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Hash Functions in ZK Proofs
- Hash functions are used inside zero-knowledge proofs within circuits to prove knowledge or membership.
- They are also crucial in recursive proofs to compress computations by generating challenges inside circuits repeatedly.
Hash Security and Circuit Efficiency
- Security of hash functions is well defined by difficulty of attacks like collision resistance.
- Circuit efficiency and finite field compatibility are critical for zero-knowledge proof systems, leading to specially designed hashes for these environments.
Trust Through Public Scrutiny
- Cryptographic constructions like hash functions lack formal proofs but are trusted after extensive public cryptanalysis over years.
- The real-world 'proof' is the absence of successful attacks and the billions of dollars secured by these systems.