SPHINCS+: A Secure Signature Solution for the Quantum Era

The development of quantum algorithms has advanced cryptography theory and signals the future of computing technology, which will profoundly impact various aspects, including scientific research, industrial production, and social life. Against this backdrop, the three PQC standards announced by NIST—Kyber, Dilithium, and SPHINCS+ algorithms—are particularly crucial. They serve as necessary safeguards for information security in the quantum era and represent significant achievements by the cryptographic community in addressing quantum computing challenges. We will focus on the SPHINCS+ algorithm and explore its unique characteristics in this issue.

SPHINCS+ (Stateless Practical Hash-based Signature Plus) is a post-quantum digital signature algorithm based on hash functions, specifically designed to address the threats posed by quantum computing. By combining a stateless design, multi-layer Merkle tree (Hypertree), and One-Time Signature (WOTS+), it offers robust quantum resistance. It has been selected as the NIST Post-Quantum Digital Signature Standard (FIPS 205) and is the only hash-based signature algorithm chosen in the NIST post-quantum project.

Core Principles

SPHINCS+ integrates the following key technologies:

1. Stateless Design:
SPHINCS+ leverages a Hypertree structure to avoid the complexity of managing signing states. The Hypertree consists of multiple layers of XMSS (eXtended Merkle Signature Scheme) trees, where each tree’s root authenticates the public key of the next layer, achieving a stateless signing process.

2. One-Time Signature (WOTS+):
The Winternitz One-Time Signature Plus (WOTS+) generates the leaf nodes for each Merkle path. WOTS+ features high efficiency and strong collision resistance, forming the foundation of SPHINCS+ security.

3. Few-Time Signature (FORS):
FORS (Forest of Random Subsets) is used to generate few-time signatures, further optimizing the efficiency and security of multiple signatures.

4. Hash Functions:
The security of SPHINCS+ relies on the collision resistance and second preimage resistance of hash functions, avoiding dependence on complex mathematical problems (e.g., lattice or isogeny-based problems) and ensuring robust quantum security.

Parameter Sizes

SPHINCS+ supports a wide range of parameter sets. For example, using SLH-DSA-SHA2-128s:

Advantages and Disadvantages

Advantages:

1. Strong Theoretical Foundation:
Built on extensively validated hash functions and Merkle tree technology, SPHINCS+ is highly reliable and avoids reliance on complex mathematical problems like lattices.

2. Stateless Design:
Eliminates the need to maintain signing states, avoiding key misuse and simplifying state management. This makes SPHINCS+ suitable for resource-constrained environments.

3. Flexible Parameters:
SPHINCS+ supports various parameter sets based on SHA-2 or SHAKE, allowing developers to balance security, signature size, and performance according to specific requirements.

4. Compact Key Sizes:
Compared to other lattice-based post-quantum signature schemes, SPHINCS+ has relatively small private and public key sizes, offering advantages in storage and transmission.

Disadvantages:

1. Large Signature Size:
Depending on the parameter set, lower-security configurations like SLH-DSA-SHA2-128s produce signatures around 8KB, while higher-security configurations like SLH-DSA-SHA2-256f can reach up to 50 KB. This makes SPHINCS+ less suitable for storage- and bandwidth-constrained applications compared to traditional algorithms (e.g., RSA or ECC).

2. High Computational Cost:
Signing and verification require extensive hash computations, leading to lower performance, especially in low-power devices or embedded systems.

3. Slower Verification Speed:
The multi-layer Merkle tree structure adds complexity to the verification process, making it less ideal for scenarios requiring high real-time performance.

4. Hardware Dependency:
Scenarios with high hash computation demands may require high-performance hardware, increasing deployment costs.

Application Scenarios

1. Long-Term Data Protection:
Ideal for government, financial, and healthcare sectors requiring data security over several decades.

2. Embedded Systems:
Stateless design simplifies key management in devices. Although computationally intensive, SPHINCS+ is well-suited for high-security embedded applications.

3. Blockchain and Digital Identity:
Suitable for securing transaction signatures in distributed ledgers and providing quantum-resistant solutions for digital identity authentication.

Conclusion

SPHINCS+ is an innovative post-quantum signature scheme that achieves a stateless design and efficient quantum security through Hypertree, FORS, and WOTS+ technologies. As one of the NIST post-quantum signature standards, SPHINCS+ stands out as the only hash-based signature scheme selected, making it well-suited for applications requiring high security. Despite challenges in signature size and computational efficiency, its robust security establishes a solid foundation for the future of digital signature systems.

As a leader in data security with 30 years of industry experience, Watchdata specializes in cryptographic algorithms, digital security protection, and secure chip operating systems. We will continue to monitor the latest developments in post-quantum algorithms, actively plan our strategic positioning, and provide comprehensive and robust digital security protection solutions for our users.