4.8 Ellipse Curve Digital Signature Algorithm

The digital signature algorithm is the key in many blockchain technologies. It can prove the ownership of the address without exposing the private key and is generally used to sign transactions, verify the sender, and prevent from being tampered with. Ellipse Curve Cryptography (ECC) and Ellipse Curve Digital Signature Algorithm (ECDSA) have been widely adopted in crypto and blockchain applications.

DxChain uses secp256k1 elliptic curve and ECDSA signature algorithm to sign transactions on the chain. In cryptography, compared to symmetric encryption algorithms, such as AES, DES, elliptic curve algorithms have higher security performance, faster processing speed, lower bandwidth requirements, and smaller storage space. ECC is different from other encryption methods based on factoring in large prime numbers, the mathematical principle it relies on is the difficulty of solving the discrete logarithm problem (DLP) on the elliptic curve. It is the difficulty of solving that provides a guarantee for data encryption.

Figure 10: An example of an elliptic curve

Using the elliptic curve point manipulation algorithm, DxChain creates a value from the private key as the public key. The elliptic curve point multiplication algorithm is a kind of trapdoor function, which is easy to calculate in one direction other than the reverse direction with an absence of certain information (trapdoor), so it can barely calculate the private key from the public key reversely. Signing by private key and verifying by public key, transactions on DxChain are fully secure and immutable.