Blockchain with Lattice Encryption

Abstract This article presents some innovative strategies that facilitate the advancement of zk-SNARKs for blockchain applications by capitalizing on lattice encryption. Considering the challenges of reliable configurations and proof sizes in today’s zk-SNARKS, namely Groth16 and PLONK, our method looks for new ways to enhance protection while introducing improvements in efficiency. Our goal is to use lattice encryption techniques that provide post-quantum security for the reduction of computational and storage costs associated with proof size as well as mitigating the limitations arising from trusted setups. This research allows the emergence of new methods that may change zk-SNARKs’ standards for the blockchain, which gives way to more efficient and secure cryptographic protocols. Table of Contents Abstract. 2 1. Introduction. 4 1.1 Overview of zk-SNARKs. 4 1.2 Objectives of the Research. 4 1.3 Structure of the Research Article. 4 2. Background.. 4 2.1 Overview of zk-SNARKs. 4 2.1.1 Fundamental Principles of zk-SNARKs. 4 2.2 Introduction to Lattice Encryption. 5 2.3 Formal Definitions. 5 3. Problem Statement 5 4. Proposed Approach. 6 5. Implementation and Evaluation. 6 6. Security Analysis. 7 7. Future Work. 7 8. Conclusion. 8 References. 9 1. Introduction 1.1 Overview of zk-SNARKs zk-SNARKs are cryptographic proof constructions that enable a certain party to provide evidence of some information without disclosing such data. Long (2019) notes that zk-SNARKs are one of the de most important developments in cryptography. Several existing zk-SNARKs have many weaknesses that restrict their implementation in the blockchain world. The biggest issues are the dependence on trusted setups which introduces vulnerabilities and raises many questions about system-wide security (Zhao, 2019). Also, the size of the proof in zk-SNARKs is still very problematic for both computational and storage costs (Liang 2021). The rationale for investigating lattice encryption as a potential lies in its promising features. The post-quantum secure solution from lattice-based cryptography is promising to be the best answer in enhancing zk – SNARKs security on the blockchain. The use of lattice encryption techniques will help us to overcome the limitations identified previously, and it will make a new way for stronger and more efficient cryptographic protocols (Zhao, 2019). 1.2 Objectives of the Research The primary goal of this research is to introduce novel enhancements to zk-SNARKs in the context of blockchain, specifically targeting the challenges related to trusted setups and proof size. By leveraging lattice encryption, we aim to mitigate security concerns associated with existing zk-SNARKs while maintaining or improving efficiency (Li, 2015). 1.3 Structure of the Research Article This article discusses the origins of zk-SNARK, along with an in-depth analysis of Groth16 and also PLONK. Then, we will delve into lattice encryption with some formalized definitions for clarity. The proposal, implementation considerations, security analysis and future work, will all be presented at the end of which we shall have a complete understanding of how lattice techniques can take zk-SNARKs in the blockchain apps (Liang, 2021). 2. Background 2.1 Overview of zk-SNARKs 2.1.1 Fundamental Principles of zk-SNARKs Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge zk-SNARKs present a revolutionary step in cryptographic protocols by enabling the prover to convince the verifier that he/she knows something without providing any information about anything. In the domain of blockchain, zk-SNARKs have attracted a lot of attention for their role in keeping the data authentic and transactions confidential (Qiu, 2009). This part delves into the basic concepts behind zk-SNARKs and defines their relevance in a broader aspect of anonymity and safety for transactions on blockchain networks. In the realm of cryptography, special structures such as Groth16 and also PLONK are significant instances (Qiu, 2009). Groth16 zk-SNARK: It is explicitly known that Groth16 Jens created was primarily distinguished with a small proof size and fast verification. It does present, however, an obstacle in the form of a trusted setup whereby public parameters are generated during the initialization phase by a trusting party. The system’s reliance on this reliable setup leads to many security concerns, and a breach at this point may disrupt the entire system (Sha, 2007) PLONK zk-SNARK: PLONK, or Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge, resolves some problems with the trusted setups. To achieve greater transparency and to reduce the impact of an infiltrated configuration, it offers a worldwide and dynamic solution. Despite its compactness, the size of PLONK’s proof is not comparable to Groth16 in terms of efficiency although it does keep up (Chen, 2014). 2.2 Introduction to Lattice Encryption One of the alternative cryptographic bases that are highly attractive when discussing post-quantum security is lattice-based encryption. A collection of loci in a multidimensional grid forms the mathematical structure of what is known as a lattice. The lattice-based cryptography pa¬nes on the hardness of particular lattices, such as LWE and the shortest vector problem (SVP) (Shao, 2006). 2.3 Formal Definitions Shortest Vector Problem (SVP): Given a lattice, find the shortest non-zero vector in the lattice. Learning with Errors (LWE): An active adversary has a problem distinguishing noisy linear equations from purely random noise. One of the most common approaches to boost the cryptographic protocol’s security is using lattice-based encryption, which contemporary quantum computers cannot break. Through the inclusion of lattice encryption, zk-SNARKs can alleviate these inherent issues that are associated with existing designs such as—especially as they concern trust setups and make security base elements in blockchain systems tighter (Shao, 2006). 3. Problem Statement However, the real issues of trusted setups and proof sizes are at heart consumed with the present design scene of zk-SNARKs, particularly Groth16 and PLONK. To trust the installed systems, incorruptible installation is always necessary which makes it very risky because any intrusion during setup can compromise the zk-SNARK system’s security as a whole. Additionally, while Groth16’s small looking-up table is very important for its efficiency at the storage and computational costs (Quan, 2011), the latter issue needs to be constantly modified in improving new proposals. This is crucial since these matters should be addressed with a view of the further development in the acceptance chain through blockchain applications. This requires innovative approaches, … Read more