Digital signatures are considered the foundation of online sovereignty. The advent of public-key cryptography in 1976 paved the way for the creation of a global communications tool — the Internet, and a completely new form of money — Bitcoin. Although the fundamental properties of public-key cryptography have not changed much since then, dozens of different open-source digital signature schemes are now available to cryptographers.

How ECDSA was incorporated into Bitcoin

Of all the options available at that time, he chose the one that met these criteria: Elliptic Curve Digital Signature Algorithm, or ECDSA.

At that time, native support for ECDSA was provided in OpenSSL, an open set of encryption tools developed by experienced cipher banks in order to increase the confidentiality of online communications. Compared to other popular schemes, ECDSA had such advantages as:

These are extremely useful features for digital money. At the same time, it provides a proportional level of security: for example, a 256-bit ECDSA key has the same level of security as a 3072-bit RSA key (Rivest, Shamir и Adleman) with a significantly smaller key size.

Basic principles of ECDSA

ECDSA two separate procedures for signing and verifying. Each procedure is an algorithm consisting of several arithmetic operations. The signature algorithm uses the private key, and the verification algorithm uses only the public key.

To use ECDSA, such protocol as Bitcoin must fix a set of parameters for the elliptic curve and its finite field, so that all users of the protocol know and apply these parameters. Otherwise, everyone will solve their own equations, which will not converge with each other, and they will never agree on anything.

For all these parameters, Bitcoin uses very, very large (well, awesomely incredibly huge) numbers. It is important. In fact, all practical applications of ECDSA use huge numbers. After all, the security of this algorithm relies on the fact that these values are too large to pick up a key with a simple brute force. The 384-bit ECDSA key is considered safe enough for the NSA’s most secretive government service (USA).

Replacement of ECDSA

Schnorr’s signature takes the process of using “keys” to a new level. It takes only 64 bytes when it gets into the block, which reduces the space occupied by transactions by 4%. Since transactions with the Schnorr signature are the same size, this makes it possible to pre-calculate the total size of the part of the block that contains such signatures. A preliminary calculation of the block size is the key to its safe increase in the future.

Originally published at https://coinjoy.io.

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