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Succinct Proofs of Lattice Equations, Revealed

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The transition to quantum-safe cryptography is currently in full swing. After conducting a six year public competition, the US institute of standards (NIST) published the two primary standards for public key encryption and digital signatures in 2024. In the last year, industry has begun incorporating these standards into real-world products with the goals of protecting their users' data from future quantum attacks and meeting worldwide legislative deadlines of being completely quantum-safe by 2035. While significant software engineering work remains, the path forward is at least clear and actionable. The same cannot be said for protocols that use cryptography beyond basic encryption and digital signatures. Various applications such as electronic id, digital currency, blockchain privacy, Signal's group messaging and deniability features, etc. will require quantum-safe cryptography for which no standards currently exist because the quantum-safe solutions are simply too inefficient for practical purposes.

This project will strive toward the goal of making advanced cryptography quantum-safe, standardized, and efficient-enough for real-world use. The manner in which advanced constructions are often built is by layering a (zero-knowledge) proof system on top of basic primitives like encryptions, commitments, and signatures. The most efficient constructions for these latter primitives are lattice-based, and so creating efficient advanced schemes will require creating optimal proof systems for proving the lattice equations that make up these primitives. Because it is natural to expect that the optimal way to introduce a proof system to a protocol is to have it share the same algebraic structure as the statements it's proving, the constructions of these proofs should be lattice-based as well. Building and standardizing such proof systems for the variety of scenarios that emerge in real-world applications is the main technical objective of this project.

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IBM RESEARCH GMBH
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