Vector Commitments over Rings and Compressed Σ -Protocols
conference paper
Compressed Sigma -Protocol Theory (CRYPTO 2020) presents an “alternative” to Bulletproofs that achieves the same communication complexity while adhering more elegantly to existing Sigma -protocol theory, which enables their techniques to be directly applicable to other widely used settings in the context of “plug & play” algorithmics. Unfortunately, their techniques are restricted to arithmetic circuits over prime fields, which rules out the possibility of using more machine-friendly moduli such as powers of 2, which have proven to improve efficiency in applications. In this work we show that such techniques can be generalized to the case of arithmetic circuits modulo any number. This enables the use of powers of 2, which can prove to be beneficial for efficiency, but it also facilitates the use of other moduli that might prove useful in different applications. In order to achieve this, we first present an instantiation of the main building block of the theory of compressed Sigma -protocols, namely compact vector commitments. Our construction, which may be of independent interest, is homomorphic modulo any positive integer m, a result that was not known in the literature before. Second, we generalize Compressed Sigma -Protocol Theory from finite fields to Zm. The main challenge here is ensuring that there are large enough challenge sets as to fulfill the necessary soundness requirements, which is achieved by considering certain ring extensions. Our techniques have direct application for example to verifiable computation on homomorphically encrypted data. (C) 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Topics
TNO Identifier
982007
ISSN
03029743
ISBN
9783031223174
Publisher
Springer Science and Business Media Deutschland GmbH
Source title
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editor(s)
Kiltz, E.
Vaikuntanathan, V.
Vaikuntanathan, V.
Pages
173-202
Files
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