The invention relates to distributed ledger technologies such as consensus-based blockchains. Computer-implemented N methods for reducing arithmetic circuits derived from smart contracts are described. The invention is implemented using a blockchain network, which may be, for example, a Bitcoin blockchain. A set of conditions encoded in a first programming language is obtained. The set of conditions is converted into a programmatic set of conditions encoded in a second programming language. The programmatic set of conditions is precompiled into precompiled program code. The precompiled program code is transformed into an arithmetic circuit. The arithmetic circuit is reduced to form a reduced arithmetic circuit, and the reduced arithmetic circuit is stored.