Foundations of Verifiable Computing

Descripción del proyecto

Una mirada más profunda a los sistemas de prueba

La computación verificable se ha convertido en un componente esencial del desarrollo futuro de las cadenas de bloques y la computación en nube. Está presente en múltiples aplicaciones técnicas relacionadas con tecnologías del mundo real y permite que un verificador vulnerable determine la precisión de enunciados computacionales complejos. En el proyecto VERICOMP, financiado con fondos europeos, se mejorará la comprensión de los sistemas de prueba con generación de pruebas en tiempo polinomial a fin de examinar su aplicabilidad práctica y estudiar sus conexiones con cuestiones fundamentales en criptografía y teoría de la complejidad. Al centrarse en sistemas de prueba interactivos para cálculos manejables, el proyecto ofrecerá una caracterización detallada de la complejidad de probar y verificar enunciados generales. A su vez, esto favorecerá avances en el estudio de los conceptos de sistemas de prueba relacionados como, por ejemplo, los argumentos criptográficos.

Objetivo

Proof systems allow a weak verifier to ascertain the correctness of complex computational statements. Efficiently-verifiable proof systems are fundamental objects in the study of computation, and have led to some of the deepest and most celebrated insights in cryptography and in complexity theory.

The vast and rich literature on proof systems focuses primarily on proving the correctness of intractable statements, e.g. ones that are NP-complete. While the verification can be efficient, the proofs themselves cannot be generated in polynomial time. This limits the applicability of such proof systems, both from a theoretical perspective and in their real-world impact. This proposal aims to obtain a comprehensive understanding of proof systems with polynomial-time proof generation, to explore their practical applicability, and to investigate their connections with foundational questions in cryptography and in complexity theory.

Our study will focus primarily on interactive proof systems for tractable computations. The proposed research aims to revolutionize our understanding of these foundational objects by providing a complete and tight characterization of the complexity or proving and verifying general statements, by achieving breakthroughs in the study of related proof system notions, such as cryptographic arguments, and by building a fine-grained “algorithmic” theory of proof systems for central polynomial-time computational problems.

Our research will leverage these advances towards diverse applications: from real-world security challenges, such as verifying the correctness of computations performed by the cloud and cryptographic “proofs of work”, to a complexity-theoretic understanding of the complexity of approximating problems in P and of solving them on random instances.