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Elliptic Curve Digital Signature Algorithm(ECDSA) is a variant of the Digital
Signature Algorithm (DSA) based on the elliptic curve cryptography. ECDSA is
widely in the blockchains of TRON, Bitcoin and Ethereum used for
transaction signature, consensus verification and many other aspects. It is
one of the cornerstone algorithms of blockchain technology.

While explaining the principle of ECDSA, this article will also describe the
two approaches of verifying the elliptic curve encryption digital signature in
Solidity. These include the widely-used Solidity function — ecrecover, and the
new function, batchvalidatesign, introduced in the TRON Solidity V 0.5.9
compiler.

Elliptic curve digital signature algorithm theory

Signature generation algorithm

ECDSA is a combination of ECC and DSA. The whole signature process is
similar to DSA. The ECDSA signature consists of a pair of integers (r, s). The
steps of how public and private keys calculate to sign the message are as
follows:

1. Select an elliptic curve Ep(a, b), and a base point G;

2. Select a set of key pair, wherein the private key k is generated by a random
number, and the public key K=kG is calculated by using the base point G;

3. Generate a random integer r (r < n), calculate the equation R = rG;

4. Calculate e = HASH(message, x, y);

5. Calculate s ≡ r - e * k (mod n)

6. Take the value of r and s as the signature. If either r or s is 0, then reexecute the process from step 3.