Cryptographic Tools for Blockchains

Cryptography plays a fundamental role in blockchain systems, ensuring security and integrity at multiple levels. Blocks are linked through cryptographic hash functions, and consensus mechanisms, such as proof-of-work, rely on these functions for validation. Transactions require authorization via digital signatures, while newer blockchain models incorporate advanced cryptographic tools, such as verifiable random functions for proof-of-stake and zero-knowledge proofs for private yet verifiable transactions. This chapter explores the cryptographic schemes essential to modern blockchain systems, discussing their role and security foundations. It follows the standard approach of defining security through asymptotic complexity and probabilistic polynomial time (PPT) adversaries. Most cryptographic schemes depend on hard mathematical problems, including RSA factorization and the discrete logarithm problem, which form the basis for many encryption and authentication protocols.