HORS: Hash-Based Few-Times Signatures for Practical Multi-Use Keys
This article explains HORS (Hash to Obtain Random Subset), a hash-based few-times signature (FTS) scheme that extends one-time signatures (OTS) to allow multiple signatures from a compact key pair. HORS replaces simple bijective selection with a subset-resilient hash function H so that signatures reveal limited private key elements and prevent finding messages whose hash-index sets are subsets of previously signed messages. The scheme: generate t private integers, publish their hashes as the public key; to sign, compute h = Hash(m), split h into k indices (i1..ik), and output the corresponding private elements as the signature. Security rests on r-subset-resilience (attackers cannot find r+1 messages whose H-sets form a subset relation) and is typically modeled via a random oracle. HORS offers shorter signatures and faster signing/verification compared to Biba-like constructions and improves reuse over OTS while retaining hash-function-only assumptions. Primary keywords: HORS, hash-based signatures, few-times signatures, subset-resilient hash, one-time signature. Secondary/semantic keywords: random oracle, signature scheme, public key, private key, indices, security assumptions.
Neutral
This is a technical cryptography exposition, not market-moving news. It explains HORS, a hash-based few-times signature scheme that enhances one-time signatures with subset-resilient hashing. For traders, such protocol-level cryptography improvements are generally neutral in the short term: they do not immediately affect token supply, network economics, or market sentiment. In the medium-to-long term, advances in signature efficiency and security can influence blockchain design choices (faster, smaller signatures reduce fees and on-chain storage), which may benefit chains adopting these schemes. Historical parallels: cryptographic improvements (e.g., Schnorr signatures, Taproot) had limited immediate price impact but enabled protocol upgrades that later supported ecosystem growth. Therefore expect neutral short-term impact; potential modest bullish structural effects if major projects adopt HORS-like schemes for efficiency and cost reduction.