Algebraic techniques for universal succinct arguments
In this thesis, we make theoretical and practical contributions to the design of succinct arguments with universal setups in the pairing-based setting. We first introduce a new primitive, Checkable Subspace Sampling (CSS) schemes, and use it to build a framework for designing zero-knowledge succinct...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/675840 |
| Acceso en línea: | http://hdl.handle.net/10803/675840 |
| Access Level: | acceso abierto |
| Palabra clave: | Cryptography Zero-knowledge Succinct Arguments SNARKs Vector commitments Cryptografía Conocimiento nulo Argumentos sucintos Compromisos a vectores 62 |
| Sumario: | In this thesis, we make theoretical and practical contributions to the design of succinct arguments with universal setups in the pairing-based setting. We first introduce a new primitive, Checkable Subspace Sampling (CSS) schemes, and use it to build a framework for designing zero-knowledge succinct arguments of knowledge (zkSNARKs) for NP-complete problems. We present several instantiations of CSS that lead to zkSNARKs whose efficiency is competitive, and in most of the cases superior to all previous constructions in the state-of-the-art. Our second contribution is to present a framework for constructing Linear-Map Vector Commitment schemes with updatability and unbounded aggregation from simpler arguments, that prove a committed vector satisfies an inner product relation. We present two constructions of such arguments, that can be used as building blocks in many different succinct arguments, and the first pairing-based maintainable linear-map vector commitment scheme with flexible space/time trade-offs in the univariate, universal SRS model. Finally, we introduce the definition of Position-Hiding linkability for vector commitments and the first scheme that achieves logarithmic prover and constant proof for membership proofs and lookup tables. |
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