Briefing
The long-standing challenge of realizing truly one-shot digital signatures, where a signing key is provably destroyed after a single use, persisted in the standard model, alongside the construction of full-domain trapdoor one-way permutations. This research introduces permutable pseudorandom permutations (permutable PRPs), a novel cryptographic primitive that facilitates the translation of oracle proofs into obfuscation-based proofs. This primitive underpins the first standard-model construction of one-shot signatures, leveraging indistinguishability obfuscation and LWE for provable security. This theoretical advance fundamentally redefines the capabilities of secure, single-use digital interactions, establishing new foundations for privacy and integrity in decentralized systems.
Context
Prior to this work, one-shot signatures (OSS) were a conceptual tool, deemed classically impossible and only explored with quantum keys or in idealized oracle models, where the sole known construction contained a fatal flaw. The cryptographic community also faced a decade-long open problem in constructing full-domain trapdoor one-way permutations from established primitives like indistinguishability obfuscation and one-way functions, limiting the foundational tools available for advanced cryptographic designs.
Analysis
The paper’s core mechanism centers on permutable pseudorandom permutations (permutable PRPs), a new cryptographic primitive. Conceptually, a permutable PRP is a pseudorandom permutation with an additional property allowing its behavior under specific transformations to be proven without revealing the permutation itself. This primitive bridges the gap between proofs in idealized oracle models and proofs in the standard model by enabling the translation of security arguments. By obfuscating these permutable PRPs, the research constructs a full-domain trapdoor one-way permutation, a long-sought cryptographic primitive.
This construction then enables the first standard-model one-shot signature, where the act of signing a message cryptographically self-destructs the signing capability, ensuring that only one signature can ever be produced from a given key. This approach establishes a robust, provably secure classical foundation, diverging from prior methods dependent on quantum properties or flawed oracle models.
Parameters
- Core Concept ∞ Permutable Pseudorandom Permutations
- New System/Protocol ∞ One-Shot Signatures (Standard-Model Construction)
- Key Authors ∞ Omri Shmueli
- Foundational Assumption ∞ Indistinguishability Obfuscation (iO) and Learning With Errors (LWE)
Outlook
This research establishes a new cryptographic bedrock, opening immediate avenues for developing highly secure, single-use digital credentials and transaction mechanisms in decentralized environments. In the next 3-5 years, this could unlock novel privacy-preserving protocols where authorization or data access is strictly one-time, enhancing security for sensitive operations and mitigating replay attacks. Academically, it invites further exploration into the properties of permutable PRPs and their potential to simplify or strengthen other complex cryptographic constructions, particularly in post-quantum settings and the design of more efficient obfuscation schemes.
Verdict
This work fundamentally advances cryptographic theory by providing the first standard-model construction of one-shot signatures and solving a decade-old problem in trapdoor permutations, establishing new foundational primitives for secure digital interactions.