Practical Exact Proofs from Lattices: New Techniques to Exploit Fully-Splitting Rings

We propose a lattice-based zero-knowledge proof system for exactly proving knowledge of a ternary solution ~s ∈ {−1, 0, 1} to a linear equation A~s = ~u over Zq, which improves upon the protocol by Bootle, Lyubashevsky and Seiler (CRYPTO 2019) by producing proofs that are shorter by a factor of 7.5. At the core lies a technique that utilizes the module-homomorphic BDLOP commitment scheme (SCN 2018) over the fully splitting cyclotomic ring Zq[X]/(X + 1) to prove scalar products with the NTT vector of a secret polynomial.

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