Various methods for implementing cryptographic systems can reduce the likelihood of security vulnerabilities. A cryptographic system can utilize a combination of cryptographic processes to securely construct immutable ledgers and/or blockchains. These cryptographic systems can be referred to as composite cryptographic systems. A device can be configured to add a block to a distributed ledger maintained by a composite cryptographic system. The device can include a network interface, memory, and a processor. The processor can be configured to obtain a first proof using a first cryptographic system, obtain a second proof using a second cryptographic system; and broadcast a block to securely add the block to a distributed ledger. The block can be capable of being validated by using the first cryptographic system to generate the first proof and by using the second cryptographic system to generate the second proof.