Hash-based signatures are a family of digital signature schemes that derive their security from the properties of cryptographic hash functions. Unlike classical schemes such as RSA or ECDSA, which rely on the hardness of number-theoretic problems, hash-based signatures are constructed using only hash functions. This makes them highly attractive in the context of post-quantum security, as hash functions are believed to remain secure even in the presence of quantum adversaries.

The fundamental idea is to use hash functions to generate one-time or few-time signature keys, which are then aggregated or structured to enable practical, multi-use digital signatures. The robustness of these schemes depends on the collision resistance and preimage resistance of the underlying hash functions. For a deeper look at the cryptographic properties of hash functions, see Hash Algorithms Explained: Secure Password Storage.

The concept of hash-based signatures dates back to the 1970s, with the introduction of the Lamport signature scheme. While Lamport signatures were simple and secure, they were limited to one-time use, making them impractical for most real-world applications. Over time, researchers developed more advanced constructions, such as Merkle signature schemes, which enabled multiple signatures by organizing one-time keys in a tree structure. For more on Merkle trees, refer to Exploring Merkle Trees and Hash Trees: A Comprehensive Guide.

The motivation for hash-based signatures has grown significantly with the advent of quantum computing. Quantum algorithms, such as Shor's algorithm, threaten to break widely used public-key cryptosystems. In contrast, hash-based schemes offer a promising alternative, as their security is rooted in the well-studied properties of hash functions, which are not efficiently broken by known quantum algorithms. For a detailed discussion on quantum threats, see the NIST SP 800-208.

SPHINCS+ is a stateless, hash-based digital signature scheme designed to provide strong security guarantees against both classical and quantum adversaries. It builds upon earlier hash-based constructions, incorporating several innovations to enable practical, multi-use signatures without the need for state management. SPHINCS+ is a leading candidate in the NIST Post-Quantum Cryptography Standardization process and is recognized for its conservative security assumptions and flexibility.

The name "SPHINCS" stands for "Stateless Practical Hash-based Incredibly Nice Cryptographic Signature," reflecting its key attributes: statelessness, practicality, and strong security.

SPHINCS+ is designed with several core principles in mind:

• Statelessness: Unlike many hash-based schemes, SPHINCS+ does not require the signer to maintain state between signatures, eliminating risks associated with state reuse or loss.
• Modularity: The scheme is constructed from well-understood cryptographic primitives, primarily hash functions, and modular components such as WOTS+, FORS, and hypertrees.
• Parameter Flexibility: SPHINCS+ supports a range of parameter sets, allowing users to balance signature size, computational efficiency, and security level.
• Post-Quantum Security: The security of SPHINCS+ is based solely on the properties of hash functions, making it resistant to both classical and quantum attacks.

The security of SPHINCS+ relies on the following assumptions:

• Collision Resistance of the underlying hash function: It should be computationally infeasible to find two distinct inputs that produce the same hash output.
• Preimage and Second-Preimage Resistance: Given a hash output, it should be infeasible to find an input that maps to it, or a second input that collides with a given input.

These properties are well-studied and widely trusted in the cryptographic community. For more on hash function security, refer to ENISA's Algorithms, Key Size and Parameters Report or see Salting Passwords Properly: 2025 Best Practices.

A defining feature of SPHINCS+ is its statelessness. Traditional hash-based signature schemes, such as Merkle signatures, require the signer to keep track of which one-time keys have been used, introducing risks if the state is lost or reused. SPHINCS+ eliminates this requirement by using a deterministic key derivation process and a hierarchical structure, ensuring that each signature is unique and secure without the need for persistent state.

This stateless design greatly simplifies implementation and reduces the risk of catastrophic key reuse, which is a critical advantage for real-world deployments.

SPHINCS+ is composed of several key building blocks:

• WOTS+ (Winternitz One-Time Signature Plus): A one-time signature scheme that provides the basic signing functionality. WOTS+ is efficient and secure, forming the foundation for higher-level structures.
• FORS (Forest of Random Subsets): A few-time signature scheme that enables efficient signing of message digests. FORS increases performance and reduces signature size compared to using only WOTS+.
• Hypertree Structure: SPHINCS+ organizes multiple layers of Merkle trees (a hypertree) to aggregate many one-time and few-time signatures, enabling practical, multi-use signatures while maintaining security.

