[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"qwpuNkg3bh":3},"# Formal Verification of Generalized Bulletproofs\n\nCode artifacts, definitions and proofs for GBP/Bulletproofs built upon VCVio.\n\n## Definitions\n\nThis repository contains definitions of:\n\n- (k1,...,kn) (Computional) Special Soundness\n- Honest Verififer Zero-Knowledge\n- Completeness\n\nFor \"sigma-style\" protocols, using the formulations/ideas from \"Compressed Sigma Protocols\" where each protocol is viewed as \nan interactive reduction from its relation to the language of accepting last round messages:\nthe statement is the verifiers state and the proof is the last round message.\n\n## Composition Theorems\n\nAdditionally, this repository contains compositions theorems stating e.g.\n\n*Soundness:*\n> If protocol $\\Pi_A$ is $(k_A^{(1)},...,k_A^{(n)})$-special sound and protocol $\\Pi_B$ is $(k_B^{(1)},...,k_B^{(n)})$-special sound.\n> \n> Then $\\Pi_B \\circ \\Pi_A$ (A followed by B) is $(k_A^{(1)},...,k_A^{(n)}, k_B^{(1)}, ..., k_B^{(n)})$-special sound\n\n*Zero-Knowledge:*\n> If protocol $\\Pi_A$ is HVZK.\n>\n> Then $\\Pi_B \\circ \\Pi_A$ is HVZK for any $\\Pi_B$\n\nThese enable \"composing\" a tower of reductions, which is how folding is expressed in this project.\n\n## Proofs\n\nFinally, this repository contains proofs of:\n\n- Generalized Bulletproofs (Arithmetization):\n  - (Computional) $(n, q+1, 2 · n' · c + 3)$-special soundness\n  - Completeness\n  - Perfect HVZK\n- Improved Generalized Bulletproofs (Arithmetization):\n  - (Computional) $(n, q+1, 2 · c+5, 2)$-special soundness (observe this protocol has an additional round).\n  - Completeness\n  - Perfect HVZK\n- Bulletproof folding:\n  - (Computional) 8-special soundness\n  - Completeness\n- Simplified Bulletproof folding:\n  - (Computional) 4-special soundness\n  - Completeness\n\n\n## Final Notes\n\nThis is part of a bigger project (hence the lack of git history), a teaser.\n\nMore exciting news to come...\n",1784558054590]