- Introduction of witness semantic security in cryptography.
- Overcomes limitations of zero-knowledge in two-round settings.
- Built on subexponential hardness of LWE problem.
- Enables strong security against malicious CRS in NIZK.
- Pioneers adaptively sound ZAP from LWE.
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TranscriptIn the landscape of cryptographic proofs, especially within the two-round publicly-verifiable setting for NP problems, the quest for comprehensive security measures has been both rigorous and challenging. Historically, the strongest notions of security achievable in this domain have been witness indistinguishability and witness hiding, with significant contributions from researchers like Dwork, Naor, Groth, Ostrovsky, and Sahai, among others. Despite these advancements, the limitations imposed by the impossibility of achieving zero-knowledge or even weak zero-knowledge in this setting, as identified by Goldreich and Oren, have highlighted a substantial gap in the theoretical understanding of cryptographic security.
To address this gap, a novel notion of security, termed witness semantic security, has been introduced. This concept endeavors to ensure that an adversary cannot learn any partial information about the prover's witness beyond what is discernible from the statement itself. Witness semantic security not only encompasses the principles of witness indistinguishability and witness hiding but also introduces a more robust and easily interpretable form of security. The foundation for this advancement is built on the assumption of the subexponential hardness of the Learning With Errors (LWE) problem, which has enabled the creation of a two-round public-coin publicly-verifiable argument that upholds witness semantic security. This development marks a significant stride towards closing the theoretical gap, offering the strongest form of security known for this setting to date.
A critical application of this work emerges in the context of non-interactive zero-knowledge (NIZK) arguments within the common reference string (CRS) model. Here, witness semantic security can be maintained even when the CRS is maliciously generated, a scenario that presents a unique challenge to cryptographic security. This achievement signifies the first construction, based on (subexponential) standard assumptions, to surpass witness indistinguishability in the face of a malicious CRS authority. The methodology to accomplish these results involved the pioneering construction of a ZAP from subexponential LWE that is adaptively sound, along with a novel notion of simulation using non-uniform advice regarding a malicious CRS. These contributions not only pave the way for a deeper understanding of cryptographic proofs but also open avenues for future research and development in the field.
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