Signatures Schnorr and the inevitability of confidentiality in Bitcoin

Cryptocurrencies

Digital signatures are the foundation of online sovereignty. The emergence in 1976 of public-key cryptography opened the way to creating a global communication 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, today dozens of different open-source digital signature schemes are available to cryptographers.

When Satoshi Nakamoto began working on Bitcoin, one of the key points that needed to be considered was which of the signature schemes should be chosen for an open and public financial system. The requirements were clear: it was necessary to create an algorithm that would be widely used, understandable, reasonably safe, easy, and, most importantly, open source. Of all the options available at the time, he chose the one that meets these criteria best: Elliptic Curve Digital Signature Algorithm (digital signature algorithm based on elliptic curves), or ECDSA.

At that time, native support for ECDSA was provided in OpenSSL, an open set of encryption tools developed by experienced workers with encryption to increase the privacy of online communications. Compared to other popular schemes, ECDSA has advantages such as less demanding computing resources and shorter keys are useful properties for digital money. At the same time, it provides a proportional security level for schemes such as RSA: for example, a 256-bit ECDSA key has an equivalent level of security compared to a 3072-bit RSA key with a significantly smaller key size.

Thanks to the hard work done by Peter Woole and his colleagues on an improved elliptic curve called secp256k1, Bitcoin ECDSA has become even faster and more efficient. However, ECDSA still has some drawbacks, which can serve as a sufficient basis for its complete replacement. After several years of research and experimentation, a new signature scheme has been established to increase the confidentiality and efficiency of Bitcoin transactions: the digital signature scheme of Schnorr.