Bitcoin, Bitcoin Cash, and most other cryptocurrencies use the Elliptic Curve Digital Signature Algorithm (ECDSA) to authenticate transactions. ECDSA can be used with a number of different elliptic curves, and Bitcoin’s creator chose the Koblitz curve Secp256k1 for Bitcoin’s digital signature system. Secp256k1 is used by most cryptocurrency
My (long) talk about Bitauth at the Atlanta Blockchain January 2017 Meetup. For a written summary, see the Bitauth2017 specification. Part 1Authenticating Bitcoin Transactions (slide →) Part 2Static Authentication vs. Scriptable Authentication (slide →) Part 3Scriptable Authentication & the Blockchain (slide →)Why use Bitcoin Script? (slide →)Why use the Blockchain for identities?