These components work together to provide a scalable, efficient, and secure signature scheme. To understand how Merkle trees and hash trees facilitate these structures, visit Exploring Merkle Trees and Hash Trees: A Comprehensive Guide.

SPHINCS+ offers a variety of parameter sets, allowing users to tailor the scheme to their specific needs. Key parameters include:

• Hash Function Choice: SPHINCS+ supports several hash functions, such as SHA-256, SHAKE256, and Haraka, each offering different trade-offs between security and performance.
• Security Level: Parameter sets are available for 128, 192, and 256-bit security levels, aligning with NIST recommendations.
• Tree Height and Layers: The structure of the hypertree (number of layers and height of each layer) affects signature size and computational cost.
• Winternitz Parameter: Controls the efficiency and size of WOTS+ signatures.

For a comprehensive list of parameter sets, consult the official SPHINCS+ documentation.

Key generation in SPHINCS+ involves creating a public and private key pair based on the chosen parameter set. The process can be summarized as follows:

1. Generate a random seed, which serves as the master secret.
2. Derive all necessary secret values (for WOTS+, FORS, and tree roots) deterministically from the seed using the hash function.
3. Compute the root of the top-level Merkle tree, which becomes the public key.

This deterministic process ensures that the same seed always produces the same key pair, supporting stateless operation.

Signing a message with SPHINCS+ involves several steps:

1. Compute a randomized message digest using the message and a randomization value derived from the secret key.
2. Sign the digest using the FORS scheme, producing a FORS signature and the corresponding root.
3. Sign the FORS root with a WOTS+ signature at the appropriate position in the hypertree.
4. Include authentication paths for each tree layer, allowing the verifier to reconstruct the path to the top-level root.

The resulting signature includes all necessary components (FORS signature, WOTS+ signature, authentication paths) to enable verification without state.

Verification in SPHINCS+ is straightforward:

1. Recompute the message digest and FORS root from the signature and message.
2. Verify the WOTS+ signature and reconstruct the authentication paths through the hypertree.
3. Check that the computed top-level root matches the public key.

If all checks pass, the signature is valid. This process relies solely on hash computations and tree traversals, ensuring efficiency and security. For more on verifying hash-based signatures, see Password Cracking Myths Busted: What Works Today.

SPHINCS+ is designed to provide robust post-quantum security. Its security is based on the hardness of finding collisions or preimages in the underlying hash function, which remains a difficult problem even for quantum computers. While Grover's algorithm can provide a quadratic speedup for brute-force search, appropriately chosen hash sizes (e.g., 256 bits) ensure that the scheme remains secure at the desired security level.

For more on post-quantum cryptography and hash-based schemes, see the NIST announcement on quantum-resistant algorithms.

SPHINCS+ is resistant to a wide range of attacks, including:

• Quantum Attacks: Security is not based on number-theoretic assumptions, making it immune to Shor's algorithm.
• Classical Cryptanalysis: The use of well-studied hash functions and conservative parameters mitigates risks from classical attacks.
• State Reuse Attacks: The stateless design eliminates vulnerabilities associated with state reuse, a common issue in earlier hash-based schemes.

The scheme has undergone extensive cryptanalysis and public scrutiny as part of the NIST PQC process.

Despite its strengths, SPHINCS+ has some limitations:

• Large Signature Sizes: Compared to classical schemes, SPHINCS+ signatures are significantly larger, which can impact bandwidth and storage requirements.
• Computational Overhead: Signature generation and verification involve many hash computations, which can be resource-intensive, especially on constrained devices.
• Implementation Complexity: Correctly implementing the scheme requires careful attention to parameter choices and cryptographic details.

These considerations must be weighed against the security benefits, especially in applications where quantum resistance is critical. For further discussion, see CISA's post-quantum cryptography resources.

One of the main trade-offs in SPHINCS+ is signature size. Depending on the parameter set, signatures typically range from 8 KB to 30 KB, which is much larger than those produced by RSA or ECDSA. The size is influenced by factors such as the number of tree layers, the Winternitz parameter, and the choice of hash function.

While large signatures can be a drawback for bandwidth-constrained environments, they are often acceptable in applications where security is paramount. For a detailed comparison of signature sizes, see the NIST PQC algorithm summary or explore Password Length vs Complexity: Which Matters More?.

