The adoption of NIST’s post-quantum cryptographic standards has accelerated the shift toward quantum-resistant systems. While many protocols like TLS, IKEv2, and Signal can integrate these standards, others still rely on primitives lacking efficient post-quantum replacements. One such primitive is the BLS signature scheme, widely used in proof-of-stake (PoS) blockchains for its ability to aggregate multiple signatures into a single compact one, reducing communication and verification overhead. Recent research has proposed post-quantum aggregate signatures to replace BLS, but existing schemes remain impractical due to high memory usage and slow aggregation. While prior solutions produce smaller signatures (hundreds of KB), they require hundreds of gigabytes of RAM to aggregate \(2^{10}\) signatures. In contrast, our scheme generates slightly larger signatures (2–3 MB) but drastically reduces aggregation time and can handle up to \(2^{16}\) signatures on a standard laptop, making it significantly more practical. In addition to improved scalability, our design is grounded in strong security principles, relying on minimal assumptions—specifically, the use of secure hash functions. For the signature primitive, we employ XMSS, a stateful hash-based signature scheme that is already standardized by NIST. To the best of our knowledge, no previous post-quantum aggregation schemes have implemented multi-level aggregation. We have implemented this capability, enabling incremental aggregation of signatures across the network. This is particularly relevant to Ethereum’s Beam chain roadmap, which emphasizes modular zk-rollup architectures and the integration of post-quantum primitives. Moreover, by enabling multi-level signature aggregation, our approach provides a practical solution for secure validator coordination and signature verification in future post-quantum Ethereum consensus mechanisms.

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HAPPIER: Hash-Based, Aggregatable, Practical Post-quantum Signatures Implemented Efficiently with Risc0

  • Arda Saygan,
  • Muhammed Said Gündoğan,
  • Atakan Arslan,
  • Mehmet Emin Gönen

摘要

The adoption of NIST’s post-quantum cryptographic standards has accelerated the shift toward quantum-resistant systems. While many protocols like TLS, IKEv2, and Signal can integrate these standards, others still rely on primitives lacking efficient post-quantum replacements. One such primitive is the BLS signature scheme, widely used in proof-of-stake (PoS) blockchains for its ability to aggregate multiple signatures into a single compact one, reducing communication and verification overhead. Recent research has proposed post-quantum aggregate signatures to replace BLS, but existing schemes remain impractical due to high memory usage and slow aggregation. While prior solutions produce smaller signatures (hundreds of KB), they require hundreds of gigabytes of RAM to aggregate \(2^{10}\) signatures. In contrast, our scheme generates slightly larger signatures (2–3 MB) but drastically reduces aggregation time and can handle up to \(2^{16}\) signatures on a standard laptop, making it significantly more practical. In addition to improved scalability, our design is grounded in strong security principles, relying on minimal assumptions—specifically, the use of secure hash functions. For the signature primitive, we employ XMSS, a stateful hash-based signature scheme that is already standardized by NIST. To the best of our knowledge, no previous post-quantum aggregation schemes have implemented multi-level aggregation. We have implemented this capability, enabling incremental aggregation of signatures across the network. This is particularly relevant to Ethereum’s Beam chain roadmap, which emphasizes modular zk-rollup architectures and the integration of post-quantum primitives. Moreover, by enabling multi-level signature aggregation, our approach provides a practical solution for secure validator coordination and signature verification in future post-quantum Ethereum consensus mechanisms.