The security of RSA mainly depends on the difficulty of constructing the inverse of the mathematical function of its encryption algorithm, which is the same as most public key cryptosystems (for example, ElGamal algorithm is based on the difficulty of discrete logarithm problem, and we call such a function one-way function. One-way function can't be directly used as a cryptographic system, because if plaintext is encrypted by one-way function, even the legitimate receiver can't restore plaintext, because the inverse operation of one-way function is difficult. There is an effective algorithm to calculate the trapdoor one-way function, that is, the function and its inverse function, which is more closely related to the cryptographic system and the method of calculating the function can be made public. The concepts of one-way function and trapdoor one-way function are the core of public key cryptography and are very important to the construction of public key cryptosystem. It can even be said that the design of public key cryptosystem is the design of trapdoor one-way function.

ECDsA algorithm applies DsA to elliptic curve equation, and the basis of security is obtained from finite field.

The difficulty of discrete logarithm becomes the difficulty of calculating discrete logarithm on elliptic curve group, and the safety foundation is changed.

Change, so that the length of the key used under the same security degree is shortened, and only the key with the length of 192 bits can be used.

In order to ensure security, DSA algorithm needs a key of 1024 bits to ensure sufficient security. improve

The new algorithm improves the efficiency of the algorithm.