm was adopted by the ISO standard. Despite the fact that EDS standards have been created quite recently and are being improved, one of the most promising of them today is ANSI X9.62 ECDSA from 1999 - DSA for elliptic curves