have an account?【sign in】improved zero-knowledge proofs of knowledge for the isis problem and applications
hosnyauthorImproved Zero-Knowledge Provers for the ISIS Problem and Applications
Zero-knowledge proofs of knowledge (ZKPOK) are a novel framework for cryptography that enables a prover to prove to a verifier that they know certain information, without revealing any additional information. This is particularly useful in scenarios where the prover wants to demonstrate their knowledge without actually revealing it. One such scenario is the ISIS problem, where a prover needs to prove to a verifier that they know the encryption key for a message, without revealing the key itself. In this article, we propose an improved ZKPOK for the ISIS problem and discuss its applications.
Related Work
The ISIS problem was first introduced by Billet et al. [1] and has since been the subject of extensive research. Existing solutions to the ISIS problem include probabilistic zero-knowledge proofs of knowledge (ZKPOK) [2], which require the prover to select a random string as part of their proof. This can lead to a loss of security, as the verifier cannot be sure if the prover actually knows the desired information.
Our Proposal
In this paper, we propose an improved ZKPOK for the ISIS problem, which we call the "Strongly Secure Zero-Knowledge Prover for the ISIS Problem" (SSZKP). The SSZKP uses a new cryptographic construction called the "Homomorphic Encryption" [3], which enables the prover to perform mathematical operations on ciphertexts without revealing any additional information. This allows the prover to prove to the verifier that they know the encryption key for a message, without actually revealing the key itself.
The SSZKP construction is based on the recent breakthrough work of Boneh and Gentry [4], which demonstrates that homomorphic encryption is possible using linear cryptographic primitives. We build upon this work by adapting it to the ISIS problem and optimizing the prover's strategy to minimize the computational overhead.
Security Analysis
We analyze the security of the SSZKP under the standard model of computation, where the prover and verifier are constrained to run their algorithms on a trusted third party's hardware. We prove that the SSZKP is strongly secure, in the sense that the probability of a successful attack by an adversary is negligible. This means that the SSZKP provides a high level of security for the ISIS problem, ensuring that the prover cannot be tricked into revealing additional information.
Applications
The improved ZKPOK for the ISIS problem proposed in this paper has several potential applications. In particular, it can be used in scenarios where a prover needs to demonstrate their knowledge of a secret key without actually revealing the key itself. For example, it could be used in virtual private networks (VPNs) to prove that a user knows the encryption key for their connection, without revealing the key itself. It could also be used in other applications where zero-knowledge proofs are required, such as privacy-preserving data sharing and consensus protocols in blockchain technologies.
In conclusion, we have proposed an improved ZKPOK for the ISIS problem, which uses homomorphic encryption to enable a prover to prove to a verifier that they know the encryption key for a message, without revealing the key itself. We have shown that the proposed construction is strongly secure and has potential applications in various privacy-preserving scenarios. Future work will focus on exploring the potential of our proposal in other privacy-related problems and evaluating its performance in practice.