Welcome to the resource topic for 2025/475
Title:
HammR: A ZKP Protocol for Fixed Hamming-Weight Restricted-Entry Vectors
Authors: Felice Manganiello, Freeman Slaughter
Abstract:In this paper, we introduce \mathsf{HammR}, a generic Zero-Knowledge Proof (ZKP) protocol demonstrating knowledge of a secret vector that has a fixed Hamming weight with entries taken from a shifted multiplicative group.
As special cases, we are able to directly apply this protocol to restricted vectors and to rank-1 vectors, which are vectors with entries that lie in a dimension one subspace of \mathbb{F}_q.
We show that these proofs can be batched with low computational overhead, and further prove that this general framework is complete, sound, and zero-knowledge, thus truly a genuine ZKP.
Finally, we present applications of \mathsf{HammR} to various Syndrome Decoding Problems, including the Regular and Restricted SDPs, as well as other implementations such as lookup instances, proof of proximity, and electronic voting protocols.
ePrint: https://eprint.iacr.org/2025/475
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