A Group-Theoretic Framework for Privacy-Preserving Monetary Systems
Conventional cryptocurrencies reveal every intermediate transfer on-chain, sacrificing confidentiality to obtain public auditability. Zero-knowledge cash (ZKC) reverses this trade-off: every transaction is provably valid, yet the ledger discloses nothing beyond the final state.
The construction presented here couples group-theoretic entropy, homomorphic commitment chains, and oracle-mediated timekeeping to yield a privacy-preserving monetary layer that remains verifiable for every participant.
By binding initial randomness to a hard discrete-logarithm group, evolving it through algebra-preserving maps, and validating each epoch with succinct zero-knowledge proofs, the system achieves computational soundness while hiding every intermediate value.
Grounded in Rényi entropy on finite groups, providing cryptographic randomness
Structure-preserving maps that maintain group law compatibility across epochs
Perfect hiding and additive homomorphism for privacy-preserving transactions
Ensuring completeness, soundness, and zero-knowledge properties
Anchoring genesis state and time-stamping epochs with cryptographic proof
Rényi Entropy: Hα(si) ≥ Hmin for initial randomness pool
Homomorphic Evolution: φH : Si → Si+1 preserving group law
Pedersen Commitments: C(m,r) = gmhr with perfect hiding
Zero-Knowledge Proofs: π ← Prove(x,w) with completeness, soundness, and ZK