SPHINCS+ is designed to be efficient, but the reliance on many hash function evaluations means that signing and verification are more computationally intensive than in classical schemes. However, hash functions are generally fast and can be efficiently implemented in hardware and software.

Verification is typically faster than signing, as it involves fewer computations. Optimizations, such as parallelization and hardware acceleration, can further improve performance.

Implementing SPHINCS+ securely and efficiently requires careful attention to detail:

• Side-Channel Resistance: Implementations must be hardened against timing and other side-channel attacks, especially in hardware environments.
• Parameter Selection: Choosing appropriate parameters is critical for balancing security, performance, and signature size.
• Interoperability: Ensuring compatibility with existing protocols and systems can be challenging due to the large signature sizes and unique structure.

For guidance on secure implementation, refer to OWASP Cryptographic Storage Cheat Sheet or Password Policy Best Practices 2025.

SPHINCS+ is one of the signature schemes selected by NIST for standardization as part of its Post-Quantum Cryptography project. As of 2024, SPHINCS+ has advanced to the final round and is expected to become a recommended standard for quantum-resistant digital signatures.

The standardization process involves rigorous evaluation of security, performance, and implementation aspects. For the latest status, visit the NIST PQC project page.

SPHINCS+ is suitable for a variety of applications where long-term security and quantum resistance are essential, including:

• Software and Firmware Signing: Ensuring the integrity of updates in critical systems.
• Secure Communications: Protecting sensitive data in government, military, and financial sectors.
• Blockchain and Distributed Ledgers: Providing quantum-resistant signatures for transactions and smart contracts. For more on blockchain cryptography and its security implications, see Blockchain Cryptography: Securing Decentralized Data.

Organizations are beginning to experiment with SPHINCS+ in pilot projects and hybrid cryptographic systems. For case studies and adoption trends, see ISACA's overview of post-quantum cryptography.

Compared to classical signature schemes like RSA and ECDSA:

• Security: SPHINCS+ offers strong post-quantum security, while RSA and ECDSA are vulnerable to quantum attacks.
• Signature Size: SPHINCS+ signatures are much larger (8-30 KB) compared to RSA (256-512 bytes) and ECDSA (64-128 bytes).
• Performance: Hash-based operations are generally faster than modular exponentiation (RSA) or elliptic curve operations (ECDSA), but the sheer number of operations in SPHINCS+ can make it slower in practice.
• Implementation: SPHINCS+ is more complex to implement due to its hierarchical structure and parameterization.

For a technical comparison, see CrowdStrike's post-quantum cryptography guide.

Among post-quantum signature schemes, SPHINCS+ is notable for its conservative security and statelessness. Other schemes, such as CRYSTALS-DILITHIUM and FALCON, are based on lattice problems and offer smaller signatures and faster operations, but rely on newer, less-understood assumptions.

Key differences:

• Security Assumptions: SPHINCS+ relies only on hash functions, while lattice-based schemes depend on the hardness of lattice problems.
• Signature Size: Lattice-based schemes typically have smaller signatures (1-2 KB) compared to SPHINCS+.
• Statelessness: SPHINCS+ is stateless by design, whereas some hash-based schemes require state management.

For a comparative overview, see the ISO/IEC 14888-4:2022 standard.

SPHINCS+ represents a significant advancement in hash-based signature technology, offering a stateless, flexible, and quantum-resistant solution for digital signatures. While it comes with trade-offs in terms of signature size and computational cost, its conservative security assumptions and adaptability make it a strong candidate for future-proof cryptographic systems. As quantum computing continues to evolve, adopting schemes like SPHINCS+ will be crucial for maintaining the integrity and trustworthiness of digital communications and transactions.

• NIST SP 800-208: Recommendation for Stateful Hash-Based Signature Schemes
• NIST Post-Quantum Cryptography Project
• SPHINCS+ Official Documentation
• ENISA Algorithms, Key Size and Parameters Report
• CISA Post-Quantum Cryptography Resources
• OWASP Cryptographic Storage Cheat Sheet
• ISACA: Post-Quantum Cryptography Overview
• CrowdStrike: Post-Quantum Cryptography Guide
• ISO/IEC 14888-4:2022: IT Security Techniques — Digital Signatures with Appendix — Part 4: Post-Quantum Digital Signatures